From 88990df54b51487b305dd7e0baa5dcadcf4a265f Mon Sep 17 00:00:00 2001
From: Daniel <dfranzani@gmail.com>
Date: Sat, 30 Nov 2024 18:12:44 -0300
Subject: [PATCH] Logo

---
 App/Logo/Ayun.jpeg | Bin 0 -> 138255 bytes
 App/server.R       |  36 +++-
 App/ui.R           |  17 +-
 docs/app.json      |   2 +-
 xtable.html        | 328 -----------------------------
 xtable.tex         | 501 ---------------------------------------------
 6 files changed, 48 insertions(+), 836 deletions(-)
 create mode 100644 App/Logo/Ayun.jpeg
 delete mode 100644 xtable.html
 delete mode 100644 xtable.tex

diff --git a/App/Logo/Ayun.jpeg b/App/Logo/Ayun.jpeg
new file mode 100644
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diff --git a/App/server.R b/App/server.R
index 0bbecb7..4209c40 100644
--- a/App/server.R
+++ b/App/server.R
@@ -1,5 +1,6 @@
 library(shiny)
 library(shinydashboard)
+library(shinydashboardPlus)
 library(Cairo)
 options(shiny.usecairo = T)
 library(kableExtra)
@@ -28,6 +29,31 @@ function(input, output, session) {
   
   ### END CUSTOM URL FOR MENUITEM IN SIDEBARMENU
   
+  output$user <- renderUser({
+    dashboardUser(
+      name = "Daniel Franzani",
+      image = "https://adminlte.io/themes/AdminLTE/dist/img/user2-160x160.jpg",
+      title = "Ciencia de Datos",
+      subtitle = "",
+      fluidRow(
+        dashboardUserItem(
+          width = 6,
+          socialButton(
+            href = "https://github.com",
+            icon = icon("github-square")
+          )
+        ),
+        dashboardUserItem(
+          width = 6,
+          socialButton(
+            href = "https://dropbox.com",
+            icon = icon("blog")
+          )
+        )
+      )
+    )
+  })
+  
   
   ### Distribuciones muestrales
   
@@ -62,7 +88,7 @@ function(input, output, session) {
   }
   
   densidad_masa = function(x, valores, tipo, graph = "p"){
-    plot(x, valores, main = paste("Función de ", tipo, " probabilidad"),
+    plot(x, valores, main = paste("Función de ", tipo, " probabilidad"), bty = "n",
          xlab = "Valores de X", ylab = "", las = 1, type = graph, pch = 16)
   }
   
@@ -73,13 +99,15 @@ function(input, output, session) {
       "valores" = unlist(valores[1:cantidad]),
       "dominio" = rep(1:cantidad, rep(largo, cantidad))
     )
-    plot(
-      datos$dominio, datos$valores,
+    boxplot(
+      datos$valores ~ datos$dominio, frame = F,
       main = paste("Primeras ", cantidad, " simulaciones"),
-      xlab = "Simulación", ylab = "Valores de X simulados", xaxt = "n",
+      xlab = "Simulación", ylab = "Valores simulados", xaxt = "n", yaxt = "n",
       las = 1, pch = 16, ylim = c(min(datos$valores), max(datos$valores)*1.4)
     )
     axis(side = 1, at = 1:cantidad, labels = paste0("S", 1:cantidad))
+    axis(side = 2, at = seq(from = min(datos$valores), to = max(datos$valores), length.out = 5),
+         labels = round(seq(from = min(datos$valores), to = max(datos$valores), length.out = 5)), las = 1)
     legend(
       "top", 
       legend = paste0(rep("S", cantidad), 1:cantidad, rep(": ", cantidad),
diff --git a/App/ui.R b/App/ui.R
index 18d0743..86968c4 100644
--- a/App/ui.R
+++ b/App/ui.R
@@ -1,11 +1,24 @@
 library(shiny)
 library(shinydashboard)
+library(shinydashboardPlus)
 library(Cairo)
 options(shiny.usecairo = T)
+library(kableExtra)
 
 # Encabezado general
 
-encabezado = dashboardHeader(title = "Estadística")
+# encabezado = dashboardHeader(title = "Estadística",
+#                              # tags$li(class = "dropdown",
+#                              #         tags$a(href = "https://www.linkedin.com/in/dfranzani/",
+#                                             # icon("linkedin"), "", target = "_blank")),
+#                              tags$li(class = "dropdown",
+#                                      tags$a(href = "https://github.com/Dfranzani",
+#                                             icon("github"), "", target = "_blank")),
+#                              tags$li(class = "dropdown",
+#                                      tags$a(href = "https://dfranzani.netlify.app/",
+#                                             icon("blog"), "", target = "_blank")))
+
+encabezado = dashboardHeader(title = "Estadística", userOutput("user"))
 
 # Panel lateral general: filtro de temas
 
@@ -165,6 +178,6 @@ cuerpo = dashboardBody(
 )
 
 # Despliegue general
-ui = dashboardPage(header = encabezado, sidebar = panelLateral, body = cuerpo, skin = "black")
+ui = dashboardPage(header = encabezado, sidebar = panelLateral, body = cuerpo, skin = "black", title = "Hola")
 
 
diff --git a/docs/app.json b/docs/app.json
index 4788d1e..bf3a5d1 100644
--- a/docs/app.json
+++ b/docs/app.json
@@ -1 +1 @@
-[{"name":"server.R","content":"library(shiny)\nlibrary(shinydashboard)\nlibrary(Cairo)\noptions(shiny.usecairo = T)\nlibrary(kableExtra)\n\nfunction(input, output, session) {\n  \n  ### CUSTOM URL FOR MENUITEM IN SIDEBARMENU\n  ### NOT WORK IN GITHUB PAGES!\n  \n  # observeEvent(getQueryString(session)$tab, {\n  #   currentQueryString <- getQueryString(session)$tab # alternative: parseQueryString(session$clientData$url_search)$tab\n  #   if(is.null(input$sidebarID) || !is.null(currentQueryString) && currentQueryString != input$sidebarID){\n  #     freezeReactiveValue(input, \"sidebarID\")\n  #     updateTabItems(session, \"sidebarID\", selected = currentQueryString)\n  #   }\n  # }, priority = 1)\n  # \n  # observeEvent(input$sidebarID, {\n  #   currentQueryString <- getQueryString(session)$tab # alternative: parseQueryString(session$clientData$url_search)$tab\n  #   pushQueryString <- paste0(\"?tab=\", input$sidebarID)\n  #   if(is.null(currentQueryString) || currentQueryString != input$sidebarID){\n  #     freezeReactiveValue(input, \"sidebarID\")\n  #     updateQueryString(pushQueryString, mode = \"push\", session)\n  #   }\n  # }, priority = 0)\n  \n  ### END CUSTOM URL FOR MENUITEM IN SIDEBARMENU\n  \n  \n  ### Distribuciones muestrales\n  \n  # observeEvent(input$distribucionDM1,{\n  #   output$Histograma_promedios = renderPlot({\n  #     plot(1, 1, col = \"white\", ylab = \"\", xlab = \"\", axes = F)\n  #   })\n  #   \n  #   output$fdp_fmp_simulaciones = renderPlot({\n  #     plot(1, 1, col = \"white\", ylab = \"\", xlab = \"\", axes = F)\n  #   })\n  # })\n  \n  histTCL = function(valores, media, desviacion, simulaciones){\n    medias = unlist(lapply(X = valores, FUN = mean))\n    factor = max(abs(media - c(min(medias), max(medias))))\n    lim_inf = media - factor; lim_sup = media + factor\n    grilla = seq(from = lim_inf, to = lim_sup, by = 0.001)\n    teoricos = dnorm(x = grilla, mean = media, sd = desviacion)\n    \n    densidad_medias = density(medias)\n    hist(x = medias, main = \"Distribución de las medias\", ylab = \"Función de densidad\",\n         xlab = \"Valores de la media en las simulaciones\", freq = FALSE, las = 1, breaks = round(1 + log2(simulaciones)),\n         xlim = c(lim_inf, lim_sup), ylim = c(0, max(densidad_medias$y, teoricos)*1.1))\n    lines(densidad_medias , col = \"darkred\")\n    lines(x = grilla, y = teoricos, col = \"darkblue\")\n    legend(\n      \"topright\", title = \"Distribución\", bty = \"n\",\n      legend = c(\"Aproximada \", paste0(\"Teórica - TCL: N(\", media, \", \", round(desviacion^2,5), \")\")),\n      lty = 1, col = c(\"darkred\", \"darkblue\")\n    )\n  }\n  \n  densidad_masa = function(x, valores, tipo, graph = \"p\"){\n    plot(x, valores, main = paste(\"Función de \", tipo, \" probabilidad\"),\n         xlab = \"Valores de X\", ylab = \"\", las = 1, type = graph, pch = 16)\n  }\n  \n  plot_simulaciones = function(valores, dominio){\n    largo = length(valores[[1]])\n    cantidad = 4\n    datos = data.frame(\n      \"valores\" = unlist(valores[1:cantidad]),\n      \"dominio\" = rep(1:cantidad, rep(largo, cantidad))\n    )\n    plot(\n      datos$dominio, datos$valores,\n      main = paste(\"Primeras \", cantidad, \" simulaciones\"),\n      xlab = \"Simulación\", ylab = \"Valores de X simulados\", xaxt = \"n\",\n      las = 1, pch = 16, ylim = c(min(datos$valores), max(datos$valores)*1.4)\n    )\n    axis(side = 1, at = 1:cantidad, labels = paste0(\"S\", 1:cantidad))\n    legend(\n      \"top\", \n      legend = paste0(rep(\"S\", cantidad), 1:cantidad, rep(\": \", cantidad),\n                      unlist(lapply(X = valores[1: cantidad], FUN = function(x){return(round(mean(x), 4))}))),\n      bty = \"n\", title = \"Media de la simulación\", ncol = 2)\n  }\n\n  observeEvent(list(input$go_DM1, input$distribucionDM1),{\n    \n    n = input$nDM1\n    simulaciones = input$simulacionesDM1\n    \n    # set.seed(2024) # Bind cache\n    \n    if(input$distribucionDM1 == \"Normal\"){\n      media = input$mediaDM1_normal\n      sigma = sqrt(input$varianzaDM1_normal)\n      desviacion = sigma/sqrt(n)\n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rnorm(n = n, mean = media, sd = sigma))\n      })\n      \n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        medias = unlist(lapply(X = valores, FUN = mean))\n        factor = max(abs(media - c(min(medias), max(medias))))\n        lim_inf = media - factor; lim_sup = media + factor\n        grilla = seq(from = lim_inf, to = lim_sup, by = 0.001)\n        teoricos = dnorm(x = grilla, mean = media, sd = desviacion)\n        \n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = grilla, valores = teoricos, tipo = \"densidad\", graph = \"l\")\n      })\n      \n    } else if(input$distribucionDM1 == \"Exponencial\"){\n      tasa = input$tasaDM1_exponencial\n      media = tasa\n      desviacion = sqrt(tasa^2/n)\n      \n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rexp(n = n, rate = 1/tasa))\n      })\n      \n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        teoricos = dexp(seq(from = 0, to = 30, by = 0.001), rate = 1/tasa)\n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = seq(from = 0, to = 30, by = 0.001), valores = teoricos, tipo = \"densidad\", graph = \"l\")\n      })\n      \n    } else if(input$distribucionDM1 == \"Binomial\") {\n      ensayos = input$nDM1_binomial\n      p = input$pDM1_binomial\n      media = ensayos*p\n      desviacion = sqrt(ensayos*p*(1-p)/n)\n      \n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rbinom(n = n, size = ensayos, prob = p))\n      })\n\n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        teoricos = dbinom(x = 0:ensayos, size = ensayos, prob = p)\n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = 0:ensayos, valores = teoricos,, tipo = \"masa\")\n      })\n      \n    } else if(input$distribucionDM1 == \"Poisson\"){\n      tasa = input$tasaDM1_poisson\n      media = tasa\n      desviacion = sqrt(tasa/n)\n      \n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rpois(n = n, lambda = tasa))\n      })\n      \n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        teoricos = dpois(x = 0:30, lambda = tasa)\n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = 0:30, valores = teoricos, tipo = \"masa\")\n      })\n    }\n  })\n  \n  \n  ### Intervalos de confianza\n  \n  hist_muestra_IC = function(x, y = NULL, nombre_media = nombre_media, control_lanzamiento = FALSE, colores){\n    \n    color = ifelse(\"red\" %in% colores, \"red\", \"grey\")\n    \n    if(nombre_media == \"Una\") {\n      titulo = ifelse(control_lanzamiento, \"Distribución de los datos de \\n la muestra del último IC\",\n                      paste(\"Distribución de los datos de la muestra \\n del IC número\", punto_seleccionado()))\n      hist(x, main = titulo, xlab = \"Valores de la muestra\", ylab = \"Frecuencia\", las = 1, col = color)\n    } else {\n      titulo = ifelse(control_lanzamiento, \"Distribuciones de los datos \\n de las muestras del último IC\",\n                      paste(\"Distribuciones de los datos de las muestras \\n del IC número\", punto_seleccionado()))\n      par(mfrow = c(2,1))\n      h1 = hist(x)\n      h2 = hist(y)\n      par(mar = c(0,5,3,3))\n      plot(h1, col = color, xlim = c(min(h1$breaks, h2$breaks), max(h1$breaks, h2$breaks)), ylim = c(0, max(h1$counts, h2$counts)),\n           las = 1, ylab = \"Frecuencias de X\", xaxt = \"n\", main = titulo)\n      par(mar = c(5,5,0,3))\n      plot(h2, col = color, xlim = c(min(h1$breaks, h2$breaks), max(h1$breaks, h2$breaks)), ylim = c(max(h1$counts, h2$counts), 0),\n           las = 1, main = \"\", ylab = \"Frecuencias de Y\", xlab = \"Valores de la muestra\")\n    }\n  }\n  \n  hist_medias_IC = function(x, nombre_media = nombre_media){\n    if(nombre_media == \"Una\") {\n      hist(x, main = \"Distribución de las medias muestrales\", xlab = \"Valores de la muestra\",\n           ylab = \"Frecuencia\", las = 1)\n    } else {\n      hist(x, main = \"Distribución de las diferencias \\n de las medias muestrales (X-Y)\", xlab = \"Valores de la muestra\",\n           ylab = \"Frecuencia\", las = 1)\n    }\n  }\n  \n  simulaciones_muestras = function(nombre_media = nombre_media){\n    muestras = lapply(X = as.list(1:input$simulacionesIC), FUN = function(sim){\n      if(nombre_media == \"Una\") {\n        data1 = rnorm(n = input$nIC, mean = input$muIC, sd = sqrt(input$sigma2IC))\n      } else {\n        data1 = rnorm(n = input$nICX, mean = input$muICX, sd = sqrt(input$varianzaUnaMediaX))\n        data2 = rnorm(n = input$nICY, mean = input$muICY, sd = sqrt(input$varianzaUnaMediaY))\n        data1 = list(\"data1\" = data1, \"data2\" = data2)\n      }\n      return(data1)\n    })\n    return(muestras)\n  }\n  \n  calculo_IC = function(data1, data2 = NULL, tipo, varianzas_conocidas, tipo_varianzas = FALSE, extremos,\n                        confianza, varianza = NA, varianzaX = NA, varianzaY = NA, tamanos_muestrales = NA, media = media){\n   \n    if(varianzas_conocidas == FALSE){\n      limites = t.test(x = data1, y = data2, conf.level = confianza, alternative = tipo, var.equal = tipo_varianzas)$conf.int[extremos]  \n    } else {\n      if (is.null(data2)) {\n        if(tipo == \"two.sided\") {\n          limites = mean(data1) + c(-1,1)*qnorm(1 - (1- confianza)/2)*sqrt(varianza/tamanos_muestrales[1])\n        } else if(tipo == \"less\") {\n          limites = mean(data1) + qnorm(confianza)*sqrt(varianza/tamanos_muestrales[1])\n        } else {\n          limites = mean(data1) - qnorm(confianza)*sqrt(varianza/tamanos_muestrales[1])\n        }\n      } else {\n        if(tipo == \"two.sided\") {\n          limites = c(mean(data1) - mean(data2) - qnorm(1 - (1- confianza)/2)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2]),\n                      mean(data1) - mean(data2) + qnorm(1 - (1 - confianza)/2)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2]))\n        } else if(tipo == \"less\") {\n          limites = mean(data1) - mean(data2) + qnorm(confianza)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2])\n        } else {\n          limites = mean(data1) - mean(data2) - qnorm(confianza)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2])\n        }\n      }\n    }\n    \n    if(tipo == \"greater\") {\n      limites = c(limites, limites[1] + 0.5*sqrt(varianza))\n      colores = c(ifelse(limites[1] > media, \"red\", \"black\"), \"white\")\n    } else if(tipo == \"less\") {\n      limites = c(limites[1] - 0.5*sqrt(varianza), limites)\n      colores = c(\"white\", ifelse(limites[2] < media, \"red\", \"black\"))\n    } else {\n      colores = rep(ifelse(limites[1] < media & limites[2] > media, \"black\", \"red\"), 2)\n    }\n    return(c(limites, colores))\n  }\n  \n  grafico_IC = function(x, y, colores, limites_x, simulaciones, media, nombre_media, tipoIC){\n    plot(\n      x = x, y = 1:simulaciones, col = colores[,1], pch = 16, las = 1, bty = \"n\",\n      ylim = c(-5, simulaciones + 5), xlim = limites_x, xaxt = \"n\", yaxt = \"n\",\n      xlab = \"Valores del IC\", ylab = \"Número de simulación\",\n      main = ifelse(nombre_media == \"Una\",\n                    \"IC para la media proveniente \\n de una distribución normal\",\n                    \"IC para la diferencia de medias (X-Y) \\n provenientes de distribuciones normales\")\n    )\n    axis(side = 1, at = c(limites_x[1], media, limites_x[2]), labels = c(limites_x[1], media, limites_x[2]), xlim = limites_x)\n    axis(side = 2, at = round(seq(from = 1, to = simulaciones, length.out = 10), 0), las = 1)\n    points(x = y, y = 1:simulaciones, pch = 16, col = colores[,2])\n    if(tipoIC == \"less\"){\n      arrows(x1 = x, x0 = y, y1 = 1:simulaciones, y0 = 1:simulaciones, length = 0.07, col = colores[,2])\n      rojos = round(sum(colores[,2] == \"red\")/length(colores[,2])*100, digits = 2)\n      negros = 100 - rojos\n    } else if(tipoIC == \"greater\") {\n      arrows(x0 = x, x1 = y, y0 = 1:simulaciones, y1 = 1:simulaciones, length = 0.07, col = colores[,1])\n      rojos = round(sum(colores[,1] == \"red\")/length(colores[,2])*100, digits = 2)\n      negros = 100 - rojos\n    } else {\n      segments(x0 = x, x1 = y, y0 = 1:simulaciones, y1 = 1:simulaciones, col = colores[,1])\n      rojos = round(sum(colores[,1] == \"red\")/length(colores[,1])*100, digits = 2)\n      negros = 100 - rojos\n    }\n    rojos = paste(rojos, \"%\")\n    negros = paste(negros, \"%\")\n    # abline(v = media, col = \"black\", lty = 2)\n    segments(x0 = media, y0 = 0, x1 = media, y1 = simulaciones+1, lty = 2)\n    legend(\"topleft\", legend = c(negros, rojos), lty = 1, col = c(\"black\", \"red\"), title = \"Proporción de IC\", bty = \"n\")\n    legend(\"bottomleft\", legend = c(\"Haga click en un IC (o cerca) \\n para ver la distribución de los \\n datos de la muestra. \\n \\n\"), bty = \"n\")\n  }\n  \n  IC = function(tipo_varianzas, tipoIC, extremos, confianza, varianza, varianzaX = NA, varianzaY = NA,\n                tamanos_muestrales, media = media, nombre_media = nombre_media){\n    muestras_simuladas = simulaciones_muestras(nombre_media = nombre_media)\n    ics = lapply(X = muestras_simuladas, FUN = function(muestra){\n      if(input$VarianzasIC != \"Conocidas\") {\n        if(input$MediasIC == \"Una\") {\n          ic = calculo_IC(data1 = muestra, tipo = tipoIC, varianzas_conocidas = FALSE, varianza = varianza,\n                          extremos = extremos, confianza = confianza, media = media)\n        } else {\n          ic = calculo_IC(data1 = muestra$data1, data2 = muestra$data2, tipo = tipoIC, varianzas_conocidas = FALSE,\n                          tipo_varianzas = tipo_varianzas, extremos = extremos, confianza = confianza, media = media,\n                          varianza = varianza,)\n        }\n      } else {\n        if(input$MediasIC == \"Una\") {\n          ic = calculo_IC(data1 = muestra, tipo = tipoIC, varianzas_conocidas = TRUE, tipo_varianzas = tipo_varianzas,\n                          extremos = extremos, confianza = confianza, varianza = varianza, tamanos_muestrales = tamanos_muestrales,\n                          media = media)\n        } else {\n          ic = calculo_IC(data1 = muestra$data1, data2 = muestra$data2, tipo = tipoIC, varianzas_conocidas = TRUE,\n                          tipo_varianzas = tipo_varianzas, extremos = extremos, confianza = confianza, varianza = varianza,\n                          varianzaX = varianzaX, varianzaY = varianzaY, tamanos_muestrales = tamanos_muestrales, media = media)\n        }\n      }\n      return(ic)\n    })\n    ics = as.data.frame(matrix(unlist(ics), ncol = 4, byrow = TRUE))\n    ics[,1] = as.numeric(ics[,1])\n    ics[,2] = as.numeric(ics[,2])\n    return(list(ics, muestras_simuladas))\n  }\n  \n  muestras = NULL\n  ic = NULL\n  nombre_media_global = NULL\n  simulaciones_global = NULL\n  \n  observeEvent(list(input$go_IC),{\n    confianza = input$ConfianzaIC/100\n    simulaciones = input$simulacionesIC\n    simulaciones_global <<- simulaciones\n    media = ifelse(input$MediasIC == \"Una\", input$muIC, input$muICX - input$muICY)\n    tipoIC = switch(input$tipoIC, \"Bilateral\" = \"two.sided\", \"Acotado por la derecha\" = \"less\", \"Acotado por la izquierda\" = \"greater\")\n    extremos = switch(tipoIC, \"two.sided\" = 1:2, \"less\" = 2, \"greater\" = 1)\n    varianza = ifelse(input$MediasIC == \"Una\", input$sigma2IC, (input$varianzaUnaMediaX + input$varianzaUnaMediaY)/2)\n    tipo_varianzas = switch(input$VarianzasICMedias, \"Iguales\" = TRUE, \"Distintas\" = FALSE)\n    nombre_media = ifelse(input$MediasIC == \"Una\", \"Una\", \"Dos\")\n    nombre_media_global <<- nombre_media\n    varianzaX = input$varianzaUnaMediaX\n    varianzaY = input$varianzaUnaMediaY\n    tamanos_muestrales = c(input$nIC, input$nICX, input$nICY)\n    \n    ic_y_muestras = IC(tipo_varianzas = tipo_varianzas, tipoIC = tipoIC, extremos = extremos, confianza = confianza,\n                       varianza = varianza, varianzaX = varianzaX, varianzaY = varianzaY,\n                       tamanos_muestrales = tamanos_muestrales, media = media, nombre_media = nombre_media)\n    ic <<- ic_y_muestras[[1]]\n    muestras <<- ic_y_muestras[[2]]\n    \n    dif_maxima = max(abs(c(media - c(ic[,1], ic[,2]))))\n    maximo = round(media + 1.5*dif_maxima, digits = 4)\n    minimo = round(media - 1.5*dif_maxima, digits = 4)\n    \n    output$plot_ic = renderPlot({\n      grafico_IC(x = ic[,1], y = ic[,2], colores = ic[,3:4], limites_x = c(minimo, maximo),\n                 simulaciones = simulaciones, media = media, nombre_media = nombre_media, tipoIC = tipoIC)\n    }, height = 800)\n    \n    punto_seleccionado(NULL)\n    output$histogramaIC = renderPlot({\n      if(nombre_media == \"Una\"){\n        hist_muestra_IC(x = muestras[[simulaciones]], nombre_media = nombre_media,\n                        control_lanzamiento = TRUE, colores = ic[simulaciones,3:4])\n      } else {\n        hist_muestra_IC(x = muestras[[simulaciones]]$data1, y = muestras[[simulaciones]]$data2,\n                        nombre_media = nombre_media, control_lanzamiento = TRUE, colores = ic[simulaciones,3:4])\n      }\n    })\n    \n    output$histograma_medias_IC = renderPlot({\n      if(nombre_media == \"Una\"){\n        hist_medias_IC(x = unlist(lapply(X = muestras, FUN = mean)), nombre_media = nombre_media)\n      } else {\n        hist_medias_IC(\n          x = unlist(lapply(X = muestras, FUN = function(muestra){\n            return(mean(muestra$data1) - mean(muestra$data2))\n          })),\n          nombre_media = nombre_media)\n      }\n    })\n  })\n  \n  punto_seleccionado = reactiveVal(NULL)\n  \n  observeEvent(input$plot_click, {\n    click_y = input$plot_click$y\n    punto_seleccionado(round(click_y))\n    if(punto_seleccionado() >= 1 & punto_seleccionado() <= simulaciones_global){\n      output$histogramaIC = renderPlot({\n        if(nombre_media_global == \"Una\"){\n          hist_muestra_IC(x = muestras[[punto_seleccionado()]], nombre_media = nombre_media_global,\n                          control_lanzamiento = FALSE, colores = ic[punto_seleccionado(), 3:4])\n        } else {\n          hist_muestra_IC(x = muestras[[punto_seleccionado()]]$data1, y = muestras[[punto_seleccionado()]]$data2,\n                          nombre_media = nombre_media_global, control_lanzamiento = FALSE, colores = ic[punto_seleccionado(), 3:4])\n        }\n      })\n    } else {\n      output$histogramaIC = renderPlot({\n        if(nombre_media_global == \"Una\"){\n          hist_muestra_IC(x = muestras[[simulaciones_global]], nombre_media = nombre_media_global,\n                          control_lanzamiento = TRUE, colores = ic[simulaciones_global, 3:4])\n        } else {\n          hist_muestra_IC(x = muestras[[simulaciones_global]]$data1, y = muestras[[simulaciones_global]]$data2,\n                           nombre_media = nombre_media_global, control_lanzamiento = TRUE, colores = ic[simulaciones_global, 3:4])\n        }\n      })\n    }\n  })\n  \n  ### Pruebas de hipótesis\n  \n  grafico_estadisticoPrueba = function(ic, mediaMuestra, varianza, mu0, tipoPH, nMuestra, est_prueba, valor_critico, confianza){\n    \n    max = max(abs(c(0 - c(est_prueba, valor_critico, 4))))\n    limites = c(0 - max * 1.2, 0 + max * 1.2)\n    \n    # print(c(limites, est_prueba, valor_critico, max))\n    \n    valores_x = seq(from = limites[1], to = limites[2], by = 0.01)\n    valores_x = c(valores_x, est_prueba, valor_critico, -est_prueba, -valor_critico)\n    valores_x = valores_x[order(valores_x)]\n    \n    plot(x = valores_x, y = dnorm(x = valores_x),\n         main = \"Distribución del estadístico de prueba\", xlab = \"Valores de Z\", ylab = \"Densidad\",\n         las = 1, xaxt = \"n\", type = \"l\", bty = \"n\", xlim = limites, ylim = c(0, 0.5))\n    axis(side = 1, at = c(limites[1], 0, limites[2]),\n         labels = round(c(limites[1], 0, limites[2]), 2), cex.axis = 1, las = 1)\n    \n    if(tipoPH == \"two.sided\") {\n      axis(side = 1, at = c(-est_prueba, est_prueba), labels = round(c(-est_prueba, est_prueba), 2),\n           col.axis = \"red\", cex.axis = 1, las = 1)\n      axis(side = 1, at = c(-valor_critico, valor_critico), labels = round(c(-valor_critico, valor_critico), 2),\n           col.axis = \"blue\", cex.axis = 1, las = 1)\n      polygon(x = c(-abs(valor_critico), valores_x[valores_x <= -abs(valor_critico)]),\n              y = c(min(dnorm(x = valores_x[valores_x <= -abs(valor_critico)])), dnorm(x = valores_x[valores_x <= -abs(valor_critico)])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(-abs(est_prueba), valores_x[valores_x <= -abs(est_prueba)]),\n              y = c(min(dnorm(x = valores_x[valores_x <= -abs(est_prueba)])), dnorm(x = valores_x[valores_x <= -abs(est_prueba)])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      polygon(x = c(abs(valor_critico), valores_x[valores_x >= abs(valor_critico)]),\n              y = c(min(dnorm(x = valores_x[valores_x >= abs(valor_critico)])), dnorm(x = valores_x[valores_x >= abs(valor_critico)])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(abs(est_prueba), valores_x[valores_x >= abs(est_prueba)]),\n              y = c(min(dnorm(x = valores_x[valores_x >= abs(est_prueba)])), dnorm(x = valores_x[valores_x >= abs(est_prueba)])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      valor_p = 2 - 2*pnorm(abs(est_prueba))\n    } else if(tipoPH == \"less\") {\n      axis(side = 1, at = c(est_prueba), labels = round(c(est_prueba), 2),\n           col.axis = \"red\", cex.axis = 1, las = 1)\n      axis(side = 1, at = c(valor_critico), labels = round(c(valor_critico), 2),\n           col.axis = \"blue\", cex.axis = 1, las = 1)\n      polygon(x = c(valor_critico, valores_x[valores_x <= valor_critico]),\n              y = c(min(dnorm(x = valores_x[valores_x <= valor_critico])), dnorm(x = valores_x[valores_x <= valor_critico])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(est_prueba, valores_x[valores_x <= est_prueba]),\n              y = c(min(dnorm(x = valores_x[valores_x <= est_prueba])), dnorm(x = valores_x[valores_x <= est_prueba])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      valor_p = pnorm(est_prueba)\n    } else {\n      axis(side = 1, at = c(est_prueba), labels = round(c(est_prueba), 2),\n           col.axis = \"red\", cex.axis = 1, las = 1)\n      axis(side = 1, at = c(valor_critico), labels = round(c(valor_critico), 2),\n           col.axis = \"blue\", cex.axis = 1, las = 1)\n      polygon(x = c(valor_critico, valores_x[valores_x >= valor_critico]),\n              y = c(min(dnorm(x = valores_x[valores_x >= valor_critico])), dnorm(x = valores_x[valores_x >= valor_critico])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(est_prueba, valores_x[valores_x >= est_prueba]),\n              y = c(min(dnorm(x = valores_x[valores_x >= est_prueba])), dnorm(x = valores_x[valores_x >= est_prueba])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      valor_p = 1 - pnorm(est_prueba)\n    }\n    legend(\"topright\", legend = paste(c(\"Valor-p:\", \"Significancia:\"), round(c(valor_p, 1 - confianza), 4)), bty = \"n\",\n           lty = 2, col = c(\"red\", \"blue\"))\n    legend(\"topleft\", legend = ifelse(valor_p  <= 1 - confianza, \"Se rechaza\", \"No se rechaza\"), bty = \"n\", title = \"Estado:\", text.font = 4)\n  }\n  \n  grafico_IC_PH = function(ic, mediaMuestra, varianza, mu0, tipoPH, nMuestra, est_prueba, valor_critico, confianza){\n    \n    max = max(abs(c(0 - c(est_prueba, valor_critico, 4))))\n    limites = c(0 - max * 1.2, 0 + max * 1.2)\n    \n    valores_x = seq(from = limites[1], to = limites[2], by = 0.01)\n    valores_x = c(valores_x, est_prueba, valor_critico, -est_prueba, -valor_critico)\n    valores_x = valores_x[order(valores_x)]\n    valores_y = dnorm(x = valores_x)\n    \n    transformacion = function(x.barra){\n      return((x.barra - mu0)/sqrt(varianza/nMuestra))\n    }\n    \n    transformacion_inversa = function(Z0){\n      return(mu0 + Z0*sqrt(varianza/nMuestra))\n    }\n    \n    plot(x = valores_x, y = valores_y,\n         main = \"Distribución de la media muestral \\n e intervalo de confianza\", xlab = \"Valores del promedio\", ylab = \"Densidad\",\n         las = 1, xaxt = \"n\", type = \"l\", bty = \"n\", xlim = limites, ylim = c(0, 0.5))\n    axis(side = 1, at = c(limites[1], 0, limites[2]),\n         labels = round(transformacion_inversa(c(limites[1], 0, limites[2])), 4), cex.axis = 1, las = 1)\n    segments(x0 = 0, x1 = 0, y0 = 0, y1 = max(valores_y), col = \"black\", lty = 2)\n    \n    ic = as.numeric(ic[1:2])\n    ic2 = transformacion(as.numeric(ic[1:2]))\n    max_y = max(valores_y)*0.5\n    \n    if(tipoPH == \"two.sided\") {\n      segments(x0 = ic2[1], x1 = ic2[2], y0 = max_y, y1 = max_y, col = \"red\", lty = 2)\n      legend(\"topleft\", legend = paste0(\"(\", round(ic[1], 4), \", \", round(ic[2], 4), \")\"),\n             bty = \"n\", title = \"IC\", lty = 2, col = \"red\")\n    } else if(tipoPH == \"less\") {\n      arrows(x1 = limites[1], x0 = ic2[2], y0 = max_y, y1 = max_y, length = 0.1, col = \"red\", lty = 2)\n      legend(\"topleft\", legend = paste0(\"(-Inf, \", round(ic[2], 4), \")\"),\n             bty = \"n\", title = \"IC\", lty = 2, col = \"red\")\n    } else {\n      arrows(x0 = ic2[1], x1 = limites[2], y0 = max_y, y1 = max_y, length = 0.1, col = \"red\", lty = 2)\n      legend(\"topleft\", legend = paste0(\"(\", round(ic[1], 4), \", Inf)\"),\n             bty = \"n\", title = \"IC\", lty = 2, col = \"red\")\n    }\n    legend(\"topright\", legend = mu0, bty = \"n\", title = \"mu_0\", lty = 2)\n  }\n  \n  valor_critico = function(confianza, tipo, mu0, varianza, nMuestra, mediaMuestra){\n    if(tipo == \"two.sided\") {\n      valor_critico = qnorm(1 - (1 - confianza)/2)\n    } else if(tipo == \"less\") {\n      valor_critico = qnorm(1 - confianza)\n    } else {\n      valor_critico = qnorm(confianza)\n    }\n    estadistico_prueba = (mediaMuestra - mu0)/(sqrt(varianza/nMuestra))\n    return(c(estadistico_prueba, valor_critico))\n  }\n  \n  observeEvent(list(input$go_PH), {\n    confianza = input$confianzaPH/100\n    mu0 = input$mu0PH\n    mediaMuestra = input$mediaMuestraPH\n    tipoPH = switch(input$tipoPH, \"Bilateral\" = \"two.sided\", \"Unilateral derecha\" = \"greater\", \"Unilateral izquierda\" = \"less\")\n    extremos = switch(tipoPH, \"two.sided\" = 1:2, \"less\" = 2, \"greater\" = 1)\n    varianza = input$sigma2PH\n    nombre_media = \"Una\"\n    nMuestra = input$nPH\n    \n    # Los argumentos data debe ser el promedio n veces para que calce con el cálculo del IC de la función \"calculo_IC\"\n    ic = calculo_IC(data1 = rep(mediaMuestra, nMuestra), tipo = tipoPH, varianzas_conocidas = TRUE, varianza = varianza,\n                    extremos = extremos, confianza = confianza, media = mediaMuestra, tamanos_muestrales = nMuestra)\n    \n    valor_critico = valor_critico(confianza = confianza, tipo = tipoPH, mu0 = mu0, varianza = varianza,\n    nMuestra = nMuestra, mediaMuestra = mediaMuestra)\n      \n    output$plot_ph = renderPlot({\n      grafico_estadisticoPrueba(ic = ic, media = mediaMuestra, varianza = varianza, mu0 = mu0, tipoPH = tipoPH, nMuestra = nMuestra,\n                    est_prueba = valor_critico[1], valor_critico = valor_critico[2], confianza = confianza)\n    }, height = 400)\n    \n    output$plot_ic_ph = renderPlot({\n      grafico_IC_PH(ic = ic, media = mediaMuestra, varianza = varianza, mu0 = mu0, tipoPH = tipoPH, nMuestra = nMuestra,\n                    est_prueba = valor_critico[1], valor_critico = valor_critico[2], confianza = confianza)\n    }, height = 400)\n    \n  })\n  \n  ### Regresión Lineal (Simple)\n  \n  regresion = function(x, y){\n    modelo = lm(y ~ x)\n    return(modelo)\n  }\n  \n  grafico_RL = function(x, y, modelo){\n    betas = modelo$coefficients\n    confidence_values = predict.lm(modelo, interval = \"confidence\")\n    prediction_values = predict.lm(modelo, newdata = data.frame(\"x\" = x, \"y\" = y), interval = \"prediction\")\n    y_confidence = confidence_values[order(confidence_values[,1]), 2:3]\n    y_prediction = prediction_values[order(prediction_values[,1]), 2:3]\n    plot(x = x, y = y, las = 1, bty = \"n\",\n         main = \"Regresión Lineal Simple\", xlab = \"Valores de X\", ylab = \"Valores de Y\",\n         ylim = c(min(c(y, y_confidence, y_prediction)), max(c(y, y_confidence, y_prediction))))\n    segments(x0 = min(x), x1 = max(x), y0 = betas[1] + betas[2]*min(x), y1 = betas[1] + betas[2]*max(x), col = \"red\", lty = 1)\n    lines(x = x[order(x)], y = y_confidence[,1], col = \"blue\", lty = 2)\n    lines(x = x[order(x)], y = y_confidence[,2], col = \"blue\", lty = 2)\n    lines(x = x[order(x)], y = y_prediction[,1], col = \"darkgreen\" ,lty = 2)\n    lines(x = x[order(x)], y = y_prediction[,2], col = \"darkgreen\", lty = 2)\n    legend(\"topleft\", legend = c(\"Recta de regresión ajustada\", \"IC del 95% para la media\", \"IC del 95% para la predicción\"),\n           lty = c(1, 2, 2), col = c(\"red\", \"blue\", \"darkgreen\"), bty = \"n\")\n  }\n  \n  grafico_supuestos = function(x, y, modelo){\n    par(mfrow = c(2,2), bty = \"n\", las = 1)\n    plot(x = modelo$fitted.values, y = residuals(modelo),\n         main = \"Linealidad\", xlab = \"Valores ajustados\", ylab = \"Residuos\")\n    acf(residuals(modelo),\n        main = \"Independenica \\n (Función de Autocorrelación: ACF)\", xlab = \"Lag\", ylab = \"ACF\")\n    plot(x = modelo$fitted.values, y = sqrt(abs(rstandard(modelo))),\n         main = \"Homocedasticidad\", xlab = \"Valores ajustados\", ylab = \"Raíz de los residuos estandarizados\")\n    qqnorm(modelo$residuals, main = \"Normalidad \\n (Cuantil - Cuantil)\", xlab = \"Cuantiles teóricos\", ylab = \"Cuantiles observados\")\n    qqline(modelo$residuals)\n  }\n  \n  violacion_supuestos = function(x, y){\n    \n    aux_y = y\n    aux_x = x\n    \n    if(!is.null(input$violacionSupuestos)){\n      \n      if (\"Linealidad\" %in% input$violacionSupuestos){\n        y = y + (x/70)^3\n      }\n      \n      if (\"Independencia\" %in% input$violacionSupuestos ){\n        y = apply(X = as.matrix(cbind(seq(from = 0, to = 45, length.out = length(y)), y)), MARGIN = 1, FUN = function(fila){\n          recorrido =  sin(fila[1])*200 + fila[2]\n          return(recorrido)\n        })\n      } \n      \n      if (\"Homocedasticidad\" %in% input$violacionSupuestos){\n        incrementos = cumsum(seq(from = 0.8, to = 1.2, length.out = length(y)))\n        y = abs(y*incrementos - max(y)/2)\n      }\n      \n      if (\"Normalidad\" %in% input$violacionSupuestos){\n        n_min = y[order(y)][8]\n        n_max = y[order(y)][(length(y)-8)]\n        y[y <= n_min] = y[y <= n_min] - y[y == n_max]*0.5\n        y[y >= n_max] = y[y >= n_max] + y[y == n_max]*0.5\n      } \n    }\n    return(y)\n  }\n  \n  observeEvent(list(input$go_RL), {\n    \n    set.seed(2024)\n    desviacion_simulacion = 100\n    x_poblacion = seq(from = 1, to = input$nPoblacionalRLS, by = 1)\n    y_poblacion = apply(X = as.matrix(x_poblacion + 100), MARGIN = 1, FUN = function(media){\n      return(rnorm(n = 1, mean = media, sd = desviacion_simulacion))\n    })\n    \n    n_muestra = sample(x = 1:input$nPoblacionalRLS, size = input$nMuestralRLS, replace = FALSE)\n    x_muestral = x_poblacion[n_muestra]\n    y_muestral = y_poblacion[n_muestra]\n    y_muestral = violacion_supuestos(x = x_muestral, y = y_muestral)\n    RL = regresion(x = x_muestral, y = y_muestral)\n    \n    output$plot_rl = renderPlot({\n      grafico_RL(x = x_muestral, y = y_muestral, modelo = RL)\n    })\n    \n    output$plot_supuestos = renderPlot({\n      grafico_supuestos(x = x_muestral, y = y_muestral, modelo = RL)\n    })\n    \n    output$resumen_rl = function(){\n      summary_RL = round(summary(RL)$coefficients, digits = 4)\n      summary_RL = ifelse(summary_RL == 0, \"<2e-16\", summary_RL)\n      rownames(summary_RL) <- c(\"β<sub>0<\/sub>\", \"β<sub>1<\/sub>\")\n      kableExtra::kbl(summary_RL, escape = FALSE, booktabs = T, align = \"c\",\n            caption = \"Resumen del modelo de regresión lineal\",\n            col.names = c(\"Estimación\", \"Error estándar\", \"Estadístico de prueba t\", \"Valor-p\")) |>\n        kableExtra::kable_styling(full_width = TRUE, bootstrap_options = c(\"condensed\", \"striped\"))\n    }\n    \n    output$resumen_rl_metricas = function(){\n      summary_RL = summary(RL)\n      metrics = round(unlist(summary_RL[c(\"fstatistic\", \"sigma\", \"r.squared\", \"adj.r.squared\")])[c(1,4:6)], digits = 4)\n      kableExtra::kbl(t(as.matrix(metrics)), escape = FALSE, booktabs = T, align = \"c\",\n        col.names = c(\"Estadístico F<sub>0<\/sub>\", \"Error estándar residual\", \"R<sup>2<\/sup>\", \"R<sup>2<\/sup> ajustado\")) |>\n        kableExtra::kable_styling(full_width = TRUE, bootstrap_options = c(\"condensed\", \"striped\"))\n    }\n\n    output$resumen_supuestos = function(){\n      \n      tests = list(\n        lmtest::bptest(formula = formula(RL), data = data.frame(\"x\" = x_muestral, \"y\" = y_muestral)),\n        lmtest::dwtest(formula = formula(RL), data = data.frame(\"x\" = x_muestral, \"y\" = y_muestral), alternative = \"two.sided\"),\n        shapiro.test(x = rstandard(RL))\n      ) |> lapply(FUN = function(test){\n        valor_p = round(test$p.value, digits = 4)\n        statistic = round(test$statistic, digits = 4)\n        valor_p = ifelse(valor_p < 0.0001, \"<1e-4\", valor_p)\n        statistic = ifelse(statistic < 0.0001, \"<1e-4\", statistic)\n        return(c(statistic, valor_p))\n      }) |> unlist() |> matrix(ncol = 2, byrow = TRUE) |> data.frame() |> setNames(c(\"Estadístico\", \"Valor-p\"))\n      \n      \n      tests$Prueba = c(\"Breusch-Pagan\", \"Durbin-Watson\", \"Shapiro-Wilk\")\n      tests$Supuesto = c(\"Homocedasticidad\", \"Independencia\", \"Normalidad\")\n      tests = tests[, c(\"Supuesto\", \"Prueba\", \"Estadístico\", \"Valor-p\")]\n      \n      kableExtra::kbl(tests, escape = FALSE, booktabs = T, align = \"c\",\n        caption = \"Prueba de hipótesis de los supuestos del modelo de regresión lineal\") |>\n        kableExtra::kable_styling(full_width = TRUE, bootstrap_options = c(\"condensed\", \"striped\"))\n    }\n\n  })\n  \n# End general function  \n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n","type":"text"},{"name":"ui.R","content":"library(shiny)\nlibrary(shinydashboard)\nlibrary(Cairo)\noptions(shiny.usecairo = T)\n\n# Encabezado general\n\nencabezado = dashboardHeader(title = \"Estadística\")\n\n# Panel lateral general: filtro de temas\n\npanelLateral = dashboardSidebar(\n  collapsed = FALSE,\n  sidebarMenu(\n    id = \"sidebarID\",\n    menuItem(\"Teorema Central del Límite\", tabName = \"DM1\"),\n    menuItem(\"IC: Intervalos de confianza\", tabName = \"IC\"),\n    menuItem(\"Pruebas de Hipótesis\", tabName = \"PH\"),\n    menuItem(\"Regresión Lineal\", tabName = \"RL\")\n  )\n)\n\n# Paneles: cuerpo de cada panel del Panel lateral\n# Un cuerpo se puede volver a dividir en otro tipo de Layout\n\nsimulador = actionButton(inputId = \"go_DM1\", label = \"Simular\")\n\ncuerpo_DM1 = sidebarLayout(\n  sidebarPanel(\n    width = 3,\n    selectInput(inputId = \"distribucionDM1\", label = \"Distribución\", choices = c(\"Normal\", \"Exponencial\", \"Binomial\", \"Poisson\")),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Normal'\",\n      sliderInput(inputId = \"mediaDM1_normal\", label = \"Media poblacional\", min = 0, max = 20, value = 12, step = 0.2),\n      sliderInput(inputId = \"varianzaDM1_normal\", label = \"Varianza poblacional\", min = 0, max = 20, value = 2, step = 0.1),\n    ),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Binomial'\",\n      sliderInput(inputId = \"nDM1_binomial\", label = \"Ensayos\", min = 1, max = 100, value = 12, step = 1),\n      sliderInput(inputId = \"pDM1_binomial\", label = \"Probabilidad de éxito\", min = 0, max = 1, value = 0.4, step = 0.05),\n    ),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Exponencial'\",\n      sliderInput(inputId = \"tasaDM1_exponencial\", label = \"Tasa\", min = 0, max = 20, value = 5, step = 0.1)\n    ),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Poisson'\",\n      sliderInput(inputId = \"tasaDM1_poisson\", label = \"Tasa\", min = 0, max = 20, value = 8, step = 0.1)\n    ),\n    sliderInput(inputId = \"nDM1\", label = \"Tamaño muestral\", min = 100, max = 1000, value = 200, step = 50),\n    sliderInput(inputId = \"simulacionesDM1\", label = \"Cantidad de simulaciones\", min = 100, max = 7000, value = 1300, step = 100),\n    simulador\n  ),\n  mainPanel(\n    width = 9,\n    plotOutput(\"Histograma_promedios\"), plotOutput(\"fdp_fmp_simulaciones\")\n  )\n)\n\nsimulador2 = actionButton(inputId = \"go_IC\", label = \"Simular\")\n\ncuerpo_IC = sidebarLayout(\n  sidebarPanel(\n    width = 3,\n    fluidRow(\n      column(width = 4, radioButtons(inputId = \"MediasIC\", label = \"Medias\", choices = c(\"Una\", \"Dos\"))),\n      column(width = 8, radioButtons(inputId = \"VarianzasIC\", label = \"Varianzas\", choices = c(\"Conocidas\", \"Desconocidas\")))\n    ),\n    conditionalPanel(\n      condition = \"input.VarianzasIC == 'Desconocidas' && input.MediasIC == 'Dos'\",\n      radioButtons(inputId = \"VarianzasICMedias\", label = \"Varianzas desconocidas\", choices = c(\"Iguales\", \"Distintas\"))\n    ),\n    sliderInput(inputId = \"ConfianzaIC\", label = \"% Confianza\", min = 10, max = 99, value = 90, step = 1),\n    radioButtons(inputId = \"tipoIC\", label = \"Tipo de IC\", choices = c(\"Bilateral\", \"Acotado por la derecha\", \"Acotado por la izquierda\")),\n    conditionalPanel(\n      condition = \"input.MediasIC == 'Una'\",\n      sliderInput(inputId = \"muIC\", label = \"Media poblacional\", min = -20, max = 20, value = 0, step = 0.1),\n      sliderInput(inputId = \"sigma2IC\", label = \"Varianza poblacional\", min = 5, max = 30, value = 10, step = 0.1),\n      sliderInput(inputId = \"nIC\", label = \"Tamaño muestral\", min = 10, max = 200, value = 120, step = 10)\n    ),\n    conditionalPanel(\n      condition = \"input.MediasIC == 'Dos'\",\n      fluidRow(\n        column(width = 6, sliderInput(inputId = \"muICX\", label = \"Media poblacional X\", min = -10, max = 10, value = 0, step = 0.5)),\n        column(width = 6, sliderInput(inputId = \"muICY\", label = \"Media poblacional Y\", min = -10, max = 10, value = 7, step = 0.5))\n      ),\n      fluidRow(\n        column(width = 6, sliderInput(inputId = \"varianzaUnaMediaX\", label = \"Varianza poblacional X\", min = 10, max = 25, value = 12, step = 0.5)),\n        column(width = 6, sliderInput(inputId = \"varianzaUnaMediaY\", label = \"Varianza poblacional Y\", min = 10, max = 25, value = 16, step = 0.5))\n      ),\n      fluidRow(\n        column(width = 6, sliderInput(inputId = \"nICX\", label = \"Tamaño muestral X\", min = 50, max = 150, value = 120, step = 10)),\n        column(width = 6, sliderInput(inputId = \"nICY\", label = \"Tamaño muestral Y\", min = 50, max = 150, value = 80, step = 10))\n      ),\n    ),\n    sliderInput(inputId = \"simulacionesIC\", label = \"Cantidad de simulaciones\", min = 10, max = 100, value = 60, step = 1),\n    simulador2\n  ),\n  mainPanel(\n    width = 9,\n    fluidRow(\n      column(width = 6, plotOutput(\"plot_ic\", click = \"plot_click\", height = \"800px\")),\n      column(width = 6, plotOutput(\"histogramaIC\"), plotOutput(\"histograma_medias_IC\"))\n    )\n  )\n)\n\nsimulador3 = actionButton(inputId = \"go_PH\", label = \"Simular\")\n\ncuerpo_PH = sidebarLayout(\n  sidebarPanel(\n    width = 3,\n    radioButtons(inputId = \"mediasPH\", label = \"Medias\", choices = c(\"Una\")),#, \"Dos\")),\n    radioButtons(inputId = \"varianazasPH\", label = \"Varianzas\", choices = c(\"Conocidas\")),#, \"Desconocidas\")),\n    radioButtons(inputId = \"tipoPH\", label = \"Tipo de prueba\", choices = c(\"Bilateral\", \"Unilateral derecha\", \"Unilateral izquierda\")),\n    sliderInput(inputId = \"mu0PH\", label = \"Media bajo Hipótesis nula\", min = -5, max = 5, value = 0, step = 0.02),\n    sliderInput(inputId = \"sigma2PH\", label = \"Varianza poblacional\", min = 1, max = 50, value = 10, step = 0.5),\n    sliderInput(inputId = \"mediaMuestraPH\", label = \"Media muestral\", min = -5, max = 5, value = 0.6, step = 0.02),\n    sliderInput(inputId = \"nPH\", label = \"Tamaño muestral\", min = 10, max = 200, value = 120, step = 10),\n    sliderInput(inputId = \"confianzaPH\", label = \"% Confianza\", min = 10, max = 99, value = 87, step = 1),\n    simulador3\n  ),\n  mainPanel(\n    width = 9,\n    fluidRow(\n      column(width = 12, plotOutput(\"plot_ph\"), plotOutput(\"plot_ic_ph\"))\n    )#,\n    # fluidRow(\n    #   column(width = 6, withMathJax(includeMarkdown(\"Regresion+Lineal/Prueba.md\")))\n    # )\n  )\n)\n\nsimulador4 = actionButton(inputId = \"go_RL\", label = \"Simular\")\ncuerpo_RL = sidebarLayout(\n  sidebarPanel(\n    width = 2,\n    radioButtons(inputId = \"tipoRL\", label = \"Tipo de regresión\", choices = c(\"Simple\")),\n    # radioButtons(inputId = \"tipoRL\", label = \"Tipo de regresión\", choices = c(\"Simple\", \"Múltiple\")),\n    conditionalPanel(\n      condition = \"input.tipoRL == 'Simple'\",\n      sliderInput(inputId = \"nPoblacionalRLS\", label = \"Tamaño poblacional\", min = 600, max = 800, value = 700, step = 10),\n      sliderInput(inputId = \"nMuestralRLS\", label = \"Tamaño muestral\",  min = 100, max = 550, value = 240, step = 10)\n    ),\n    checkboxGroupInput(inputId = \"violacionSupuestos\", label = \"Violación de supuestos\",\n                       choices = c(\"Linealidad\", \"Normalidad\", \"Homocedasticidad\", \"Independencia\")),\n    simulador4\n  ),\n  mainPanel(\n    width = 10,\n    fluidRow(\n      column(width = 6, plotOutput(\"plot_rl\", height = \"500px\"), br(), tableOutput(\"resumen_rl\"), tableOutput(\"resumen_rl_metricas\")),\n      column(width = 6, plotOutput(\"plot_supuestos\", height = \"500px\"), br(), tableOutput(\"resumen_supuestos\"))\n    )\n  )\n)\n# Asignando los cuerpos por filtro\nhoja_DM = tabItem(tabName = \"DM1\", fluidPage(cuerpo_DM1))\nhoja_IC = tabItem(tabName = \"IC\", fluidPage(cuerpo_IC))\nhoja_PH = tabItem(tabName = \"PH\", fluidPage(cuerpo_PH))\nhoja_RL = tabItem(tabName = \"RL\", fluidPage(cuerpo_RL))\n\ncuerpo = dashboardBody(\n  tabItems(hoja_DM, hoja_IC, hoja_PH, hoja_RL)\n)\n\n# Despliegue general\nui = dashboardPage(header = encabezado, sidebar = panelLateral, body = cuerpo, skin = \"black\")\n\n\n","type":"text"},{"name":"Regresion+Lineal/Prueba.md","content":"# Probando elementos de inscrustación\n\n$$\nA + B = C\n$$\n\n1. Hola\n\n2. CHao\n\n**HOLA**S","type":"text"}]
+[{"name":"server.R","content":"library(shiny)\nlibrary(shinydashboard)\n# library(shinydashboardPlus)\nlibrary(Cairo)\noptions(shiny.usecairo = T)\nlibrary(kableExtra)\n\nfunction(input, output, session) {\n  \n  ### CUSTOM URL FOR MENUITEM IN SIDEBARMENU\n  ### NOT WORK IN GITHUB PAGES!\n  \n  # observeEvent(getQueryString(session)$tab, {\n  #   currentQueryString <- getQueryString(session)$tab # alternative: parseQueryString(session$clientData$url_search)$tab\n  #   if(is.null(input$sidebarID) || !is.null(currentQueryString) && currentQueryString != input$sidebarID){\n  #     freezeReactiveValue(input, \"sidebarID\")\n  #     updateTabItems(session, \"sidebarID\", selected = currentQueryString)\n  #   }\n  # }, priority = 1)\n  # \n  # observeEvent(input$sidebarID, {\n  #   currentQueryString <- getQueryString(session)$tab # alternative: parseQueryString(session$clientData$url_search)$tab\n  #   pushQueryString <- paste0(\"?tab=\", input$sidebarID)\n  #   if(is.null(currentQueryString) || currentQueryString != input$sidebarID){\n  #     freezeReactiveValue(input, \"sidebarID\")\n  #     updateQueryString(pushQueryString, mode = \"push\", session)\n  #   }\n  # }, priority = 0)\n  \n  ### END CUSTOM URL FOR MENUITEM IN SIDEBARMENU\n  \n  \n  # output$user <- renderUser({\n  #   dashboardUser(\n  #     name = \"Divad Nojnarg\", \n  #     image = \"https://adminlte.io/themes/AdminLTE/dist/img/user2-160x160.jpg\", \n  #     title = \"shinydashboardPlus\",\n  #     subtitle = \"Author\", \n  #     footer = p(\"The footer\", class = \"text-center\"),\n  #     fluidRow(\n  #       dashboardUserItem(\n  #         width = 6,\n  #         socialButton(\n  #           href = \"https://dropbox.com\",\n  #           icon = icon(\"dropbox\")\n  #         )\n  #       ),\n  #       dashboardUserItem(\n  #         width = 6,\n  #         socialButton(\n  #           href = \"https://github.com\",\n  #           icon = icon(\"github\")\n  #         )\n  #       )\n  #     )\n  #   )\n  # })\n  \n  \n  ### Distribuciones muestrales\n  \n  # observeEvent(input$distribucionDM1,{\n  #   output$Histograma_promedios = renderPlot({\n  #     plot(1, 1, col = \"white\", ylab = \"\", xlab = \"\", axes = F)\n  #   })\n  #   \n  #   output$fdp_fmp_simulaciones = renderPlot({\n  #     plot(1, 1, col = \"white\", ylab = \"\", xlab = \"\", axes = F)\n  #   })\n  # })\n  \n  histTCL = function(valores, media, desviacion, simulaciones){\n    medias = unlist(lapply(X = valores, FUN = mean))\n    factor = max(abs(media - c(min(medias), max(medias))))\n    lim_inf = media - factor; lim_sup = media + factor\n    grilla = seq(from = lim_inf, to = lim_sup, by = 0.001)\n    teoricos = dnorm(x = grilla, mean = media, sd = desviacion)\n    \n    densidad_medias = density(medias)\n    hist(x = medias, main = \"Distribución de las medias\", ylab = \"Función de densidad\",\n         xlab = \"Valores de la media en las simulaciones\", freq = FALSE, las = 1, breaks = round(1 + log2(simulaciones)),\n         xlim = c(lim_inf, lim_sup), ylim = c(0, max(densidad_medias$y, teoricos)*1.1))\n    lines(densidad_medias , col = \"darkred\")\n    lines(x = grilla, y = teoricos, col = \"darkblue\")\n    legend(\n      \"topright\", title = \"Distribución\", bty = \"n\",\n      legend = c(\"Aproximada \", paste0(\"Teórica - TCL: N(\", media, \", \", round(desviacion^2,5), \")\")),\n      lty = 1, col = c(\"darkred\", \"darkblue\")\n    )\n  }\n  \n  densidad_masa = function(x, valores, tipo, graph = \"p\"){\n    plot(x, valores, main = paste(\"Función de \", tipo, \" probabilidad\"), bty = \"n\",\n         xlab = \"Valores de X\", ylab = \"\", las = 1, type = graph, pch = 16)\n  }\n  \n  plot_simulaciones = function(valores, dominio){\n    largo = length(valores[[1]])\n    cantidad = 4\n    datos = data.frame(\n      \"valores\" = unlist(valores[1:cantidad]),\n      \"dominio\" = rep(1:cantidad, rep(largo, cantidad))\n    )\n    boxplot(\n      datos$valores ~ datos$dominio, frame = F,\n      main = paste(\"Primeras \", cantidad, \" simulaciones\"),\n      xlab = \"Simulación\", ylab = \"Valores simulados\", xaxt = \"n\", yaxt = \"n\",\n      las = 1, pch = 16, ylim = c(min(datos$valores), max(datos$valores)*1.4)\n    )\n    axis(side = 1, at = 1:cantidad, labels = paste0(\"S\", 1:cantidad))\n    axis(side = 2, at = seq(from = min(datos$valores), to = max(datos$valores), length.out = 5),\n         labels = round(seq(from = min(datos$valores), to = max(datos$valores), length.out = 5)), las = 1)\n    legend(\n      \"top\", \n      legend = paste0(rep(\"S\", cantidad), 1:cantidad, rep(\": \", cantidad),\n                      unlist(lapply(X = valores[1: cantidad], FUN = function(x){return(round(mean(x), 4))}))),\n      bty = \"n\", title = \"Media de la simulación\", ncol = 2)\n  }\n\n  observeEvent(list(input$go_DM1, input$distribucionDM1),{\n    \n    n = input$nDM1\n    simulaciones = input$simulacionesDM1\n    \n    # set.seed(2024) # Bind cache\n    \n    if(input$distribucionDM1 == \"Normal\"){\n      media = input$mediaDM1_normal\n      sigma = sqrt(input$varianzaDM1_normal)\n      desviacion = sigma/sqrt(n)\n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rnorm(n = n, mean = media, sd = sigma))\n      })\n      \n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        medias = unlist(lapply(X = valores, FUN = mean))\n        factor = max(abs(media - c(min(medias), max(medias))))\n        lim_inf = media - factor; lim_sup = media + factor\n        grilla = seq(from = lim_inf, to = lim_sup, by = 0.001)\n        teoricos = dnorm(x = grilla, mean = media, sd = desviacion)\n        \n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = grilla, valores = teoricos, tipo = \"densidad\", graph = \"l\")\n      })\n      \n    } else if(input$distribucionDM1 == \"Exponencial\"){\n      tasa = input$tasaDM1_exponencial\n      media = tasa\n      desviacion = sqrt(tasa^2/n)\n      \n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rexp(n = n, rate = 1/tasa))\n      })\n      \n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        teoricos = dexp(seq(from = 0, to = 30, by = 0.001), rate = 1/tasa)\n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = seq(from = 0, to = 30, by = 0.001), valores = teoricos, tipo = \"densidad\", graph = \"l\")\n      })\n      \n    } else if(input$distribucionDM1 == \"Binomial\") {\n      ensayos = input$nDM1_binomial\n      p = input$pDM1_binomial\n      media = ensayos*p\n      desviacion = sqrt(ensayos*p*(1-p)/n)\n      \n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rbinom(n = n, size = ensayos, prob = p))\n      })\n\n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        teoricos = dbinom(x = 0:ensayos, size = ensayos, prob = p)\n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = 0:ensayos, valores = teoricos,, tipo = \"masa\")\n      })\n      \n    } else if(input$distribucionDM1 == \"Poisson\"){\n      tasa = input$tasaDM1_poisson\n      media = tasa\n      desviacion = sqrt(tasa/n)\n      \n      valores = lapply(X = as.list(1:simulaciones), FUN = function(sim){\n        return(rpois(n = n, lambda = tasa))\n      })\n      \n      output$Histograma_promedios = renderPlot({\n        histTCL(valores, media, desviacion, simulaciones)\n      })\n      \n      output$fdp_fmp_simulaciones = renderPlot({\n        teoricos = dpois(x = 0:30, lambda = tasa)\n        par(mfrow = c(1,2))\n        plot_simulaciones(valores)\n        densidad_masa(x = 0:30, valores = teoricos, tipo = \"masa\")\n      })\n    }\n  })\n  \n  \n  ### Intervalos de confianza\n  \n  hist_muestra_IC = function(x, y = NULL, nombre_media = nombre_media, control_lanzamiento = FALSE, colores){\n    \n    color = ifelse(\"red\" %in% colores, \"red\", \"grey\")\n    \n    if(nombre_media == \"Una\") {\n      titulo = ifelse(control_lanzamiento, \"Distribución de los datos de \\n la muestra del último IC\",\n                      paste(\"Distribución de los datos de la muestra \\n del IC número\", punto_seleccionado()))\n      hist(x, main = titulo, xlab = \"Valores de la muestra\", ylab = \"Frecuencia\", las = 1, col = color)\n    } else {\n      titulo = ifelse(control_lanzamiento, \"Distribuciones de los datos \\n de las muestras del último IC\",\n                      paste(\"Distribuciones de los datos de las muestras \\n del IC número\", punto_seleccionado()))\n      par(mfrow = c(2,1))\n      h1 = hist(x)\n      h2 = hist(y)\n      par(mar = c(0,5,3,3))\n      plot(h1, col = color, xlim = c(min(h1$breaks, h2$breaks), max(h1$breaks, h2$breaks)), ylim = c(0, max(h1$counts, h2$counts)),\n           las = 1, ylab = \"Frecuencias de X\", xaxt = \"n\", main = titulo)\n      par(mar = c(5,5,0,3))\n      plot(h2, col = color, xlim = c(min(h1$breaks, h2$breaks), max(h1$breaks, h2$breaks)), ylim = c(max(h1$counts, h2$counts), 0),\n           las = 1, main = \"\", ylab = \"Frecuencias de Y\", xlab = \"Valores de la muestra\")\n    }\n  }\n  \n  hist_medias_IC = function(x, nombre_media = nombre_media){\n    if(nombre_media == \"Una\") {\n      hist(x, main = \"Distribución de las medias muestrales\", xlab = \"Valores de la muestra\",\n           ylab = \"Frecuencia\", las = 1)\n    } else {\n      hist(x, main = \"Distribución de las diferencias \\n de las medias muestrales (X-Y)\", xlab = \"Valores de la muestra\",\n           ylab = \"Frecuencia\", las = 1)\n    }\n  }\n  \n  simulaciones_muestras = function(nombre_media = nombre_media){\n    muestras = lapply(X = as.list(1:input$simulacionesIC), FUN = function(sim){\n      if(nombre_media == \"Una\") {\n        data1 = rnorm(n = input$nIC, mean = input$muIC, sd = sqrt(input$sigma2IC))\n      } else {\n        data1 = rnorm(n = input$nICX, mean = input$muICX, sd = sqrt(input$varianzaUnaMediaX))\n        data2 = rnorm(n = input$nICY, mean = input$muICY, sd = sqrt(input$varianzaUnaMediaY))\n        data1 = list(\"data1\" = data1, \"data2\" = data2)\n      }\n      return(data1)\n    })\n    return(muestras)\n  }\n  \n  calculo_IC = function(data1, data2 = NULL, tipo, varianzas_conocidas, tipo_varianzas = FALSE, extremos,\n                        confianza, varianza = NA, varianzaX = NA, varianzaY = NA, tamanos_muestrales = NA, media = media){\n   \n    if(varianzas_conocidas == FALSE){\n      limites = t.test(x = data1, y = data2, conf.level = confianza, alternative = tipo, var.equal = tipo_varianzas)$conf.int[extremos]  \n    } else {\n      if (is.null(data2)) {\n        if(tipo == \"two.sided\") {\n          limites = mean(data1) + c(-1,1)*qnorm(1 - (1- confianza)/2)*sqrt(varianza/tamanos_muestrales[1])\n        } else if(tipo == \"less\") {\n          limites = mean(data1) + qnorm(confianza)*sqrt(varianza/tamanos_muestrales[1])\n        } else {\n          limites = mean(data1) - qnorm(confianza)*sqrt(varianza/tamanos_muestrales[1])\n        }\n      } else {\n        if(tipo == \"two.sided\") {\n          limites = c(mean(data1) - mean(data2) - qnorm(1 - (1- confianza)/2)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2]),\n                      mean(data1) - mean(data2) + qnorm(1 - (1 - confianza)/2)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2]))\n        } else if(tipo == \"less\") {\n          limites = mean(data1) - mean(data2) + qnorm(confianza)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2])\n        } else {\n          limites = mean(data1) - mean(data2) - qnorm(confianza)*sqrt(varianzaX/tamanos_muestrales[1] + varianzaY/tamanos_muestrales[2])\n        }\n      }\n    }\n    \n    if(tipo == \"greater\") {\n      limites = c(limites, limites[1] + 0.5*sqrt(varianza))\n      colores = c(ifelse(limites[1] > media, \"red\", \"black\"), \"white\")\n    } else if(tipo == \"less\") {\n      limites = c(limites[1] - 0.5*sqrt(varianza), limites)\n      colores = c(\"white\", ifelse(limites[2] < media, \"red\", \"black\"))\n    } else {\n      colores = rep(ifelse(limites[1] < media & limites[2] > media, \"black\", \"red\"), 2)\n    }\n    return(c(limites, colores))\n  }\n  \n  grafico_IC = function(x, y, colores, limites_x, simulaciones, media, nombre_media, tipoIC){\n    plot(\n      x = x, y = 1:simulaciones, col = colores[,1], pch = 16, las = 1, bty = \"n\",\n      ylim = c(-5, simulaciones + 5), xlim = limites_x, xaxt = \"n\", yaxt = \"n\",\n      xlab = \"Valores del IC\", ylab = \"Número de simulación\",\n      main = ifelse(nombre_media == \"Una\",\n                    \"IC para la media proveniente \\n de una distribución normal\",\n                    \"IC para la diferencia de medias (X-Y) \\n provenientes de distribuciones normales\")\n    )\n    axis(side = 1, at = c(limites_x[1], media, limites_x[2]), labels = c(limites_x[1], media, limites_x[2]), xlim = limites_x)\n    axis(side = 2, at = round(seq(from = 1, to = simulaciones, length.out = 10), 0), las = 1)\n    points(x = y, y = 1:simulaciones, pch = 16, col = colores[,2])\n    if(tipoIC == \"less\"){\n      arrows(x1 = x, x0 = y, y1 = 1:simulaciones, y0 = 1:simulaciones, length = 0.07, col = colores[,2])\n      rojos = round(sum(colores[,2] == \"red\")/length(colores[,2])*100, digits = 2)\n      negros = 100 - rojos\n    } else if(tipoIC == \"greater\") {\n      arrows(x0 = x, x1 = y, y0 = 1:simulaciones, y1 = 1:simulaciones, length = 0.07, col = colores[,1])\n      rojos = round(sum(colores[,1] == \"red\")/length(colores[,2])*100, digits = 2)\n      negros = 100 - rojos\n    } else {\n      segments(x0 = x, x1 = y, y0 = 1:simulaciones, y1 = 1:simulaciones, col = colores[,1])\n      rojos = round(sum(colores[,1] == \"red\")/length(colores[,1])*100, digits = 2)\n      negros = 100 - rojos\n    }\n    rojos = paste(rojos, \"%\")\n    negros = paste(negros, \"%\")\n    # abline(v = media, col = \"black\", lty = 2)\n    segments(x0 = media, y0 = 0, x1 = media, y1 = simulaciones+1, lty = 2)\n    legend(\"topleft\", legend = c(negros, rojos), lty = 1, col = c(\"black\", \"red\"), title = \"Proporción de IC\", bty = \"n\")\n    legend(\"bottomleft\", legend = c(\"Haga click en un IC (o cerca) \\n para ver la distribución de los \\n datos de la muestra. \\n \\n\"), bty = \"n\")\n  }\n  \n  IC = function(tipo_varianzas, tipoIC, extremos, confianza, varianza, varianzaX = NA, varianzaY = NA,\n                tamanos_muestrales, media = media, nombre_media = nombre_media){\n    muestras_simuladas = simulaciones_muestras(nombre_media = nombre_media)\n    ics = lapply(X = muestras_simuladas, FUN = function(muestra){\n      if(input$VarianzasIC != \"Conocidas\") {\n        if(input$MediasIC == \"Una\") {\n          ic = calculo_IC(data1 = muestra, tipo = tipoIC, varianzas_conocidas = FALSE, varianza = varianza,\n                          extremos = extremos, confianza = confianza, media = media)\n        } else {\n          ic = calculo_IC(data1 = muestra$data1, data2 = muestra$data2, tipo = tipoIC, varianzas_conocidas = FALSE,\n                          tipo_varianzas = tipo_varianzas, extremos = extremos, confianza = confianza, media = media,\n                          varianza = varianza,)\n        }\n      } else {\n        if(input$MediasIC == \"Una\") {\n          ic = calculo_IC(data1 = muestra, tipo = tipoIC, varianzas_conocidas = TRUE, tipo_varianzas = tipo_varianzas,\n                          extremos = extremos, confianza = confianza, varianza = varianza, tamanos_muestrales = tamanos_muestrales,\n                          media = media)\n        } else {\n          ic = calculo_IC(data1 = muestra$data1, data2 = muestra$data2, tipo = tipoIC, varianzas_conocidas = TRUE,\n                          tipo_varianzas = tipo_varianzas, extremos = extremos, confianza = confianza, varianza = varianza,\n                          varianzaX = varianzaX, varianzaY = varianzaY, tamanos_muestrales = tamanos_muestrales, media = media)\n        }\n      }\n      return(ic)\n    })\n    ics = as.data.frame(matrix(unlist(ics), ncol = 4, byrow = TRUE))\n    ics[,1] = as.numeric(ics[,1])\n    ics[,2] = as.numeric(ics[,2])\n    return(list(ics, muestras_simuladas))\n  }\n  \n  muestras = NULL\n  ic = NULL\n  nombre_media_global = NULL\n  simulaciones_global = NULL\n  \n  observeEvent(list(input$go_IC),{\n    confianza = input$ConfianzaIC/100\n    simulaciones = input$simulacionesIC\n    simulaciones_global <<- simulaciones\n    media = ifelse(input$MediasIC == \"Una\", input$muIC, input$muICX - input$muICY)\n    tipoIC = switch(input$tipoIC, \"Bilateral\" = \"two.sided\", \"Acotado por la derecha\" = \"less\", \"Acotado por la izquierda\" = \"greater\")\n    extremos = switch(tipoIC, \"two.sided\" = 1:2, \"less\" = 2, \"greater\" = 1)\n    varianza = ifelse(input$MediasIC == \"Una\", input$sigma2IC, (input$varianzaUnaMediaX + input$varianzaUnaMediaY)/2)\n    tipo_varianzas = switch(input$VarianzasICMedias, \"Iguales\" = TRUE, \"Distintas\" = FALSE)\n    nombre_media = ifelse(input$MediasIC == \"Una\", \"Una\", \"Dos\")\n    nombre_media_global <<- nombre_media\n    varianzaX = input$varianzaUnaMediaX\n    varianzaY = input$varianzaUnaMediaY\n    tamanos_muestrales = c(input$nIC, input$nICX, input$nICY)\n    \n    ic_y_muestras = IC(tipo_varianzas = tipo_varianzas, tipoIC = tipoIC, extremos = extremos, confianza = confianza,\n                       varianza = varianza, varianzaX = varianzaX, varianzaY = varianzaY,\n                       tamanos_muestrales = tamanos_muestrales, media = media, nombre_media = nombre_media)\n    ic <<- ic_y_muestras[[1]]\n    muestras <<- ic_y_muestras[[2]]\n    \n    dif_maxima = max(abs(c(media - c(ic[,1], ic[,2]))))\n    maximo = round(media + 1.5*dif_maxima, digits = 4)\n    minimo = round(media - 1.5*dif_maxima, digits = 4)\n    \n    output$plot_ic = renderPlot({\n      grafico_IC(x = ic[,1], y = ic[,2], colores = ic[,3:4], limites_x = c(minimo, maximo),\n                 simulaciones = simulaciones, media = media, nombre_media = nombre_media, tipoIC = tipoIC)\n    }, height = 800)\n    \n    punto_seleccionado(NULL)\n    output$histogramaIC = renderPlot({\n      if(nombre_media == \"Una\"){\n        hist_muestra_IC(x = muestras[[simulaciones]], nombre_media = nombre_media,\n                        control_lanzamiento = TRUE, colores = ic[simulaciones,3:4])\n      } else {\n        hist_muestra_IC(x = muestras[[simulaciones]]$data1, y = muestras[[simulaciones]]$data2,\n                        nombre_media = nombre_media, control_lanzamiento = TRUE, colores = ic[simulaciones,3:4])\n      }\n    })\n    \n    output$histograma_medias_IC = renderPlot({\n      if(nombre_media == \"Una\"){\n        hist_medias_IC(x = unlist(lapply(X = muestras, FUN = mean)), nombre_media = nombre_media)\n      } else {\n        hist_medias_IC(\n          x = unlist(lapply(X = muestras, FUN = function(muestra){\n            return(mean(muestra$data1) - mean(muestra$data2))\n          })),\n          nombre_media = nombre_media)\n      }\n    })\n  })\n  \n  punto_seleccionado = reactiveVal(NULL)\n  \n  observeEvent(input$plot_click, {\n    click_y = input$plot_click$y\n    punto_seleccionado(round(click_y))\n    if(punto_seleccionado() >= 1 & punto_seleccionado() <= simulaciones_global){\n      output$histogramaIC = renderPlot({\n        if(nombre_media_global == \"Una\"){\n          hist_muestra_IC(x = muestras[[punto_seleccionado()]], nombre_media = nombre_media_global,\n                          control_lanzamiento = FALSE, colores = ic[punto_seleccionado(), 3:4])\n        } else {\n          hist_muestra_IC(x = muestras[[punto_seleccionado()]]$data1, y = muestras[[punto_seleccionado()]]$data2,\n                          nombre_media = nombre_media_global, control_lanzamiento = FALSE, colores = ic[punto_seleccionado(), 3:4])\n        }\n      })\n    } else {\n      output$histogramaIC = renderPlot({\n        if(nombre_media_global == \"Una\"){\n          hist_muestra_IC(x = muestras[[simulaciones_global]], nombre_media = nombre_media_global,\n                          control_lanzamiento = TRUE, colores = ic[simulaciones_global, 3:4])\n        } else {\n          hist_muestra_IC(x = muestras[[simulaciones_global]]$data1, y = muestras[[simulaciones_global]]$data2,\n                           nombre_media = nombre_media_global, control_lanzamiento = TRUE, colores = ic[simulaciones_global, 3:4])\n        }\n      })\n    }\n  })\n  \n  ### Pruebas de hipótesis\n  \n  grafico_estadisticoPrueba = function(ic, mediaMuestra, varianza, mu0, tipoPH, nMuestra, est_prueba, valor_critico, confianza){\n    \n    max = max(abs(c(0 - c(est_prueba, valor_critico, 4))))\n    limites = c(0 - max * 1.2, 0 + max * 1.2)\n    \n    # print(c(limites, est_prueba, valor_critico, max))\n    \n    valores_x = seq(from = limites[1], to = limites[2], by = 0.01)\n    valores_x = c(valores_x, est_prueba, valor_critico, -est_prueba, -valor_critico)\n    valores_x = valores_x[order(valores_x)]\n    \n    plot(x = valores_x, y = dnorm(x = valores_x),\n         main = \"Distribución del estadístico de prueba\", xlab = \"Valores de Z\", ylab = \"Densidad\",\n         las = 1, xaxt = \"n\", type = \"l\", bty = \"n\", xlim = limites, ylim = c(0, 0.5))\n    axis(side = 1, at = c(limites[1], 0, limites[2]),\n         labels = round(c(limites[1], 0, limites[2]), 2), cex.axis = 1, las = 1)\n    \n    if(tipoPH == \"two.sided\") {\n      axis(side = 1, at = c(-est_prueba, est_prueba), labels = round(c(-est_prueba, est_prueba), 2),\n           col.axis = \"red\", cex.axis = 1, las = 1)\n      axis(side = 1, at = c(-valor_critico, valor_critico), labels = round(c(-valor_critico, valor_critico), 2),\n           col.axis = \"blue\", cex.axis = 1, las = 1)\n      polygon(x = c(-abs(valor_critico), valores_x[valores_x <= -abs(valor_critico)]),\n              y = c(min(dnorm(x = valores_x[valores_x <= -abs(valor_critico)])), dnorm(x = valores_x[valores_x <= -abs(valor_critico)])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(-abs(est_prueba), valores_x[valores_x <= -abs(est_prueba)]),\n              y = c(min(dnorm(x = valores_x[valores_x <= -abs(est_prueba)])), dnorm(x = valores_x[valores_x <= -abs(est_prueba)])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      polygon(x = c(abs(valor_critico), valores_x[valores_x >= abs(valor_critico)]),\n              y = c(min(dnorm(x = valores_x[valores_x >= abs(valor_critico)])), dnorm(x = valores_x[valores_x >= abs(valor_critico)])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(abs(est_prueba), valores_x[valores_x >= abs(est_prueba)]),\n              y = c(min(dnorm(x = valores_x[valores_x >= abs(est_prueba)])), dnorm(x = valores_x[valores_x >= abs(est_prueba)])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      valor_p = 2 - 2*pnorm(abs(est_prueba))\n    } else if(tipoPH == \"less\") {\n      axis(side = 1, at = c(est_prueba), labels = round(c(est_prueba), 2),\n           col.axis = \"red\", cex.axis = 1, las = 1)\n      axis(side = 1, at = c(valor_critico), labels = round(c(valor_critico), 2),\n           col.axis = \"blue\", cex.axis = 1, las = 1)\n      polygon(x = c(valor_critico, valores_x[valores_x <= valor_critico]),\n              y = c(min(dnorm(x = valores_x[valores_x <= valor_critico])), dnorm(x = valores_x[valores_x <= valor_critico])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(est_prueba, valores_x[valores_x <= est_prueba]),\n              y = c(min(dnorm(x = valores_x[valores_x <= est_prueba])), dnorm(x = valores_x[valores_x <= est_prueba])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      valor_p = pnorm(est_prueba)\n    } else {\n      axis(side = 1, at = c(est_prueba), labels = round(c(est_prueba), 2),\n           col.axis = \"red\", cex.axis = 1, las = 1)\n      axis(side = 1, at = c(valor_critico), labels = round(c(valor_critico), 2),\n           col.axis = \"blue\", cex.axis = 1, las = 1)\n      polygon(x = c(valor_critico, valores_x[valores_x >= valor_critico]),\n              y = c(min(dnorm(x = valores_x[valores_x >= valor_critico])), dnorm(x = valores_x[valores_x >= valor_critico])),\n              lty = 2, density = 5, col = \"blue\")\n      polygon(x = c(est_prueba, valores_x[valores_x >= est_prueba]),\n              y = c(min(dnorm(x = valores_x[valores_x >= est_prueba])), dnorm(x = valores_x[valores_x >= est_prueba])),\n              lty = 2, density = 5, col = \"red\", angle = 135)\n      valor_p = 1 - pnorm(est_prueba)\n    }\n    legend(\"topright\", legend = paste(c(\"Valor-p:\", \"Significancia:\"), round(c(valor_p, 1 - confianza), 4)), bty = \"n\",\n           lty = 2, col = c(\"red\", \"blue\"))\n    legend(\"topleft\", legend = ifelse(valor_p  <= 1 - confianza, \"Se rechaza\", \"No se rechaza\"), bty = \"n\", title = \"Estado:\", text.font = 4)\n  }\n  \n  grafico_IC_PH = function(ic, mediaMuestra, varianza, mu0, tipoPH, nMuestra, est_prueba, valor_critico, confianza){\n    \n    max = max(abs(c(0 - c(est_prueba, valor_critico, 4))))\n    limites = c(0 - max * 1.2, 0 + max * 1.2)\n    \n    valores_x = seq(from = limites[1], to = limites[2], by = 0.01)\n    valores_x = c(valores_x, est_prueba, valor_critico, -est_prueba, -valor_critico)\n    valores_x = valores_x[order(valores_x)]\n    valores_y = dnorm(x = valores_x)\n    \n    transformacion = function(x.barra){\n      return((x.barra - mu0)/sqrt(varianza/nMuestra))\n    }\n    \n    transformacion_inversa = function(Z0){\n      return(mu0 + Z0*sqrt(varianza/nMuestra))\n    }\n    \n    plot(x = valores_x, y = valores_y,\n         main = \"Distribución de la media muestral \\n e intervalo de confianza\", xlab = \"Valores del promedio\", ylab = \"Densidad\",\n         las = 1, xaxt = \"n\", type = \"l\", bty = \"n\", xlim = limites, ylim = c(0, 0.5))\n    axis(side = 1, at = c(limites[1], 0, limites[2]),\n         labels = round(transformacion_inversa(c(limites[1], 0, limites[2])), 4), cex.axis = 1, las = 1)\n    segments(x0 = 0, x1 = 0, y0 = 0, y1 = max(valores_y), col = \"black\", lty = 2)\n    \n    ic = as.numeric(ic[1:2])\n    ic2 = transformacion(as.numeric(ic[1:2]))\n    max_y = max(valores_y)*0.5\n    \n    if(tipoPH == \"two.sided\") {\n      segments(x0 = ic2[1], x1 = ic2[2], y0 = max_y, y1 = max_y, col = \"red\", lty = 2)\n      legend(\"topleft\", legend = paste0(\"(\", round(ic[1], 4), \", \", round(ic[2], 4), \")\"),\n             bty = \"n\", title = \"IC\", lty = 2, col = \"red\")\n    } else if(tipoPH == \"less\") {\n      arrows(x1 = limites[1], x0 = ic2[2], y0 = max_y, y1 = max_y, length = 0.1, col = \"red\", lty = 2)\n      legend(\"topleft\", legend = paste0(\"(-Inf, \", round(ic[2], 4), \")\"),\n             bty = \"n\", title = \"IC\", lty = 2, col = \"red\")\n    } else {\n      arrows(x0 = ic2[1], x1 = limites[2], y0 = max_y, y1 = max_y, length = 0.1, col = \"red\", lty = 2)\n      legend(\"topleft\", legend = paste0(\"(\", round(ic[1], 4), \", Inf)\"),\n             bty = \"n\", title = \"IC\", lty = 2, col = \"red\")\n    }\n    legend(\"topright\", legend = mu0, bty = \"n\", title = \"mu_0\", lty = 2)\n  }\n  \n  valor_critico = function(confianza, tipo, mu0, varianza, nMuestra, mediaMuestra){\n    if(tipo == \"two.sided\") {\n      valor_critico = qnorm(1 - (1 - confianza)/2)\n    } else if(tipo == \"less\") {\n      valor_critico = qnorm(1 - confianza)\n    } else {\n      valor_critico = qnorm(confianza)\n    }\n    estadistico_prueba = (mediaMuestra - mu0)/(sqrt(varianza/nMuestra))\n    return(c(estadistico_prueba, valor_critico))\n  }\n  \n  observeEvent(list(input$go_PH), {\n    confianza = input$confianzaPH/100\n    mu0 = input$mu0PH\n    mediaMuestra = input$mediaMuestraPH\n    tipoPH = switch(input$tipoPH, \"Bilateral\" = \"two.sided\", \"Unilateral derecha\" = \"greater\", \"Unilateral izquierda\" = \"less\")\n    extremos = switch(tipoPH, \"two.sided\" = 1:2, \"less\" = 2, \"greater\" = 1)\n    varianza = input$sigma2PH\n    nombre_media = \"Una\"\n    nMuestra = input$nPH\n    \n    # Los argumentos data debe ser el promedio n veces para que calce con el cálculo del IC de la función \"calculo_IC\"\n    ic = calculo_IC(data1 = rep(mediaMuestra, nMuestra), tipo = tipoPH, varianzas_conocidas = TRUE, varianza = varianza,\n                    extremos = extremos, confianza = confianza, media = mediaMuestra, tamanos_muestrales = nMuestra)\n    \n    valor_critico = valor_critico(confianza = confianza, tipo = tipoPH, mu0 = mu0, varianza = varianza,\n    nMuestra = nMuestra, mediaMuestra = mediaMuestra)\n      \n    output$plot_ph = renderPlot({\n      grafico_estadisticoPrueba(ic = ic, media = mediaMuestra, varianza = varianza, mu0 = mu0, tipoPH = tipoPH, nMuestra = nMuestra,\n                    est_prueba = valor_critico[1], valor_critico = valor_critico[2], confianza = confianza)\n    }, height = 400)\n    \n    output$plot_ic_ph = renderPlot({\n      grafico_IC_PH(ic = ic, media = mediaMuestra, varianza = varianza, mu0 = mu0, tipoPH = tipoPH, nMuestra = nMuestra,\n                    est_prueba = valor_critico[1], valor_critico = valor_critico[2], confianza = confianza)\n    }, height = 400)\n    \n  })\n  \n  ### Regresión Lineal (Simple)\n  \n  regresion = function(x, y){\n    modelo = lm(y ~ x)\n    return(modelo)\n  }\n  \n  grafico_RL = function(x, y, modelo){\n    betas = modelo$coefficients\n    confidence_values = predict.lm(modelo, interval = \"confidence\")\n    prediction_values = predict.lm(modelo, newdata = data.frame(\"x\" = x, \"y\" = y), interval = \"prediction\")\n    y_confidence = confidence_values[order(confidence_values[,1]), 2:3]\n    y_prediction = prediction_values[order(prediction_values[,1]), 2:3]\n    plot(x = x, y = y, las = 1, bty = \"n\",\n         main = \"Regresión Lineal Simple\", xlab = \"Valores de X\", ylab = \"Valores de Y\",\n         ylim = c(min(c(y, y_confidence, y_prediction)), max(c(y, y_confidence, y_prediction))))\n    segments(x0 = min(x), x1 = max(x), y0 = betas[1] + betas[2]*min(x), y1 = betas[1] + betas[2]*max(x), col = \"red\", lty = 1)\n    lines(x = x[order(x)], y = y_confidence[,1], col = \"blue\", lty = 2)\n    lines(x = x[order(x)], y = y_confidence[,2], col = \"blue\", lty = 2)\n    lines(x = x[order(x)], y = y_prediction[,1], col = \"darkgreen\" ,lty = 2)\n    lines(x = x[order(x)], y = y_prediction[,2], col = \"darkgreen\", lty = 2)\n    legend(\"topleft\", legend = c(\"Recta de regresión ajustada\", \"IC del 95% para la media\", \"IC del 95% para la predicción\"),\n           lty = c(1, 2, 2), col = c(\"red\", \"blue\", \"darkgreen\"), bty = \"n\")\n  }\n  \n  grafico_supuestos = function(x, y, modelo){\n    par(mfrow = c(2,2), bty = \"n\", las = 1)\n    plot(x = modelo$fitted.values, y = residuals(modelo),\n         main = \"Linealidad\", xlab = \"Valores ajustados\", ylab = \"Residuos\")\n    acf(residuals(modelo),\n        main = \"Independenica \\n (Función de Autocorrelación: ACF)\", xlab = \"Lag\", ylab = \"ACF\")\n    plot(x = modelo$fitted.values, y = sqrt(abs(rstandard(modelo))),\n         main = \"Homocedasticidad\", xlab = \"Valores ajustados\", ylab = \"Raíz de los residuos estandarizados\")\n    qqnorm(modelo$residuals, main = \"Normalidad \\n (Cuantil - Cuantil)\", xlab = \"Cuantiles teóricos\", ylab = \"Cuantiles observados\")\n    qqline(modelo$residuals)\n  }\n  \n  violacion_supuestos = function(x, y){\n    \n    aux_y = y\n    aux_x = x\n    \n    if(!is.null(input$violacionSupuestos)){\n      \n      if (\"Linealidad\" %in% input$violacionSupuestos){\n        y = y + (x/70)^3\n      }\n      \n      if (\"Independencia\" %in% input$violacionSupuestos ){\n        y = apply(X = as.matrix(cbind(seq(from = 0, to = 45, length.out = length(y)), y)), MARGIN = 1, FUN = function(fila){\n          recorrido =  sin(fila[1])*200 + fila[2]\n          return(recorrido)\n        })\n      } \n      \n      if (\"Homocedasticidad\" %in% input$violacionSupuestos){\n        incrementos = cumsum(seq(from = 0.8, to = 1.2, length.out = length(y)))\n        y = abs(y*incrementos - max(y)/2)\n      }\n      \n      if (\"Normalidad\" %in% input$violacionSupuestos){\n        n_min = y[order(y)][8]\n        n_max = y[order(y)][(length(y)-8)]\n        y[y <= n_min] = y[y <= n_min] - y[y == n_max]*0.5\n        y[y >= n_max] = y[y >= n_max] + y[y == n_max]*0.5\n      } \n    }\n    return(y)\n  }\n  \n  observeEvent(list(input$go_RL), {\n    \n    set.seed(2024)\n    desviacion_simulacion = 100\n    x_poblacion = seq(from = 1, to = input$nPoblacionalRLS, by = 1)\n    y_poblacion = apply(X = as.matrix(x_poblacion + 100), MARGIN = 1, FUN = function(media){\n      return(rnorm(n = 1, mean = media, sd = desviacion_simulacion))\n    })\n    \n    n_muestra = sample(x = 1:input$nPoblacionalRLS, size = input$nMuestralRLS, replace = FALSE)\n    x_muestral = x_poblacion[n_muestra]\n    y_muestral = y_poblacion[n_muestra]\n    y_muestral = violacion_supuestos(x = x_muestral, y = y_muestral)\n    RL = regresion(x = x_muestral, y = y_muestral)\n    \n    output$plot_rl = renderPlot({\n      grafico_RL(x = x_muestral, y = y_muestral, modelo = RL)\n    })\n    \n    output$plot_supuestos = renderPlot({\n      grafico_supuestos(x = x_muestral, y = y_muestral, modelo = RL)\n    })\n    \n    output$resumen_rl = function(){\n      summary_RL = round(summary(RL)$coefficients, digits = 4)\n      summary_RL = ifelse(summary_RL == 0, \"<2e-16\", summary_RL)\n      rownames(summary_RL) <- c(\"β<sub>0<\/sub>\", \"β<sub>1<\/sub>\")\n      kableExtra::kbl(summary_RL, escape = FALSE, booktabs = T, align = \"c\",\n            caption = \"Resumen del modelo de regresión lineal\",\n            col.names = c(\"Estimación\", \"Error estándar\", \"Estadístico de prueba t\", \"Valor-p\")) |>\n        kableExtra::kable_styling(full_width = TRUE, bootstrap_options = c(\"condensed\", \"striped\"))\n    }\n    \n    output$resumen_rl_metricas = function(){\n      summary_RL = summary(RL)\n      metrics = round(unlist(summary_RL[c(\"fstatistic\", \"sigma\", \"r.squared\", \"adj.r.squared\")])[c(1,4:6)], digits = 4)\n      kableExtra::kbl(t(as.matrix(metrics)), escape = FALSE, booktabs = T, align = \"c\",\n        col.names = c(\"Estadístico F<sub>0<\/sub>\", \"Error estándar residual\", \"R<sup>2<\/sup>\", \"R<sup>2<\/sup> ajustado\")) |>\n        kableExtra::kable_styling(full_width = TRUE, bootstrap_options = c(\"condensed\", \"striped\"))\n    }\n\n    output$resumen_supuestos = function(){\n      \n      tests = list(\n        lmtest::bptest(formula = formula(RL), data = data.frame(\"x\" = x_muestral, \"y\" = y_muestral)),\n        lmtest::dwtest(formula = formula(RL), data = data.frame(\"x\" = x_muestral, \"y\" = y_muestral), alternative = \"two.sided\"),\n        shapiro.test(x = rstandard(RL))\n      ) |> lapply(FUN = function(test){\n        valor_p = round(test$p.value, digits = 4)\n        statistic = round(test$statistic, digits = 4)\n        valor_p = ifelse(valor_p < 0.0001, \"<1e-4\", valor_p)\n        statistic = ifelse(statistic < 0.0001, \"<1e-4\", statistic)\n        return(c(statistic, valor_p))\n      }) |> unlist() |> matrix(ncol = 2, byrow = TRUE) |> data.frame() |> setNames(c(\"Estadístico\", \"Valor-p\"))\n      \n      \n      tests$Prueba = c(\"Breusch-Pagan\", \"Durbin-Watson\", \"Shapiro-Wilk\")\n      tests$Supuesto = c(\"Homocedasticidad\", \"Independencia\", \"Normalidad\")\n      tests = tests[, c(\"Supuesto\", \"Prueba\", \"Estadístico\", \"Valor-p\")]\n      \n      kableExtra::kbl(tests, escape = FALSE, booktabs = T, align = \"c\",\n        caption = \"Prueba de hipótesis de los supuestos del modelo de regresión lineal\") |>\n        kableExtra::kable_styling(full_width = TRUE, bootstrap_options = c(\"condensed\", \"striped\"))\n    }\n\n  })\n  \n# End general function  \n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n","type":"text"},{"name":"ui.R","content":"library(shiny)\nlibrary(shinydashboard)\n# library(shinydashboardPlus)\nlibrary(Cairo)\noptions(shiny.usecairo = T)\nlibrary(kableExtra)\n\n# Encabezado general\n\nencabezado = dashboardHeader(title = \"Estadística\",\n                             # tags$li(class = \"dropdown\",\n                             #         tags$a(href = \"https://www.linkedin.com/in/dfranzani/\",\n                                            # icon(\"linkedin\"), \"\", target = \"_blank\")),\n                             tags$li(class = \"dropdown\",\n                                     tags$a(href = \"https://github.com/Dfranzani\",\n                                            icon(\"github\"), \"\", target = \"_blank\")),\n                             tags$li(class = \"dropdown\",\n                                     tags$a(href = \"https://dfranzani.netlify.app/\",\n                                            icon(\"blog\"), \"\", target = \"_blank\")))\n\n# encabezado = dashboardHeader(userOutput(\"user\"))\n\n# Panel lateral general: filtro de temas\n\npanelLateral = dashboardSidebar(\n  collapsed = FALSE,\n  sidebarMenu(\n    id = \"sidebarID\",\n    menuItem(\"Teorema Central del Límite\", tabName = \"DM1\"),\n    menuItem(\"IC: Intervalos de confianza\", tabName = \"IC\"),\n    menuItem(\"Pruebas de Hipótesis\", tabName = \"PH\"),\n    menuItem(\"Regresión Lineal\", tabName = \"RL\")\n  )\n)\n\n# Paneles: cuerpo de cada panel del Panel lateral\n# Un cuerpo se puede volver a dividir en otro tipo de Layout\n\nsimulador = actionButton(inputId = \"go_DM1\", label = \"Simular\")\n\ncuerpo_DM1 = sidebarLayout(\n  sidebarPanel(\n    width = 3,\n    selectInput(inputId = \"distribucionDM1\", label = \"Distribución\", choices = c(\"Normal\", \"Exponencial\", \"Binomial\", \"Poisson\")),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Normal'\",\n      sliderInput(inputId = \"mediaDM1_normal\", label = \"Media poblacional\", min = 0, max = 20, value = 12, step = 0.2),\n      sliderInput(inputId = \"varianzaDM1_normal\", label = \"Varianza poblacional\", min = 0, max = 20, value = 2, step = 0.1),\n    ),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Binomial'\",\n      sliderInput(inputId = \"nDM1_binomial\", label = \"Ensayos\", min = 1, max = 100, value = 12, step = 1),\n      sliderInput(inputId = \"pDM1_binomial\", label = \"Probabilidad de éxito\", min = 0, max = 1, value = 0.4, step = 0.05),\n    ),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Exponencial'\",\n      sliderInput(inputId = \"tasaDM1_exponencial\", label = \"Tasa\", min = 0, max = 20, value = 5, step = 0.1)\n    ),\n    conditionalPanel(\n      condition = \"input.distribucionDM1 == 'Poisson'\",\n      sliderInput(inputId = \"tasaDM1_poisson\", label = \"Tasa\", min = 0, max = 20, value = 8, step = 0.1)\n    ),\n    sliderInput(inputId = \"nDM1\", label = \"Tamaño muestral\", min = 100, max = 1000, value = 200, step = 50),\n    sliderInput(inputId = \"simulacionesDM1\", label = \"Cantidad de simulaciones\", min = 100, max = 7000, value = 1300, step = 100),\n    simulador\n  ),\n  mainPanel(\n    width = 9,\n    plotOutput(\"Histograma_promedios\"), plotOutput(\"fdp_fmp_simulaciones\")\n  )\n)\n\nsimulador2 = actionButton(inputId = \"go_IC\", label = \"Simular\")\n\ncuerpo_IC = sidebarLayout(\n  sidebarPanel(\n    width = 3,\n    fluidRow(\n      column(width = 4, radioButtons(inputId = \"MediasIC\", label = \"Medias\", choices = c(\"Una\", \"Dos\"))),\n      column(width = 8, radioButtons(inputId = \"VarianzasIC\", label = \"Varianzas\", choices = c(\"Conocidas\", \"Desconocidas\")))\n    ),\n    conditionalPanel(\n      condition = \"input.VarianzasIC == 'Desconocidas' && input.MediasIC == 'Dos'\",\n      radioButtons(inputId = \"VarianzasICMedias\", label = \"Varianzas desconocidas\", choices = c(\"Iguales\", \"Distintas\"))\n    ),\n    sliderInput(inputId = \"ConfianzaIC\", label = \"% Confianza\", min = 10, max = 99, value = 90, step = 1),\n    radioButtons(inputId = \"tipoIC\", label = \"Tipo de IC\", choices = c(\"Bilateral\", \"Acotado por la derecha\", \"Acotado por la izquierda\")),\n    conditionalPanel(\n      condition = \"input.MediasIC == 'Una'\",\n      sliderInput(inputId = \"muIC\", label = \"Media poblacional\", min = -20, max = 20, value = 0, step = 0.1),\n      sliderInput(inputId = \"sigma2IC\", label = \"Varianza poblacional\", min = 5, max = 30, value = 10, step = 0.1),\n      sliderInput(inputId = \"nIC\", label = \"Tamaño muestral\", min = 10, max = 200, value = 120, step = 10)\n    ),\n    conditionalPanel(\n      condition = \"input.MediasIC == 'Dos'\",\n      fluidRow(\n        column(width = 6, sliderInput(inputId = \"muICX\", label = \"Media poblacional X\", min = -10, max = 10, value = 0, step = 0.5)),\n        column(width = 6, sliderInput(inputId = \"muICY\", label = \"Media poblacional Y\", min = -10, max = 10, value = 7, step = 0.5))\n      ),\n      fluidRow(\n        column(width = 6, sliderInput(inputId = \"varianzaUnaMediaX\", label = \"Varianza poblacional X\", min = 10, max = 25, value = 12, step = 0.5)),\n        column(width = 6, sliderInput(inputId = \"varianzaUnaMediaY\", label = \"Varianza poblacional Y\", min = 10, max = 25, value = 16, step = 0.5))\n      ),\n      fluidRow(\n        column(width = 6, sliderInput(inputId = \"nICX\", label = \"Tamaño muestral X\", min = 50, max = 150, value = 120, step = 10)),\n        column(width = 6, sliderInput(inputId = \"nICY\", label = \"Tamaño muestral Y\", min = 50, max = 150, value = 80, step = 10))\n      ),\n    ),\n    sliderInput(inputId = \"simulacionesIC\", label = \"Cantidad de simulaciones\", min = 10, max = 100, value = 60, step = 1),\n    simulador2\n  ),\n  mainPanel(\n    width = 9,\n    fluidRow(\n      column(width = 6, plotOutput(\"plot_ic\", click = \"plot_click\", height = \"800px\")),\n      column(width = 6, plotOutput(\"histogramaIC\"), plotOutput(\"histograma_medias_IC\"))\n    )\n  )\n)\n\nsimulador3 = actionButton(inputId = \"go_PH\", label = \"Simular\")\n\ncuerpo_PH = sidebarLayout(\n  sidebarPanel(\n    width = 3,\n    radioButtons(inputId = \"mediasPH\", label = \"Medias\", choices = c(\"Una\")),#, \"Dos\")),\n    radioButtons(inputId = \"varianazasPH\", label = \"Varianzas\", choices = c(\"Conocidas\")),#, \"Desconocidas\")),\n    radioButtons(inputId = \"tipoPH\", label = \"Tipo de prueba\", choices = c(\"Bilateral\", \"Unilateral derecha\", \"Unilateral izquierda\")),\n    sliderInput(inputId = \"mu0PH\", label = \"Media bajo Hipótesis nula\", min = -5, max = 5, value = 0, step = 0.02),\n    sliderInput(inputId = \"sigma2PH\", label = \"Varianza poblacional\", min = 1, max = 50, value = 10, step = 0.5),\n    sliderInput(inputId = \"mediaMuestraPH\", label = \"Media muestral\", min = -5, max = 5, value = 0.6, step = 0.02),\n    sliderInput(inputId = \"nPH\", label = \"Tamaño muestral\", min = 10, max = 200, value = 120, step = 10),\n    sliderInput(inputId = \"confianzaPH\", label = \"% Confianza\", min = 10, max = 99, value = 87, step = 1),\n    simulador3\n  ),\n  mainPanel(\n    width = 9,\n    fluidRow(\n      column(width = 12, plotOutput(\"plot_ph\"), plotOutput(\"plot_ic_ph\"))\n    )#,\n    # fluidRow(\n    #   column(width = 6, withMathJax(includeMarkdown(\"Regresion+Lineal/Prueba.md\")))\n    # )\n  )\n)\n\nsimulador4 = actionButton(inputId = \"go_RL\", label = \"Simular\")\ncuerpo_RL = sidebarLayout(\n  sidebarPanel(\n    width = 2,\n    radioButtons(inputId = \"tipoRL\", label = \"Tipo de regresión\", choices = c(\"Simple\")),\n    # radioButtons(inputId = \"tipoRL\", label = \"Tipo de regresión\", choices = c(\"Simple\", \"Múltiple\")),\n    conditionalPanel(\n      condition = \"input.tipoRL == 'Simple'\",\n      sliderInput(inputId = \"nPoblacionalRLS\", label = \"Tamaño poblacional\", min = 600, max = 800, value = 700, step = 10),\n      sliderInput(inputId = \"nMuestralRLS\", label = \"Tamaño muestral\",  min = 100, max = 550, value = 240, step = 10)\n    ),\n    checkboxGroupInput(inputId = \"violacionSupuestos\", label = \"Violación de supuestos\",\n                       choices = c(\"Linealidad\", \"Normalidad\", \"Homocedasticidad\", \"Independencia\")),\n    simulador4\n  ),\n  mainPanel(\n    width = 10,\n    fluidRow(\n      column(width = 6, plotOutput(\"plot_rl\", height = \"500px\"), br(), tableOutput(\"resumen_rl\"), tableOutput(\"resumen_rl_metricas\")),\n      column(width = 6, plotOutput(\"plot_supuestos\", height = \"500px\"), br(), tableOutput(\"resumen_supuestos\"))\n    )\n  )\n)\n# Asignando los cuerpos por filtro\nhoja_DM = tabItem(tabName = \"DM1\", fluidPage(cuerpo_DM1))\nhoja_IC = tabItem(tabName = \"IC\", fluidPage(cuerpo_IC))\nhoja_PH = tabItem(tabName = \"PH\", fluidPage(cuerpo_PH))\nhoja_RL = tabItem(tabName = \"RL\", fluidPage(cuerpo_RL))\n\ncuerpo = dashboardBody(\n  tabItems(hoja_DM, hoja_IC, hoja_PH, hoja_RL)\n)\n\n# Despliegue general\nui = dashboardPage(header = encabezado, sidebar = panelLateral, body = cuerpo, skin = \"black\", title = \"Hola\")\n\n\n","type":"text"},{"name":"Regresion+Lineal/Prueba.md","content":"# Probando elementos de inscrustación\n\n$$\nA + B = C\n$$\n\n1. Hola\n\n2. CHao\n\n**HOLA**S","type":"text"}]
diff --git a/xtable.html b/xtable.html
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+++ /dev/null
@@ -1,328 +0,0 @@
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> grade </th> <th> sex </th> <th> disadvg </th> <th> ethnicty </th> <th> tlimth </th>  </tr>
-  <tr> <td align="right"> 1 </td> <td align="right"> 6 </td> <td> M </td> <td> YES </td> <td> HISPANIC </td> <td align="right"> 43 </td> </tr>
-  <tr> <td align="right"> 2 </td> <td align="right"> 7.0 </td> <td> M </td> <td> NO </td> <td> BLACK </td> <td align="right"> 88.0 </td> </tr>
-  <tr> <td align="right"> 3 </td> <td align="right"> 5.00 </td> <td> F </td> <td> YES </td> <td> HISPANIC </td> <td align="right"> 34.00 </td> </tr>
-  <tr> <td align="right"> 4 </td> <td align="right"> 3.000 </td> <td> M </td> <td> YES </td> <td> HISPANIC </td> <td align="right"> 65.000 </td> </tr>
-  <tr> <td align="right"> 5 </td> <td align="right"> 8.0000 </td> <td> M </td> <td> YES </td> <td> WHITE </td> <td align="right"> 75.0000 </td> </tr>
-  <tr> <td align="right"> 6 </td> <td align="right"> 5 </td> <td> M </td> <td> NO </td> <td> BLACK </td> <td align="right"> 74 </td> </tr>
-  <tr> <td align="right"> 7 </td> <td align="right"> 8.0 </td> <td> F </td> <td> YES </td> <td> HISPANIC </td> <td align="right"> 72.0 </td> </tr>
-  <tr> <td align="right"> 8 </td> <td align="right"> 4.00 </td> <td> M </td> <td> YES </td> <td> BLACK </td> <td align="right"> 79.00 </td> </tr>
-  <tr> <td align="right"> 9 </td> <td align="right"> 6.000 </td> <td> M </td> <td> NO </td> <td> WHITE </td> <td align="right"> 88.000 </td> </tr>
-  <tr> <td align="right"> 10 </td> <td align="right"> 7.0000 </td> <td> M </td> <td> YES </td> <td> HISPANIC </td> <td align="right"> 87.0000 </td> </tr>
-  <tr> <td align="right"> 11 </td> <td align="right"> 3 </td> <td> M </td> <td> NO </td> <td> WHITE </td> <td align="right"> 79 </td> </tr>
-  <tr> <td align="right"> 12 </td> <td align="right"> 6.0 </td> <td> F </td> <td> NO </td> <td> WHITE </td> <td align="right"> 84.0 </td> </tr>
-  <tr> <td align="right"> 13 </td> <td align="right"> 8.00 </td> <td> M </td> <td> NO </td> <td> WHITE </td> <td align="right"> 90.00 </td> </tr>
-  <tr> <td align="right"> 14 </td> <td align="right"> 5.000 </td> <td> M </td> <td> NO </td> <td> WHITE </td> <td align="right"> 73.000 </td> </tr>
-  <tr> <td align="right"> 15 </td> <td align="right"> 8.0000 </td> <td> F </td> <td> NO </td> <td> WHITE </td> <td align="right"> 72.0000 </td> </tr>
-  <tr> <td align="right"> 16 </td> <td align="right"> 6 </td> <td> F </td> <td> NO </td> <td> BLACK </td> <td align="right"> 82 </td> </tr>
-  <tr> <td align="right"> 17 </td> <td align="right"> 4.0 </td> <td> M </td> <td> NO </td> <td> WHITE </td> <td align="right"> 69.0 </td> </tr>
-  <tr> <td align="right"> 18 </td> <td align="right"> 3.00 </td> <td> F </td> <td> YES </td> <td> HISPANIC </td> <td align="right"> 17.00 </td> </tr>
-  <tr> <td align="right"> 19 </td> <td align="right"> 3.000 </td> <td> M </td> <td> NO </td> <td> HISPANIC </td> <td align="right"> 37.000 </td> </tr>
-  <tr> <td align="right"> 20 </td> <td align="right"> 5.0000 </td> <td> M </td> <td> NO </td> <td> WHITE </td> <td align="right"> 70.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> (Intercept) </th> <th> sexM </th> <th> grade </th> <th> sexM:grade </th>  </tr>
-  <tr> <td> 1 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 6 </td> <td align="right"> 6 </td> </tr>
-  <tr> <td> 2 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 7 </td> <td align="right"> 7 </td> </tr>
-  <tr> <td> 3 </td> <td align="right"> 1 </td> <td align="right"> 0 </td> <td align="right"> 5 </td> <td align="right"> 0 </td> </tr>
-  <tr> <td> 4 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 3 </td> <td align="right"> 3 </td> </tr>
-  <tr> <td> 5 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 8 </td> <td align="right"> 8 </td> </tr>
-  <tr> <td> 6 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 5 </td> <td align="right"> 5 </td> </tr>
-  <tr> <td> 7 </td> <td align="right"> 1 </td> <td align="right"> 0 </td> <td align="right"> 8 </td> <td align="right"> 0 </td> </tr>
-  <tr> <td> 8 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 4 </td> <td align="right"> 4 </td> </tr>
-  <tr> <td> 9 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 6 </td> <td align="right"> 6 </td> </tr>
-  <tr> <td> 10 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 7 </td> <td align="right"> 7 </td> </tr>
-  <tr> <td> 11 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 3 </td> <td align="right"> 3 </td> </tr>
-  <tr> <td> 12 </td> <td align="right"> 1 </td> <td align="right"> 0 </td> <td align="right"> 6 </td> <td align="right"> 0 </td> </tr>
-  <tr> <td> 13 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 8 </td> <td align="right"> 8 </td> </tr>
-  <tr> <td> 14 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 5 </td> <td align="right"> 5 </td> </tr>
-  <tr> <td> 15 </td> <td align="right"> 1 </td> <td align="right"> 0 </td> <td align="right"> 8 </td> <td align="right"> 0 </td> </tr>
-  <tr> <td> 16 </td> <td align="right"> 1 </td> <td align="right"> 0 </td> <td align="right"> 6 </td> <td align="right"> 0 </td> </tr>
-  <tr> <td> 17 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 4 </td> <td align="right"> 4 </td> </tr>
-  <tr> <td> 18 </td> <td align="right"> 1 </td> <td align="right"> 0 </td> <td align="right"> 3 </td> <td align="right"> 0 </td> </tr>
-  <tr> <td> 19 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 3 </td> <td align="right"> 3 </td> </tr>
-  <tr> <td> 20 </td> <td align="right"> 1 </td> <td align="right"> 1 </td> <td align="right"> 5 </td> <td align="right"> 5 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> sex </td> <td align="right"> 1 </td> <td align="right"> 75.37 </td> <td align="right"> 75.37 </td> <td align="right"> 0.38 </td> <td align="right"> 0.5417 </td> </tr>
-  <tr> <td> ethnicty </td> <td align="right"> 3 </td> <td align="right"> 2572.15 </td> <td align="right"> 857.38 </td> <td align="right"> 4.27 </td> <td align="right"> 0.0072 </td> </tr>
-  <tr> <td> grade </td> <td align="right"> 1 </td> <td align="right"> 36.31 </td> <td align="right"> 36.31 </td> <td align="right"> 0.18 </td> <td align="right"> 0.6717 </td> </tr>
-  <tr> <td> disadvg </td> <td align="right"> 1 </td> <td align="right"> 59.30 </td> <td align="right"> 59.30 </td> <td align="right"> 0.30 </td> <td align="right"> 0.5882 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 93 </td> <td align="right"> 18682.87 </td> <td align="right"> 200.89 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> t value </th> <th> Pr(&gt;|t|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 73.6364 </td> <td align="right"> 4.2502 </td> <td align="right"> 17.33 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td align="right"> sexM </td> <td align="right"> -1.6364 </td> <td align="right"> 5.8842 </td> <td align="right"> -0.28 </td> <td align="right"> 0.7816 </td> </tr>
-  <tr> <td align="right"> ethnictyHISPANIC </td> <td align="right"> -9.7614 </td> <td align="right"> 6.5501 </td> <td align="right"> -1.49 </td> <td align="right"> 0.1395 </td> </tr>
-  <tr> <td align="right"> ethnictyOTHER </td> <td align="right"> 15.8636 </td> <td align="right"> 10.8360 </td> <td align="right"> 1.46 </td> <td align="right"> 0.1466 </td> </tr>
-  <tr> <td align="right"> ethnictyWHITE </td> <td align="right"> 4.7970 </td> <td align="right"> 4.9687 </td> <td align="right"> 0.97 </td> <td align="right"> 0.3368 </td> </tr>
-  <tr> <td align="right"> sexM:ethnictyHISPANIC </td> <td align="right"> 10.6780 </td> <td align="right"> 8.7190 </td> <td align="right"> 1.22 </td> <td align="right"> 0.2238 </td> </tr>
-  <tr> <td align="right"> sexM:ethnictyWHITE </td> <td align="right"> 5.1230 </td> <td align="right"> 7.0140 </td> <td align="right"> 0.73 </td> <td align="right"> 0.4670 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> t value </th> <th> Pr(&gt;|t|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 73.6364 </td> <td align="right"> 4.2502 </td> <td align="right"> 17.33 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td align="right"> sexM </td> <td align="right"> -1.6364 </td> <td align="right"> 5.8842 </td> <td align="right"> -0.28 </td> <td align="right"> 0.7816 </td> </tr>
-  <tr> <td align="right"> ethnictyHISPANIC </td> <td align="right"> -9.7614 </td> <td align="right"> 6.5501 </td> <td align="right"> -1.49 </td> <td align="right"> 0.1395 </td> </tr>
-  <tr> <td align="right"> ethnictyOTHER </td> <td align="right"> 15.8636 </td> <td align="right"> 10.8360 </td> <td align="right"> 1.46 </td> <td align="right"> 0.1466 </td> </tr>
-  <tr> <td align="right"> ethnictyWHITE </td> <td align="right"> 4.7970 </td> <td align="right"> 4.9687 </td> <td align="right"> 0.97 </td> <td align="right"> 0.3368 </td> </tr>
-  <tr> <td align="right"> sexM:ethnictyHISPANIC </td> <td align="right"> 10.6780 </td> <td align="right"> 8.7190 </td> <td align="right"> 1.22 </td> <td align="right"> 0.2238 </td> </tr>
-  <tr> <td align="right"> sexM:ethnictyWHITE </td> <td align="right"> 5.1230 </td> <td align="right"> 7.0140 </td> <td align="right"> 0.73 </td> <td align="right"> 0.4670 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> sex </td> <td align="right"> 1 </td> <td align="right"> 75.37 </td> <td align="right"> 75.37 </td> <td align="right"> 0.38 </td> <td align="right"> 0.5395 </td> </tr>
-  <tr> <td> ethnicty </td> <td align="right"> 3 </td> <td align="right"> 2572.15 </td> <td align="right"> 857.38 </td> <td align="right"> 4.31 </td> <td align="right"> 0.0068 </td> </tr>
-  <tr> <td> sex:ethnicty </td> <td align="right"> 2 </td> <td align="right"> 298.43 </td> <td align="right"> 149.22 </td> <td align="right"> 0.75 </td> <td align="right"> 0.4748 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 93 </td> <td align="right"> 18480.04 </td> <td align="right"> 198.71 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Res.Df </th> <th> RSS </th> <th> Df </th> <th> Sum of Sq </th> <th> F </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> 1 </td> <td align="right"> 96 </td> <td align="right"> 19053.59 </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> </tr>
-  <tr> <td> 2 </td> <td align="right"> 93 </td> <td align="right"> 18480.04 </td> <td align="right"> 3 </td> <td align="right"> 573.55 </td> <td align="right"> 0.96 </td> <td align="right"> 0.4141 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> z value </th> <th> Pr(&gt;|z|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 3.1888 </td> <td align="right"> 1.5966 </td> <td align="right"> 2.00 </td> <td align="right"> 0.0458 </td> </tr>
-  <tr> <td align="right"> ethnictyHISPANIC </td> <td align="right"> -0.2848 </td> <td align="right"> 2.4808 </td> <td align="right"> -0.11 </td> <td align="right"> 0.9086 </td> </tr>
-  <tr> <td align="right"> ethnictyOTHER </td> <td align="right"> 212.1701 </td> <td align="right"> 22122.7093 </td> <td align="right"> 0.01 </td> <td align="right"> 0.9923 </td> </tr>
-  <tr> <td align="right"> ethnictyWHITE </td> <td align="right"> -8.8150 </td> <td align="right"> 3.3355 </td> <td align="right"> -2.64 </td> <td align="right"> 0.0082 </td> </tr>
-  <tr> <td align="right"> grade </td> <td align="right"> -0.5308 </td> <td align="right"> 0.2892 </td> <td align="right"> -1.84 </td> <td align="right"> 0.0665 </td> </tr>
-  <tr> <td align="right"> ethnictyHISPANIC:grade </td> <td align="right"> 0.2448 </td> <td align="right"> 0.4357 </td> <td align="right"> 0.56 </td> <td align="right"> 0.5742 </td> </tr>
-  <tr> <td align="right"> ethnictyOTHER:grade </td> <td align="right"> -32.6014 </td> <td align="right"> 3393.4687 </td> <td align="right"> -0.01 </td> <td align="right"> 0.9923 </td> </tr>
-  <tr> <td align="right"> ethnictyWHITE:grade </td> <td align="right"> 1.0171 </td> <td align="right"> 0.5185 </td> <td align="right"> 1.96 </td> <td align="right"> 0.0498 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Deviance </th> <th> Resid. Df </th> <th> Resid. Dev </th> <th> Pr(&gt;Chi) </th>  </tr>
-  <tr> <td> NULL </td> <td align="right">  </td> <td align="right">  </td> <td align="right"> 99 </td> <td align="right"> 129.49 </td> <td align="right">  </td> </tr>
-  <tr> <td> ethnicty </td> <td align="right"> 3 </td> <td align="right"> 47.24 </td> <td align="right"> 96 </td> <td align="right"> 82.25 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td> grade </td> <td align="right"> 1 </td> <td align="right"> 1.73 </td> <td align="right"> 95 </td> <td align="right"> 80.52 </td> <td align="right"> 0.1884 </td> </tr>
-  <tr> <td> ethnicty:grade </td> <td align="right"> 3 </td> <td align="right"> 7.20 </td> <td align="right"> 92 </td> <td align="right"> 73.32 </td> <td align="right"> 0.0657 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> block </td> <td align="right"> 5 </td> <td align="right"> 343.30 </td> <td align="right"> 68.66 </td> <td align="right"> 4.45 </td> <td align="right"> 0.0159 </td> </tr>
-  <tr> <td> N </td> <td align="right"> 1 </td> <td align="right"> 189.28 </td> <td align="right"> 189.28 </td> <td align="right"> 12.26 </td> <td align="right"> 0.0044 </td> </tr>
-  <tr> <td> P </td> <td align="right"> 1 </td> <td align="right"> 8.40 </td> <td align="right"> 8.40 </td> <td align="right"> 0.54 </td> <td align="right"> 0.4749 </td> </tr>
-  <tr> <td> K </td> <td align="right"> 1 </td> <td align="right"> 95.20 </td> <td align="right"> 95.20 </td> <td align="right"> 6.17 </td> <td align="right"> 0.0288 </td> </tr>
-  <tr> <td> N:P </td> <td align="right"> 1 </td> <td align="right"> 21.28 </td> <td align="right"> 21.28 </td> <td align="right"> 1.38 </td> <td align="right"> 0.2632 </td> </tr>
-  <tr> <td> N:K </td> <td align="right"> 1 </td> <td align="right"> 33.14 </td> <td align="right"> 33.14 </td> <td align="right"> 2.15 </td> <td align="right"> 0.1686 </td> </tr>
-  <tr> <td> P:K </td> <td align="right"> 1 </td> <td align="right"> 0.48 </td> <td align="right"> 0.48 </td> <td align="right"> 0.03 </td> <td align="right"> 0.8628 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 12 </td> <td align="right"> 185.29 </td> <td align="right"> 15.44 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> block </td> <td align="right"> 5 </td> <td align="right"> 343.30 </td> <td align="right"> 68.66 </td> <td align="right"> 4.45 </td> <td align="right"> 0.0159 </td> </tr>
-  <tr> <td> N </td> <td align="right"> 1 </td> <td align="right"> 189.28 </td> <td align="right"> 189.28 </td> <td align="right"> 12.26 </td> <td align="right"> 0.0044 </td> </tr>
-  <tr> <td> P </td> <td align="right"> 1 </td> <td align="right"> 8.40 </td> <td align="right"> 8.40 </td> <td align="right"> 0.54 </td> <td align="right"> 0.4749 </td> </tr>
-  <tr> <td> K </td> <td align="right"> 1 </td> <td align="right"> 95.20 </td> <td align="right"> 95.20 </td> <td align="right"> 6.17 </td> <td align="right"> 0.0288 </td> </tr>
-  <tr> <td> N:P </td> <td align="right"> 1 </td> <td align="right"> 21.28 </td> <td align="right"> 21.28 </td> <td align="right"> 1.38 </td> <td align="right"> 0.2632 </td> </tr>
-  <tr> <td> N:K </td> <td align="right"> 1 </td> <td align="right"> 33.14 </td> <td align="right"> 33.14 </td> <td align="right"> 2.15 </td> <td align="right"> 0.1686 </td> </tr>
-  <tr> <td> P:K </td> <td align="right"> 1 </td> <td align="right"> 0.48 </td> <td align="right"> 0.48 </td> <td align="right"> 0.03 </td> <td align="right"> 0.8628 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 12 </td> <td align="right"> 185.29 </td> <td align="right"> 15.44 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> block       </td> <td align="right"> 5 </td> <td align="right"> 343.30 </td> <td align="right"> 68.66 </td> <td align="right"> 4.45 </td> <td align="right"> 0.0159 </td> </tr>
-  <tr> <td> N           </td> <td align="right"> 1 </td> <td align="right"> 189.28 </td> <td align="right"> 189.28 </td> <td align="right"> 12.26 </td> <td align="right"> 0.0044 </td> </tr>
-  <tr> <td> P           </td> <td align="right"> 1 </td> <td align="right"> 8.40 </td> <td align="right"> 8.40 </td> <td align="right"> 0.54 </td> <td align="right"> 0.4749 </td> </tr>
-  <tr> <td> K           </td> <td align="right"> 1 </td> <td align="right"> 95.20 </td> <td align="right"> 95.20 </td> <td align="right"> 6.17 </td> <td align="right"> 0.0288 </td> </tr>
-  <tr> <td> N:P         </td> <td align="right"> 1 </td> <td align="right"> 21.28 </td> <td align="right"> 21.28 </td> <td align="right"> 1.38 </td> <td align="right"> 0.2632 </td> </tr>
-  <tr> <td> N:K         </td> <td align="right"> 1 </td> <td align="right"> 33.14 </td> <td align="right"> 33.14 </td> <td align="right"> 2.15 </td> <td align="right"> 0.1686 </td> </tr>
-  <tr> <td> P:K         </td> <td align="right"> 1 </td> <td align="right"> 0.48 </td> <td align="right"> 0.48 </td> <td align="right"> 0.03 </td> <td align="right"> 0.8628 </td> </tr>
-  <tr> <td> Residuals   </td> <td align="right"> 12 </td> <td align="right"> 185.29 </td> <td align="right"> 15.44 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> N:P:K     </td> <td align="right"> 1 </td> <td align="right"> 37.00 </td> <td align="right"> 37.00 </td> <td align="right"> 0.48 </td> <td align="right"> 0.5252 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 4 </td> <td align="right"> 306.29 </td> <td align="right"> 76.57 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-  <tr> <td> N         </td> <td align="right"> 1 </td> <td align="right"> 189.28 </td> <td align="right"> 189.28 </td> <td align="right"> 12.26 </td> <td align="right"> 0.0044 </td> </tr>
-  <tr> <td> P         </td> <td align="right"> 1 </td> <td align="right"> 8.40 </td> <td align="right"> 8.40 </td> <td align="right"> 0.54 </td> <td align="right"> 0.4749 </td> </tr>
-  <tr> <td> K         </td> <td align="right"> 1 </td> <td align="right"> 95.20 </td> <td align="right"> 95.20 </td> <td align="right"> 6.17 </td> <td align="right"> 0.0288 </td> </tr>
-  <tr> <td> N:P       </td> <td align="right"> 1 </td> <td align="right"> 21.28 </td> <td align="right"> 21.28 </td> <td align="right"> 1.38 </td> <td align="right"> 0.2632 </td> </tr>
-  <tr> <td> N:K       </td> <td align="right"> 1 </td> <td align="right"> 33.13 </td> <td align="right"> 33.13 </td> <td align="right"> 2.15 </td> <td align="right"> 0.1686 </td> </tr>
-  <tr> <td> P:K       </td> <td align="right"> 1 </td> <td align="right"> 0.48 </td> <td align="right"> 0.48 </td> <td align="right"> 0.03 </td> <td align="right"> 0.8628 </td> </tr>
-  <tr> <td> Residuals1 </td> <td align="right"> 12 </td> <td align="right"> 185.29 </td> <td align="right"> 15.44 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> N:P:K     </td> <td align="right"> 1 </td> <td align="right"> 37.00 </td> <td align="right"> 37.00 </td> <td align="right"> 0.48 </td> <td align="right"> 0.5252 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 4 </td> <td align="right"> 306.29 </td> <td align="right"> 76.57 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-  <tr> <td> N         </td> <td align="right"> 1 </td> <td align="right"> 189.28 </td> <td align="right"> 189.28 </td> <td align="right"> 12.26 </td> <td align="right"> 0.0044 </td> </tr>
-  <tr> <td> P         </td> <td align="right"> 1 </td> <td align="right"> 8.40 </td> <td align="right"> 8.40 </td> <td align="right"> 0.54 </td> <td align="right"> 0.4749 </td> </tr>
-  <tr> <td> K         </td> <td align="right"> 1 </td> <td align="right"> 95.20 </td> <td align="right"> 95.20 </td> <td align="right"> 6.17 </td> <td align="right"> 0.0288 </td> </tr>
-  <tr> <td> N:P       </td> <td align="right"> 1 </td> <td align="right"> 21.28 </td> <td align="right"> 21.28 </td> <td align="right"> 1.38 </td> <td align="right"> 0.2632 </td> </tr>
-  <tr> <td> N:K       </td> <td align="right"> 1 </td> <td align="right"> 33.13 </td> <td align="right"> 33.13 </td> <td align="right"> 2.15 </td> <td align="right"> 0.1686 </td> </tr>
-  <tr> <td> P:K       </td> <td align="right"> 1 </td> <td align="right"> 0.48 </td> <td align="right"> 0.48 </td> <td align="right"> 0.03 </td> <td align="right"> 0.8628 </td> </tr>
-  <tr> <td> Residuals1 </td> <td align="right"> 12 </td> <td align="right"> 185.29 </td> <td align="right"> 15.44 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> t value </th> <th> Pr(&gt;|t|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 5.0320 </td> <td align="right"> 0.2202 </td> <td align="right"> 22.85 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td align="right"> groupTrt </td> <td align="right"> -0.3710 </td> <td align="right"> 0.3114 </td> <td align="right"> -1.19 </td> <td align="right"> 0.2490 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> t value </th> <th> Pr(&gt;|t|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 5.0320 </td> <td align="right"> 0.2202 </td> <td align="right"> 22.85 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td align="right"> groupTrt </td> <td align="right"> -0.3710 </td> <td align="right"> 0.3114 </td> <td align="right"> -1.19 </td> <td align="right"> 0.2490 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> t value </th> <th> Pr(&gt;|t|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 5.0320 </td> <td align="right"> 0.2202 </td> <td align="right"> 22.85 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td align="right"> groupTrt </td> <td align="right"> -0.3710 </td> <td align="right"> 0.3114 </td> <td align="right"> -1.19 </td> <td align="right"> 0.2490 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Sum Sq </th> <th> Mean Sq </th> <th> F value </th> <th> Pr(&gt;F) </th>  </tr>
-  <tr> <td> group </td> <td align="right"> 1 </td> <td align="right"> 0.69 </td> <td align="right"> 0.69 </td> <td align="right"> 1.42 </td> <td align="right"> 0.2490 </td> </tr>
-  <tr> <td> Residuals </td> <td align="right"> 18 </td> <td align="right"> 8.73 </td> <td align="right"> 0.48 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> z value </th> <th> Pr(&gt;|z|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td align="right"> 3.0445 </td> <td align="right"> 0.1709 </td> <td align="right"> 17.81 </td> <td align="right"> 0.0000 </td> </tr>
-  <tr> <td align="right"> outcome2 </td> <td align="right"> -0.4543 </td> <td align="right"> 0.2022 </td> <td align="right"> -2.25 </td> <td align="right"> 0.0246 </td> </tr>
-  <tr> <td align="right"> outcome3 </td> <td align="right"> -0.2930 </td> <td align="right"> 0.1927 </td> <td align="right"> -1.52 </td> <td align="right"> 0.1285 </td> </tr>
-  <tr> <td align="right"> treatment2 </td> <td align="right"> 0.0000 </td> <td align="right"> 0.2000 </td> <td align="right"> 0.00 </td> <td align="right"> 1.0000 </td> </tr>
-  <tr> <td align="right"> treatment3 </td> <td align="right"> 0.0000 </td> <td align="right"> 0.2000 </td> <td align="right"> 0.00 </td> <td align="right"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Deviance </th> <th> Resid. Df </th> <th> Resid. Dev </th> <th> Pr(&gt;Chi) </th>  </tr>
-  <tr> <td> NULL </td> <td align="right">  </td> <td align="right">  </td> <td align="right"> 8 </td> <td align="right"> 10.58 </td> <td align="right">  </td> </tr>
-  <tr> <td> outcome </td> <td align="right"> 2 </td> <td align="right"> 5.45 </td> <td align="right"> 6 </td> <td align="right"> 5.13 </td> <td align="right"> 0.0655 </td> </tr>
-  <tr> <td> treatment </td> <td align="right"> 2 </td> <td align="right"> 0.00 </td> <td align="right"> 4 </td> <td align="right"> 5.13 </td> <td align="right"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th> Estimate </th> <th> Std. Error </th> <th> z value </th> <th> Pr(&gt;|z|) </th>  </tr>
-  <tr> <td> 3.0445 </td> <td> 0.1709 </td> <td align="right"> 17.81 </td> <td align="center"> 0.0000 </td> </tr>
-  <tr> <td> -0.4543 </td> <td> 0.2022 </td> <td align="right"> -2.25 </td> <td align="center"> 0.0246 </td> </tr>
-  <tr> <td> -0.2930 </td> <td> 0.1927 </td> <td align="right"> -1.52 </td> <td align="center"> 0.1285 </td> </tr>
-  <tr> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-  <tr> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-  <tr> <td align="right"> (Intercept) </td> <td> 3.0445 </td> <td> 0.1709 </td> <td align="right"> 17.81 </td> <td align="center"> 0.0000 </td> </tr>
-  <tr> <td align="right"> outcome2 </td> <td> -0.4543 </td> <td> 0.2022 </td> <td align="right"> -2.25 </td> <td align="center"> 0.0246 </td> </tr>
-  <tr> <td align="right"> outcome3 </td> <td> -0.2930 </td> <td> 0.1927 </td> <td align="right"> -1.52 </td> <td align="center"> 0.1285 </td> </tr>
-  <tr> <td align="right"> treatment2 </td> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-  <tr> <td align="right"> treatment3 </td> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-  <tr> <td> 3.0445 </td> <td> 0.1709 </td> <td align="right"> 17.81 </td> <td align="center"> 0.0000 </td> </tr>
-  <tr> <td> -0.4543 </td> <td> 0.2022 </td> <td align="right"> -2.25 </td> <td align="center"> 0.0246 </td> </tr>
-  <tr> <td> -0.2930 </td> <td> 0.1927 </td> <td align="right"> -1.52 </td> <td align="center"> 0.1285 </td> </tr>
-  <tr> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-  <tr> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Estimate </th> <th> Std. Error </th> <th> z value </th> <th> Pr(&gt;|z|) </th>  </tr>
-  <tr> <td align="right"> (Intercept) </td> <td> 3.0445 </td> <td> 0.1709 </td> <td align="right"> 17.81 </td> <td align="center"> 0.0000 </td> </tr>
-  <tr> <td align="right"> outcome2 </td> <td> -0.4543 </td> <td> 0.2022 </td> <td align="right"> -2.25 </td> <td align="center"> 0.0246 </td> </tr>
-  <tr> <td align="right"> outcome3 </td> <td> -0.2930 </td> <td> 0.1927 </td> <td align="right"> -1.52 </td> <td align="center"> 0.1285 </td> </tr>
-  <tr> <td align="right"> treatment2 </td> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-  <tr> <td align="right"> treatment3 </td> <td> 0.0000 </td> <td> 0.2000 </td> <td align="right"> 0.00 </td> <td align="center"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> Df </th> <th> Deviance </th> <th> Resid. Df </th> <th> Resid. Dev </th> <th> Pr(&gt;Chi) </th>  </tr>
- <tr> <td> NULL </td> <td align="right">  </td> <td align="right">  </td> <td align="right"> 8 </td> <td align="right"> 10.58 </td> <td align="right">  </td> </tr>
-   <tr> <td> outcome </td> <td align="right"> 2 </td> <td align="right"> 5.45 </td> <td align="right"> 6 </td> <td align="right"> 5.13 </td> <td align="right"> 0.0655 </td> </tr>
-  <tr> <td> treatment </td> <td align="right"> 2 </td> <td align="right"> 0.00 </td> <td align="right"> 4 </td> <td align="right"> 5.13 </td> <td align="right"> 1.0000 </td> </tr>
-  </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> PC1 </th> <th> PC2 </th> <th> PC3 </th> <th> PC4 </th>  </tr>
-  <tr> <td align="right"> Murder </td> <td align="right"> 0.0417 </td> <td align="right"> -0.0448 </td> <td align="right"> 0.0799 </td> <td align="right"> -0.9949 </td> </tr>
-  <tr> <td align="right"> Assault </td> <td align="right"> 0.9952 </td> <td align="right"> -0.0588 </td> <td align="right"> -0.0676 </td> <td align="right"> 0.0389 </td> </tr>
-  <tr> <td align="right"> UrbanPop </td> <td align="right"> 0.0463 </td> <td align="right"> 0.9769 </td> <td align="right"> -0.2005 </td> <td align="right"> -0.0582 </td> </tr>
-  <tr> <td align="right"> Rape </td> <td align="right"> 0.0752 </td> <td align="right"> 0.2007 </td> <td align="right"> 0.9741 </td> <td align="right"> 0.0723 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<tr> <th>  </th> <th> PC1 </th> <th> PC2 </th> <th> PC3 </th> <th> PC4 </th>  </tr>
-  <tr> <td align="right"> Standard deviation </td> <td align="right"> 83.7324 </td> <td align="right"> 14.2124 </td> <td align="right"> 6.4894 </td> <td align="right"> 2.4828 </td> </tr>
-  <tr> <td align="right"> Proportion of Variance </td> <td align="right"> 0.9655 </td> <td align="right"> 0.0278 </td> <td align="right"> 0.0058 </td> <td align="right"> 0.0008 </td> </tr>
-  <tr> <td align="right"> Cumulative Proportion </td> <td align="right"> 0.9655 </td> <td align="right"> 0.9933 </td> <td align="right"> 0.9991 </td> <td align="right"> 1.0000 </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<caption align="top"> Time series example </caption>
-<tr> <th>  </th> <th> Jan </th> <th> Feb </th> <th> Mar </th> <th> Apr </th> <th> May </th> <th> Jun </th> <th> Jul </th> <th> Aug </th> <th> Sep </th> <th> Oct </th> <th> Nov </th> <th> Dec </th>  </tr>
-  <tr> <td align="right"> 1954 </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right"> 0.38 </td> <td align="right"> 0.47 </td> <td align="right"> 1.51 </td> <td align="right"> 3.05 </td> <td align="right"> 1.73 </td> <td align="right"> 2.85 </td> </tr>
-  <tr> <td align="right"> 1955 </td> <td align="right"> 3.41 </td> <td align="right"> 5.19 </td> <td align="right"> 6.30 </td> <td align="right"> 9.05 </td> <td align="right"> 10.15 </td> <td align="right"> 11.30 </td> <td align="right"> 13.54 </td> <td align="right"> 14.06 </td> <td align="right"> 14.44 </td> <td align="right"> 15.02 </td> <td align="right"> 16.36 </td> <td align="right"> 18.34 </td> </tr>
-  <tr> <td align="right"> 1956 </td> <td align="right"> 18.67 </td> <td align="right"> 19.40 </td> <td align="right"> 21.24 </td> <td align="right"> 20.57 </td> <td align="right"> 21.57 </td> <td align="right"> 22.03 </td> <td align="right"> 22.87 </td> <td align="right"> 24.95 </td> <td align="right"> 26.46 </td> <td align="right"> 27.89 </td> <td align="right"> 30.84 </td> <td align="right"> 31.93 </td> </tr>
-  <tr> <td align="right"> 1957 </td> <td align="right"> 34.05 </td> <td align="right"> 35.22 </td> <td align="right"> 36.28 </td> <td align="right"> 35.23 </td> <td align="right"> 37.96 </td> <td align="right"> 37.57 </td> <td align="right"> 38.96 </td> <td align="right"> 40.35 </td> <td align="right"> 42.42 </td> <td align="right"> 42.60 </td> <td align="right"> 45.85 </td> <td align="right"> 46.37 </td> </tr>
-  <tr> <td align="right"> 1958 </td> <td align="right"> 49.21 </td> <td align="right"> 50.30 </td> <td align="right"> 51.65 </td> <td align="right"> 52.08 </td> <td align="right"> 52.02 </td> <td align="right"> 55.52 </td> <td align="right"> 55.89 </td> <td align="right"> 57.20 </td> <td align="right"> 58.64 </td> <td align="right"> 61.40 </td> <td align="right"> 62.51 </td> <td align="right"> 63.32 </td> </tr>
-  <tr> <td align="right"> 1959 </td> <td align="right"> 64.03 </td> <td align="right"> 64.23 </td> <td align="right"> 64.28 </td> <td align="right"> 67.00 </td> <td align="right"> 67.35 </td> <td align="right"> 67.05 </td> <td align="right"> 70.36 </td> <td align="right"> 71.41 </td> <td align="right"> 72.19 </td> <td align="right"> 73.59 </td> <td align="right"> 75.01 </td> <td align="right"> 75.50 </td> </tr>
-  <tr> <td align="right"> 1960 </td> <td align="right"> 76.72 </td> <td align="right"> 76.80 </td> <td align="right"> 77.96 </td> <td align="right"> 77.98 </td> <td align="right"> 78.77 </td> <td align="right"> 81.12 </td> <td align="right"> 81.84 </td> <td align="right"> 83.19 </td> <td align="right"> 85.80 </td> <td align="right"> 86.85 </td> <td align="right"> 89.68 </td> <td align="right"> 91.00 </td> </tr>
-  <tr> <td align="right"> 1961 </td> <td align="right"> 91.79 </td> <td align="right"> 92.63 </td> <td align="right"> 92.84 </td> <td align="right"> 94.27 </td> <td align="right"> 93.54 </td> <td align="right"> 94.56 </td> <td align="right"> 95.53 </td> <td align="right"> 95.78 </td> <td align="right"> 96.86 </td> <td align="right"> 99.43 </td> <td align="right"> 101.54 </td> <td align="right"> 103.07 </td> </tr>
-  <tr> <td align="right"> 1962 </td> <td align="right"> 104.12 </td> <td align="right"> 105.51 </td> <td align="right"> 106.33 </td> <td align="right"> 107.78 </td> <td align="right"> 107.84 </td> <td align="right"> 107.71 </td> <td align="right"> 108.67 </td> <td align="right"> 109.27 </td> <td align="right"> 111.17 </td> <td align="right"> 112.05 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
-<!-- html table generated in R 4.4.2 by xtable 1.8-4 package -->
-<!-- Thu Nov 28 15:09:15 2024 -->
-<table border=1>
-<caption align="bottom"> Time series example </caption>
-<tr> <th>  </th> <th> Jan </th> <th> Feb </th> <th> Mar </th> <th> Apr </th> <th> May </th> <th> Jun </th> <th> Jul </th> <th> Aug </th> <th> Sep </th> <th> Oct </th> <th> Nov </th> <th> Dec </th>  </tr>
-  <tr> <td align="right"> 1954 </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> <td align="right"> 0.38 </td> <td align="right"> 0.47 </td> <td align="right"> 1.51 </td> <td align="right"> 3.05 </td> <td align="right"> 1.73 </td> <td align="right"> 2.85 </td> </tr>
-  <tr> <td align="right"> 1955 </td> <td align="right"> 3.41 </td> <td align="right"> 5.19 </td> <td align="right"> 6.30 </td> <td align="right"> 9.05 </td> <td align="right"> 10.15 </td> <td align="right"> 11.30 </td> <td align="right"> 13.54 </td> <td align="right"> 14.06 </td> <td align="right"> 14.44 </td> <td align="right"> 15.02 </td> <td align="right"> 16.36 </td> <td align="right"> 18.34 </td> </tr>
-  <tr> <td align="right"> 1956 </td> <td align="right"> 18.67 </td> <td align="right"> 19.40 </td> <td align="right"> 21.24 </td> <td align="right"> 20.57 </td> <td align="right"> 21.57 </td> <td align="right"> 22.03 </td> <td align="right"> 22.87 </td> <td align="right"> 24.95 </td> <td align="right"> 26.46 </td> <td align="right"> 27.89 </td> <td align="right"> 30.84 </td> <td align="right"> 31.93 </td> </tr>
-  <tr> <td align="right"> 1957 </td> <td align="right"> 34.05 </td> <td align="right"> 35.22 </td> <td align="right"> 36.28 </td> <td align="right"> 35.23 </td> <td align="right"> 37.96 </td> <td align="right"> 37.57 </td> <td align="right"> 38.96 </td> <td align="right"> 40.35 </td> <td align="right"> 42.42 </td> <td align="right"> 42.60 </td> <td align="right"> 45.85 </td> <td align="right"> 46.37 </td> </tr>
-  <tr> <td align="right"> 1958 </td> <td align="right"> 49.21 </td> <td align="right"> 50.30 </td> <td align="right"> 51.65 </td> <td align="right"> 52.08 </td> <td align="right"> 52.02 </td> <td align="right"> 55.52 </td> <td align="right"> 55.89 </td> <td align="right"> 57.20 </td> <td align="right"> 58.64 </td> <td align="right"> 61.40 </td> <td align="right"> 62.51 </td> <td align="right"> 63.32 </td> </tr>
-  <tr> <td align="right"> 1959 </td> <td align="right"> 64.03 </td> <td align="right"> 64.23 </td> <td align="right"> 64.28 </td> <td align="right"> 67.00 </td> <td align="right"> 67.35 </td> <td align="right"> 67.05 </td> <td align="right"> 70.36 </td> <td align="right"> 71.41 </td> <td align="right"> 72.19 </td> <td align="right"> 73.59 </td> <td align="right"> 75.01 </td> <td align="right"> 75.50 </td> </tr>
-  <tr> <td align="right"> 1960 </td> <td align="right"> 76.72 </td> <td align="right"> 76.80 </td> <td align="right"> 77.96 </td> <td align="right"> 77.98 </td> <td align="right"> 78.77 </td> <td align="right"> 81.12 </td> <td align="right"> 81.84 </td> <td align="right"> 83.19 </td> <td align="right"> 85.80 </td> <td align="right"> 86.85 </td> <td align="right"> 89.68 </td> <td align="right"> 91.00 </td> </tr>
-  <tr> <td align="right"> 1961 </td> <td align="right"> 91.79 </td> <td align="right"> 92.63 </td> <td align="right"> 92.84 </td> <td align="right"> 94.27 </td> <td align="right"> 93.54 </td> <td align="right"> 94.56 </td> <td align="right"> 95.53 </td> <td align="right"> 95.78 </td> <td align="right"> 96.86 </td> <td align="right"> 99.43 </td> <td align="right"> 101.54 </td> <td align="right"> 103.07 </td> </tr>
-  <tr> <td align="right"> 1962 </td> <td align="right"> 104.12 </td> <td align="right"> 105.51 </td> <td align="right"> 106.33 </td> <td align="right"> 107.78 </td> <td align="right"> 107.84 </td> <td align="right"> 107.71 </td> <td align="right"> 108.67 </td> <td align="right"> 109.27 </td> <td align="right"> 111.17 </td> <td align="right"> 112.05 </td> <td align="right">  </td> <td align="right">  </td> </tr>
-   </table>
diff --git a/xtable.tex b/xtable.tex
deleted file mode 100644
index 6cc4b38..0000000
--- a/xtable.tex
+++ /dev/null
@@ -1,501 +0,0 @@
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrlllr}
-  \hline
- & grade & sex & disadvg & ethnicty & tlimth \\ 
-  \hline
-1 & 6 & M & YES & HISPANIC & 43 \\ 
-  2 & 7.0 & M & NO & BLACK & 88.0 \\ 
-  3 & 5.00 & F & YES & HISPANIC & 34.00 \\ 
-  4 & 3.000 & M & YES & HISPANIC & 65.000 \\ 
-  5 & 8.0000 & M & YES & WHITE & 75.0000 \\ 
-  6 & 5 & M & NO & BLACK & 74 \\ 
-  7 & 8.0 & F & YES & HISPANIC & 72.0 \\ 
-  8 & 4.00 & M & YES & BLACK & 79.00 \\ 
-  9 & 6.000 & M & NO & WHITE & 88.000 \\ 
-  10 & 7.0000 & M & YES & HISPANIC & 87.0000 \\ 
-  11 & 3 & M & NO & WHITE & 79 \\ 
-  12 & 6.0 & F & NO & WHITE & 84.0 \\ 
-  13 & 8.00 & M & NO & WHITE & 90.00 \\ 
-  14 & 5.000 & M & NO & WHITE & 73.000 \\ 
-  15 & 8.0000 & F & NO & WHITE & 72.0000 \\ 
-  16 & 6 & F & NO & BLACK & 82 \\ 
-  17 & 4.0 & M & NO & WHITE & 69.0 \\ 
-  18 & 3.00 & F & YES & HISPANIC & 17.00 \\ 
-  19 & 3.000 & M & NO & HISPANIC & 37.000 \\ 
-  20 & 5.0000 & M & NO & WHITE & 70.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrr}
-  \hline
- & (Intercept) & sexM & grade & sexM:grade \\ 
-  \hline
-1 & 1 & 1 & 6 & 6 \\ 
-  2 & 1 & 1 & 7 & 7 \\ 
-  3 & 1 & 0 & 5 & 0 \\ 
-  4 & 1 & 1 & 3 & 3 \\ 
-  5 & 1 & 1 & 8 & 8 \\ 
-  6 & 1 & 1 & 5 & 5 \\ 
-  7 & 1 & 0 & 8 & 0 \\ 
-  8 & 1 & 1 & 4 & 4 \\ 
-  9 & 1 & 1 & 6 & 6 \\ 
-  10 & 1 & 1 & 7 & 7 \\ 
-  11 & 1 & 1 & 3 & 3 \\ 
-  12 & 1 & 0 & 6 & 0 \\ 
-  13 & 1 & 1 & 8 & 8 \\ 
-  14 & 1 & 1 & 5 & 5 \\ 
-  15 & 1 & 0 & 8 & 0 \\ 
-  16 & 1 & 0 & 6 & 0 \\ 
-  17 & 1 & 1 & 4 & 4 \\ 
-  18 & 1 & 0 & 3 & 0 \\ 
-  19 & 1 & 1 & 3 & 3 \\ 
-  20 & 1 & 1 & 5 & 5 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-sex & 1 & 75.37 & 75.37 & 0.38 & 0.5417 \\ 
-  ethnicty & 3 & 2572.15 & 857.38 & 4.27 & 0.0072 \\ 
-  grade & 1 & 36.31 & 36.31 & 0.18 & 0.6717 \\ 
-  disadvg & 1 & 59.30 & 59.30 & 0.30 & 0.5882 \\ 
-  Residuals & 93 & 18682.87 & 200.89 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & t value & Pr($>$$|$t$|$) \\ 
-  \hline
-(Intercept) & 73.6364 & 4.2502 & 17.33 & 0.0000 \\ 
-  sexM & -1.6364 & 5.8842 & -0.28 & 0.7816 \\ 
-  ethnictyHISPANIC & -9.7614 & 6.5501 & -1.49 & 0.1395 \\ 
-  ethnictyOTHER & 15.8636 & 10.8360 & 1.46 & 0.1466 \\ 
-  ethnictyWHITE & 4.7970 & 4.9687 & 0.97 & 0.3368 \\ 
-  sexM:ethnictyHISPANIC & 10.6780 & 8.7190 & 1.22 & 0.2238 \\ 
-  sexM:ethnictyWHITE & 5.1230 & 7.0140 & 0.73 & 0.4670 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & t value & Pr($>$$|$t$|$) \\ 
-  \hline
-(Intercept) & 73.6364 & 4.2502 & 17.33 & 0.0000 \\ 
-  sexM & $-$1.6364 & 5.8842 & $-$0.28 & 0.7816 \\ 
-  ethnictyHISPANIC & $-$9.7614 & 6.5501 & $-$1.49 & 0.1395 \\ 
-  ethnictyOTHER & 15.8636 & 10.8360 & 1.46 & 0.1466 \\ 
-  ethnictyWHITE & 4.7970 & 4.9687 & 0.97 & 0.3368 \\ 
-  sexM:ethnictyHISPANIC & 10.6780 & 8.7190 & 1.22 & 0.2238 \\ 
-  sexM:ethnictyWHITE & 5.1230 & 7.0140 & 0.73 & 0.4670 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-sex & 1 & 75.37 & 75.37 & 0.38 & 0.5395 \\ 
-  ethnicty & 3 & 2572.15 & 857.38 & 4.31 & 0.0068 \\ 
-  sex:ethnicty & 2 & 298.43 & 149.22 & 0.75 & 0.4748 \\ 
-  Residuals & 93 & 18480.04 & 198.71 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrrr}
-  \hline
- & Res.Df & RSS & Df & Sum of Sq & F & Pr($>$F) \\ 
-  \hline
-1 & 96 & 19053.59 &  &  &  &  \\ 
-  2 & 93 & 18480.04 & 3 & 573.55 & 0.96 & 0.4141 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & z value & Pr($>$$|$z$|$) \\ 
-  \hline
-(Intercept) & 3.1888 & 1.5966 & 2.00 & 0.0458 \\ 
-  ethnictyHISPANIC & -0.2848 & 2.4808 & -0.11 & 0.9086 \\ 
-  ethnictyOTHER & 212.1701 & 22122.7093 & 0.01 & 0.9923 \\ 
-  ethnictyWHITE & -8.8150 & 3.3355 & -2.64 & 0.0082 \\ 
-  grade & -0.5308 & 0.2892 & -1.84 & 0.0665 \\ 
-  ethnictyHISPANIC:grade & 0.2448 & 0.4357 & 0.56 & 0.5742 \\ 
-  ethnictyOTHER:grade & -32.6014 & 3393.4687 & -0.01 & 0.9923 \\ 
-  ethnictyWHITE:grade & 1.0171 & 0.5185 & 1.96 & 0.0498 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Deviance & Resid. Df & Resid. Dev & Pr($>$Chi) \\ 
-  \hline
-NULL &  &  & 99 & 129.49 &  \\ 
-  ethnicty & 3 & 47.24 & 96 & 82.25 & 0.0000 \\ 
-  grade & 1 & 1.73 & 95 & 80.52 & 0.1884 \\ 
-  ethnicty:grade & 3 & 7.20 & 92 & 73.32 & 0.0657 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-block & 5 & 343.30 & 68.66 & 4.45 & 0.0159 \\ 
-  N & 1 & 189.28 & 189.28 & 12.26 & 0.0044 \\ 
-  P & 1 & 8.40 & 8.40 & 0.54 & 0.4749 \\ 
-  K & 1 & 95.20 & 95.20 & 6.17 & 0.0288 \\ 
-  N:P & 1 & 21.28 & 21.28 & 1.38 & 0.2632 \\ 
-  N:K & 1 & 33.14 & 33.14 & 2.15 & 0.1686 \\ 
-  P:K & 1 & 0.48 & 0.48 & 0.03 & 0.8628 \\ 
-  Residuals & 12 & 185.29 & 15.44 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-block & 5 & 343.30 & 68.66 & 4.45 & 0.0159 \\ 
-  N & 1 & 189.28 & 189.28 & 12.26 & 0.0044 \\ 
-  P & 1 & 8.40 & 8.40 & 0.54 & 0.4749 \\ 
-  K & 1 & 95.20 & 95.20 & 6.17 & 0.0288 \\ 
-  N:P & 1 & 21.28 & 21.28 & 1.38 & 0.2632 \\ 
-  N:K & 1 & 33.14 & 33.14 & 2.15 & 0.1686 \\ 
-  P:K & 1 & 0.48 & 0.48 & 0.03 & 0.8628 \\ 
-  Residuals & 12 & 185.29 & 15.44 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-block       & 5 & 343.30 & 68.66 & 4.45 & 0.0159 \\ 
-  N           & 1 & 189.28 & 189.28 & 12.26 & 0.0044 \\ 
-  P           & 1 & 8.40 & 8.40 & 0.54 & 0.4749 \\ 
-  K           & 1 & 95.20 & 95.20 & 6.17 & 0.0288 \\ 
-  N:P         & 1 & 21.28 & 21.28 & 1.38 & 0.2632 \\ 
-  N:K         & 1 & 33.14 & 33.14 & 2.15 & 0.1686 \\ 
-  P:K         & 1 & 0.48 & 0.48 & 0.03 & 0.8628 \\ 
-  Residuals   & 12 & 185.29 & 15.44 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-N:P:K     & 1 & 37.00 & 37.00 & 0.48 & 0.5252 \\ 
-  Residuals & 4 & 306.29 & 76.57 &  &  \\ 
-  N         & 1 & 189.28 & 189.28 & 12.26 & 0.0044 \\ 
-  P         & 1 & 8.40 & 8.40 & 0.54 & 0.4749 \\ 
-  K         & 1 & 95.20 & 95.20 & 6.17 & 0.0288 \\ 
-  N:P       & 1 & 21.28 & 21.28 & 1.38 & 0.2632 \\ 
-  N:K       & 1 & 33.13 & 33.13 & 2.15 & 0.1686 \\ 
-  P:K       & 1 & 0.48 & 0.48 & 0.03 & 0.8628 \\ 
-  Residuals1 & 12 & 185.29 & 15.44 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-N:P:K     & 1 & 37.00 & 37.00 & 0.48 & 0.5252 \\ 
-  Residuals & 4 & 306.29 & 76.57 &  &  \\ 
-  N         & 1 & 189.28 & 189.28 & 12.26 & 0.0044 \\ 
-  P         & 1 & 8.40 & 8.40 & 0.54 & 0.4749 \\ 
-  K         & 1 & 95.20 & 95.20 & 6.17 & 0.0288 \\ 
-  N:P       & 1 & 21.28 & 21.28 & 1.38 & 0.2632 \\ 
-  N:K       & 1 & 33.13 & 33.13 & 2.15 & 0.1686 \\ 
-  P:K       & 1 & 0.48 & 0.48 & 0.03 & 0.8628 \\ 
-  Residuals1 & 12 & 185.29 & 15.44 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-\clearpage
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & t value & Pr($>$$|$t$|$) \\ 
-  \hline
-(Intercept) & 5.0320 & 0.2202 & 22.85 & 0.0000 \\ 
-  groupTrt & -0.3710 & 0.3114 & -1.19 & 0.2490 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & t value & Pr($>$$|$t$|$) \\ 
-  \hline
-(Intercept) & 5.0320 & 0.2202 & 22.85 & 0.0000 \\ 
-  groupTrt & -0.3710 & 0.3114 & -1.19 & 0.2490 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & t value & Pr($>$$|$t$|$) \\ 
-  \hline
-(Intercept) & 5.0320 & 0.2202 & 22.85 & 0.0000 \\ 
-  groupTrt & -0.3710 & 0.3114 & -1.19 & 0.2490 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Sum Sq & Mean Sq & F value & Pr($>$F) \\ 
-  \hline
-group & 1 & 0.69 & 0.69 & 1.42 & 0.2490 \\ 
-  Residuals & 18 & 8.73 & 0.48 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & Estimate & Std. Error & z value & Pr($>$$|$z$|$) \\ 
-  \hline
-(Intercept) & 3.0445 & 0.1709 & 17.81 & 0.0000 \\ 
-  outcome2 & -0.4543 & 0.2022 & -2.25 & 0.0246 \\ 
-  outcome3 & -0.2930 & 0.1927 & -1.52 & 0.1285 \\ 
-  treatment2 & 0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-  treatment3 & 0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{lrrrrr}
-  \hline
- & Df & Deviance & Resid. Df & Resid. Dev & Pr($>$Chi) \\ 
-  \hline
-NULL &  &  & 8 & 10.58 &  \\ 
-  outcome & 2 & 5.45 & 6 & 5.13 & 0.0655 \\ 
-  treatment & 2 & 0.00 & 4 & 5.13 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{|llrc}
-  \hline
-Estimate & Std. Error & z value & Pr($>$$|$z$|$) \\ 
-  \hline
-3.0445 & 0.1709 & 17.81 & 0.0000 \\ 
-  -0.4543 & 0.2022 & -2.25 & 0.0246 \\ 
-  -0.2930 & 0.1927 & -1.52 & 0.1285 \\ 
-  0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-  0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{r||llrc}
-  \hline
-  \hline
-(Intercept) & 3.0445 & 0.1709 & 17.81 & 0.0000 \\ 
-  outcome2 & -0.4543 & 0.2022 & -2.25 & 0.0246 \\ 
-  outcome3 & -0.2930 & 0.1927 & -1.52 & 0.1285 \\ 
-  treatment2 & 0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-  treatment3 & 0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{||llrc}
-  \hline
-  \hline
-3.0445 & 0.1709 & 17.81 & 0.0000 \\ 
-  -0.4543 & 0.2022 & -2.25 & 0.0246 \\ 
-  -0.2930 & 0.1927 & -1.52 & 0.1285 \\ 
-  0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-  0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{|r||llrc|}
-  \hline
- & Estimate & Std. Error & z value & Pr($>$$|$z$|$) \\ 
-  \hline
-(Intercept) & 3.0445 & 0.1709 & 17.81 & 0.0000 \\ 
-  outcome2 & -0.4543 & 0.2022 & -2.25 & 0.0246 \\ 
-  outcome3 & -0.2930 & 0.1927 & -1.52 & 0.1285 \\ 
-  treatment2 & 0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-  treatment3 & 0.0000 & 0.2000 & 0.00 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begingroup\small
-\begin{tabular}{lrrrrr}
-  & Df & Deviance & Resid. Df & Resid. Dev & Pr($>$Chi) \\ 
- NULL &  &  & 8 & 10.58 &  \\ 
-   \hline
-outcome & 2 & 5.45 & 6 & 5.13 & 0.0655 \\ 
-  treatment & 2 & 0.00 & 4 & 5.13 & 1.0000 \\ 
-  \end{tabular}
-\endgroup
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & PC1 & PC2 & PC3 & PC4 \\ 
-  \hline
-Murder & 0.0417 & -0.0448 & 0.0799 & -0.9949 \\ 
-  Assault & 0.9952 & -0.0588 & -0.0676 & 0.0389 \\ 
-  UrbanPop & 0.0463 & 0.9769 & -0.2005 & -0.0582 \\ 
-  Rape & 0.0752 & 0.2007 & 0.9741 & 0.0723 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[ht]
-\centering
-\begin{tabular}{rrrrr}
-  \hline
- & PC1 & PC2 & PC3 & PC4 \\ 
-  \hline
-Standard deviation & 83.7324 & 14.2124 & 6.4894 & 2.4828 \\ 
-  Proportion of Variance & 0.9655 & 0.0278 & 0.0058 & 0.0008 \\ 
-  Cumulative Proportion & 0.9655 & 0.9933 & 0.9991 & 1.0000 \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[h]
-\centering
-\caption{Time series example} 
-\begin{tabular}{rrrrrrrrrrrrr}
-  \hline
- & Jan & Feb & Mar & Apr & May & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\ 
-  \hline
-1954 &  &  &  &  &  &  & 0.66 & 1.59 & 1.95 & 4.14 & 5.68 & 8.83 \\ 
-  1955 & 8.20 & 7.16 & 7.80 & 9.57 & 9.87 & 12.45 & 14.02 & 17.17 & 18.69 & 18.43 & 19.84 & 20.50 \\ 
-  1956 & 23.17 & 23.45 & 25.57 & 25.10 & 26.85 & 27.50 & 29.36 & 31.18 & 31.48 & 31.79 & 32.99 & 34.06 \\ 
-  1957 & 35.48 & 36.17 & 38.56 & 40.20 & 40.68 & 42.89 & 43.98 & 45.28 & 47.61 & 48.80 & 50.60 & 52.23 \\ 
-  1958 & 53.09 & 53.50 & 56.32 & 57.35 & 58.53 & 58.66 & 60.83 & 61.35 & 61.84 & 60.36 & 61.77 & 62.69 \\ 
-  1959 & 63.70 & 66.14 & 66.54 & 67.75 & 69.33 & 69.84 & 70.52 & 72.26 & 72.90 & 73.34 & 74.00 & 72.85 \\ 
-  1960 & 75.48 & 76.96 & 76.86 & 77.80 & 78.61 & 80.79 & 81.84 & 83.19 & 86.19 & 88.13 & 89.47 & 91.29 \\ 
-  1961 & 93.62 & 94.15 & 95.85 & 96.35 & 96.97 & 98.54 & 98.28 & 99.44 & 99.30 & 100.71 & 102.13 & 103.45 \\ 
-  1962 & 103.86 & 105.09 & 104.57 & 106.13 & 106.24 & 106.59 & 108.23 & 108.20 & 108.30 & 108.04 &  &  \\ 
-   \hline
-\end{tabular}
-\end{table}
-% latex table generated in R 4.4.2 by xtable 1.8-4 package
-% Thu Nov 28 15:09:15 2024
-\begin{table}[htb]
-\centering
-\begin{tabular}{rrrrrrrrrrrrr}
-  \hline
- & Jan & Feb & Mar & Apr & May & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\ 
-  \hline
-1954 &  &  &  &  &  &  & 0.66 & 1.59 & 1.95 & 4.14 & 5.68 & 8.83 \\ 
-  1955 & 8.20 & 7.16 & 7.80 & 9.57 & 9.87 & 12.45 & 14.02 & 17.17 & 18.69 & 18.43 & 19.84 & 20.50 \\ 
-  1956 & 23.17 & 23.45 & 25.57 & 25.10 & 26.85 & 27.50 & 29.36 & 31.18 & 31.48 & 31.79 & 32.99 & 34.06 \\ 
-  1957 & 35.48 & 36.17 & 38.56 & 40.20 & 40.68 & 42.89 & 43.98 & 45.28 & 47.61 & 48.80 & 50.60 & 52.23 \\ 
-  1958 & 53.09 & 53.50 & 56.32 & 57.35 & 58.53 & 58.66 & 60.83 & 61.35 & 61.84 & 60.36 & 61.77 & 62.69 \\ 
-  1959 & 63.70 & 66.14 & 66.54 & 67.75 & 69.33 & 69.84 & 70.52 & 72.26 & 72.90 & 73.34 & 74.00 & 72.85 \\ 
-  1960 & 75.48 & 76.96 & 76.86 & 77.80 & 78.61 & 80.79 & 81.84 & 83.19 & 86.19 & 88.13 & 89.47 & 91.29 \\ 
-  1961 & 93.62 & 94.15 & 95.85 & 96.35 & 96.97 & 98.54 & 98.28 & 99.44 & 99.30 & 100.71 & 102.13 & 103.45 \\ 
-  1962 & 103.86 & 105.09 & 104.57 & 106.13 & 106.24 & 106.59 & 108.23 & 108.20 & 108.30 & 108.04 &  &  \\ 
-   \hline
-\end{tabular}
-\caption{Time series example} 
-\end{table}