Regression Modelling 02. There is value in visually examining the data, don't just compare the model params.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Modelling 2\n",
    "## Regression Modelling 2. There is value in visually examining the data, don't just compare the model params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in install.packages(\"tidyverse\"):\n",
      "“installation of package ‘tidyverse’ had non-zero exit status”Updating HTML index of packages in '.Library'\n",
      "Making 'packages.html' ... done\n",
      "Loading required package: tidyverse\n",
      "Warning message in library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, :\n",
      "“there is no package called ‘tidyverse’”"
     ]
    }
   ],
   "source": [
    "install.packages(\"tidyverse\")\n",
    "require(tidyverse)\n",
    "\n",
    "compare_df <- read.table(url(\"http://jupyter-regressions.s3.eu-west-1.amazonaws.com/compare.csv\"), \n",
    "                       sep=\",\", header = T, stringsAsFactors = F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Y</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>X3</th><th scope=col>X4</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.40</td><td>1.02</td><td>0.02</td><td>1.12</td><td>0.30</td></tr>\n",
       "\t<tr><td>1.35</td><td>0.91</td><td>0.11</td><td>1.01</td><td>0.38</td></tr>\n",
       "\t<tr><td>2.27</td><td>1.73</td><td>0.23</td><td>1.73</td><td>0.38</td></tr>\n",
       "\t<tr><td>3.22</td><td>2.99</td><td>0.89</td><td>2.69</td><td>0.77</td></tr>\n",
       "\t<tr><td>3.37</td><td>1.08</td><td>1.18</td><td>1.98</td><td>0.85</td></tr>\n",
       "\t<tr><td>3.43</td><td>2.93</td><td>1.33</td><td>2.53</td><td>0.75</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " Y & X1 & X2 & X3 & X4\\\\\n",
       "\\hline\n",
       "\t 0.40 & 1.02 & 0.02 & 1.12 & 0.30\\\\\n",
       "\t 1.35 & 0.91 & 0.11 & 1.01 & 0.38\\\\\n",
       "\t 2.27 & 1.73 & 0.23 & 1.73 & 0.38\\\\\n",
       "\t 3.22 & 2.99 & 0.89 & 2.69 & 0.77\\\\\n",
       "\t 3.37 & 1.08 & 1.18 & 1.98 & 0.85\\\\\n",
       "\t 3.43 & 2.93 & 1.33 & 2.53 & 0.75\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| Y | X1 | X2 | X3 | X4 |\n",
       "|---|---|---|---|---|\n",
       "| 0.40 | 1.02 | 0.02 | 1.12 | 0.30 |\n",
       "| 1.35 | 0.91 | 0.11 | 1.01 | 0.38 |\n",
       "| 2.27 | 1.73 | 0.23 | 1.73 | 0.38 |\n",
       "| 3.22 | 2.99 | 0.89 | 2.69 | 0.77 |\n",
       "| 3.37 | 1.08 | 1.18 | 1.98 | 0.85 |\n",
       "| 3.43 | 2.93 | 1.33 | 2.53 | 0.75 |\n",
       "\n"
      ],
      "text/plain": [
       "  Y    X1   X2   X3   X4  \n",
       "1 0.40 1.02 0.02 1.12 0.30\n",
       "2 1.35 0.91 0.11 1.01 0.38\n",
       "3 2.27 1.73 0.23 1.73 0.38\n",
       "4 3.22 2.99 0.89 2.69 0.77\n",
       "5 3.37 1.08 1.18 1.98 0.85\n",
       "6 3.43 2.93 1.33 2.53 0.75"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(compare_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vrgY+cvstynqZcAJUlgAcy6/zfnq83H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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AQW8LnxI1IvqCEnrFW5HLZF0h1AGgILKLtpUPdsrp3y/AKi4x677u+jUo+YUaev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\naWves82gbMU9vUZiTr3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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OTpR0+fa4tJqZcApCWwgDB7LT+y+Xi1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\nSgBaCCzgm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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2f/bDubRxwRNw6A0hFYEOad/ie3nSf1X2vR26bm3jyicVa/Rn3zld5tedl8fK9X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\nnsTOoghgJlgAADPBAgCYCRYAwCweZocQhYC81wAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=20, repr.plot.height=9)\n",
    "plot(Y~X1, data=compare_df)\n",
    "plot(Y~X2, data=compare_df)\n",
    "plot(Y~X3, data=compare_df)\n",
    "plot(Y~X4, data=compare_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Y ~ X1, data = compare_df)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.9784 -0.6855  0.2459  0.7101  2.0322 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  1.57049    0.37571    4.18 0.000123 ***\n",
       "X1           1.07647    0.07611   14.14  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 1.07 on 48 degrees of freedom\n",
       "Multiple R-squared:  0.8065,\tAdjusted R-squared:  0.8024 \n",
       "F-statistic:   200 on 1 and 48 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmX1 = lm(Y~X1, compare_df)\n",
    "summary(lmX1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jNfRcECAECgeMw3Q2r0xQb5+xr7pW3B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\nJrAAAIIJLACAYAILACDY/wK0q9gJiOTVPwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(Y~X1, data=compare_df)\n",
    "abline(lmX1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time I am going to repeat part (a), but this time use X2 as the predictor. Do the values of s, R2, and 1*6,1 suggest a worse or better fit than the model from part (a)? Does the visual appearance of the scatterplot for the X2 model confirm or contradict the numerical findings?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Y ~ X2, data = compare_df)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-2.44514 -0.34997  0.03797  0.50361  2.30698 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  2.42555    0.30323   7.999 2.21e-10 ***\n",
       "X2           0.88722    0.05906  15.023  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 1.019 on 48 degrees of freedom\n",
       "Multiple R-squared:  0.8246,\tAdjusted R-squared:  0.821 \n",
       "F-statistic: 225.7 on 1 and 48 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GIcyCPkAJIrHWNra57kQ0s/MHahjzsW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\nMcgAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmX2 = lm(Y~X2, compare_df)\n",
    "summary(lmX2)\n",
    "\n",
    "plot(Y~X2, data=compare_df)\n",
    "abline(lmX2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From a visual interpretations of this graph, I would suggests there is bias in theses estimates. The assumption of zero homoscedasticity (constant variance) is clearly not present in the residuals. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) Repeat part (a), but this time use X3 as the predictor. Do the values of s, R2, and tb1 I suggest a worse or better fit than the model from part (a)? Does the visual appearance of the scatterplot for the X3 model confirm or contradict the numerical findings? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Y ~ X3, data = compare_df)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.8241 -0.5524 -0.1154  0.4667  2.1975 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  2.11793    0.32146   6.589 3.15e-08 ***\n",
       "X3           0.98766    0.06576  15.020  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 1.019 on 48 degrees of freedom\n",
       "Multiple R-squared:  0.8246,\tAdjusted R-squared:  0.8209 \n",
       "F-statistic: 225.6 on 1 and 48 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1ml3wcfw/E2ZpunyHvabJtlWZdtiiw7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\noE0C/xd2HLap31wAxQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmX3 = lm(Y~X3, compare_df)\n",
    "summary(lmX3)\n",
    "\n",
    "plot(Y~X3, data=compare_df)\n",
    "abline(lmX3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From a visual interpretations of this graph, I would suggests there is bias in theses estimates. \n",
    "\n",
    "Firstly the errors in the data suggest that the mean of residuals across the regression line is not equal to zero. At several points on the graph there is a clear skew, with the residuals in the left and right corners of the graph mostly beneath the regression line. This suggests the zero mean assumption is not upheld.\n",
    "\n",
    "The second assumption that may be broken here is the constant variance, again we see a large difference in the width of residual error between sections of the plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(d) Repeat part (a), but this time use X4 as the predictor. Do the values of s, R2, and tb1 I suggest a worse or better fit than the model from part (a)? Does the visual appearance of the scatterplot for the X4 model confirm or contradict the numerical findings?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Y ~ X4, data = compare_df)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.7266 -0.6456 -0.1058  1.0528  1.7842 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  2.85659    0.27838   10.26 1.08e-13 ***\n",
       "X4           0.90016    0.05993   15.02  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 1.019 on 48 degrees of freedom\n",
       "Multiple R-squared:  0.8245,\tAdjusted R-squared:  0.8209 \n",
       "F-statistic: 225.6 on 1 and 48 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Oe/I7nELs/LWt6DVNYj53YroIACCiig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\ngAABAgQIECBAgAABAgQIECDQAoH/D2+su0IibKyJAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmX4 = lm(Y~X4, compare_df)\n",
    "summary(lmX4)\n",
    "\n",
    "plot(Y~X4, data=compare_df)\n",
    "abline(lmX4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This one fails them all, zero mean, normality, independance and constant variance. Just look at it."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}