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diff --git a/Homework 1/solution_2.2-1.R b/Homework 1/solution_2.2-1.R
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+# -------------------- Code for Question 2.2 part 1 -----------------------------
+# Clear environment
+
+rm(list = ls())
+
+# Load the kernlab library (which contains the ksvm function) and read in the data
+#
+
+library(kernlab)
+
+# ---------------------------- Data manipulation -------------------------------------
+
+data <- read.table("/Users/Chewy/Downloads/credit_card_data.txt", stringsAsFactors = FALSE, header = FALSE)
+
+#
+# optional check to make sure the data is read correctly
+#
+
+head(data)
+
+# Console output for head(data)
+##   V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
+## 1 1 30.83 0.000 1.25 1 0 1 1 202 0 1
+## 2 0 58.67 4.460 3.04 1 0 6 1 43 560 1
+## 3 0 24.50 0.500 1.50 1 1 0 1 280 824 1
+## 4 1 27.83 1.540 3.75 1 0 5 0 100 3 1
+## 5 1 20.17 5.625 1.71 1 1 0 1 120 0 1
+## 6 1 32.08 4.000 2.50 1 1 0 0 360 0 1
+# NOTE: ALL ROWS OF THIS FILE STARTING WITH "##" DENOTE R OUTPUT
+#
+
+# Setting the random number generator seed so that our results are reproducible
+# (Your solution doesn't need this, but it's usually good practice to do)
+
+set.seed(1)
+
+# -------------------------- Creating the models ------------------------------------
+
+# -------------------------- Scaled=TRUE model ------------------------------------
+
+# Fit the model using scaled=TRUE.
+# V11 is response, other variables are predictors
+#
+
+model_scaled <- ksvm(as.matrix(data[,1:10]),as.factor(data[,11]),
+		   type = "C-svc", # Use C-classification method
+              kernel = "vanilladot", # Use simple linear kernel
+              C = 100,
+		   scaled=TRUE) # have ksvm scale the data for you
+
+# or you could use this call; it does the same thing
+
+model_scaled <- ksvm(V11~.,data=data,
+              type = "C-svc", # Use C-classification method
+              kernel = "vanilladot", # Use simple linear kernel
+              C = 100,
+		   scaled=TRUE) # have ksvm scale the data for you
+
+#Attributes model show what the data structure model has to reference
+#For example, we use model@b to get the intercept and model@coef to get the coefficients
+#Those references (b and coef) can be found listed in the console by using attributes(model)
+
+attributes(model_scaled)
+
+# Console output for attributes(model_scaled) is left out since it is a long output
+
+#model lists some high level information about the model data structure
+
+model_scaled
+
+# Console output for model_scaled
+##
+## Support Vector Machine object of class "ksvm"
+## SV type: C-svc (classification)
+## parameter : cost C = 100
+## Linear (vanilla) kernel function.
+## Number of Support Vectors : 189 
+## Objective Function Value : -17887.92 
+## Training error : 0.136086
+
+# -------------------------- Calculating the a coefficients ------------------------------------
+#
+#Classification is done using linear kernel, a*scaled(x) + a0. 
+# Unfortunately, the model does not output a directly, but we can use the model output to find a.
+# calculate a1 to am using the stored data point values in the model data structure and corresponding coefficients
+# multiplying the xmatrix by the coef gives the linear combination of data points that define a1,...,am
+# we use the xmatrix attribute since the model stores these data points as scaled
+
+a_scaled <- colSums(model_scaled@xmatrix[[1]] * model_scaled@coef[[1]])
+
+#
+# a0 is just -model_scaled@b
+
+a0_scaled<- -model_scaled@b
+
+#
+
+a_scaled
+a0_scaled
+
+#Console output for a_scaled 
+## V1            V2            V3            V4            V5           
+## -0.0010065348 -0.0011729048 -0.0016261967  0.0030064203  1.0049405641 
+## V6            V7            V8            V9           V10 
+## -0.0028259432 0.0002600295 -0.0005349551 -0.0012283758  0.1063633995 
+
+#Console output for a0_scaled
+## [1] 0.08158492
+
+# -------------------------- Calculating the predicted values ------------------------------------
+#
+#The ksvm package provides a predict() function that implements this for us, but we also
+#show how to get the predicted values using the a coefficients
+
+# Calculate the predicted values using the a's we got above and our data set.
+# The coefficients for this model are based on the SCALED data points, so we need to 
+# scale our data points to get the correct predictions. We do this by using the scaled
+# mean and standard deviation values for V1 to V10 stored in the model data structure as:
+# model@scaling$x.scale$`scaled:center` (means for V1 to V10)
+# model@scaling$x.scale$`scaled:scale` (standard deviation for V1 to V10)
+# Then we transform the data points into their scaled equivalent by using the function:
+# scaled data point[i,1:10] = (data point[i,1:10] - model@scaling$x.scale$`scaled:center`)/model@scaling$x.scale$`scaled:scale`
+#
+#Create predicted vector (to hold our calculated predicted values)
+
+predicted_scaled<-rep(0,nrow(data))
+
+#For each data point, perform the transformation, calculate a*scaled(data point)+a0, 
+#and predict value of data point based on the resulting value
+
+for (i in 1:nrow(data)){
+
+  #If the data point is above the classifier, predicted value = 1
+
+  if (sum(a_scaled*(data[i,1:10]-model_scaled@scaling$x.scale$`scaled:center`)/model_scaled@scaling$x.scale$`scaled:scale`) + a0_scaled >= 0){
+    predicted_scaled[i] <- 1
+  }
+
+  #If the data point is below the classifier, predicted value = 0
+
+  if (sum(a_scaled*(data[i,1:10]-model_scaled@scaling$x.scale$`scaled:center`)/model_scaled@scaling$x.scale$`scaled:scale`) + a0_scaled < 0){
+    predicted_scaled[i] <- 0
+  }
+}
+predicted_scaled
+
+# Output from predicted_scaled
+##  [1] 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+##  [42] 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
+##  [83] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+##  [124] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+##  [165] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+##  [206] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
+##  [247] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+##  [288] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+##  [329] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+##  [370] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+##  [411] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+##  [452] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+##  [493] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+##  [534] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1
+##  [575] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+##  [616] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+
+
+# Get prediction from ksvm model we created, model_scaled
+# Note that we could also get the predicted values of the model using model_scaled@fitted
+#
+
+pred_scaled <- predict(model_scaled,data[,1:10])
+pred_scaled
+
+#Output from pred_scaled
+## [1] 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [42] 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
+## [83] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [124] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [165] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [206] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
+## [247] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [288] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [329] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [370] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [411] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [452] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [493] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [534] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1
+## [575] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [616] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+
+# typing "pred_scaled" will give the sequence of 1s and 0s showing the model's classification
+# As you can see in the outputs, pred and predicted have the same predicted values
+# so we know that our a coefficients are correct for the SCALED data version of the model
+
+# -------------------------- Calculating the model's accuracy ------------------------------------
+#
+# I will use a simple accuracy measure that outputs the
+# percent of testing observations that are correctly classified.
+
+sum(pred_scaled == data$V11) / nrow(data)
+sum(predicted_scaled == data$V11) / nrow(data)
+
+#Output from sum(pred_scaled == data$V11) / nrow(data)
+## [1] 0.8639144
+#
+#Output from sum(predicted_scaled == data$V11) / nrow(data)
+## [1] 0.8639144
+# Note that this result is found by a wide range of values of C.
+
+
+
+
+
+
+
+
+
+# -------------------------- Scaled=FALSE model ------------------------------------
+
+# Fit the model using scaled=FALSE.
+# V11 is response, other variables are predictors
+#
+
+model_unscaled <- ksvm(as.matrix(data[,1:10]),as.factor(data[,11]),
+		   type = "C-svc", # Use C-classification method
+              kernel = "vanilladot", # Use simple linear kernel
+              C = 100,
+		   scaled=FALSE) # ksvm will not scale the data for you
+
+# or you could use this call; it does the same thing
+
+model_unscaled <- ksvm(V11~.,data=data,
+              type = "C-svc", # Use C-classification method
+              kernel = "vanilladot", # Use simple linear kernel
+              C = 100,
+		   scaled=FALSE) # ksvm will not scale the data for you
+
+#Attributes model show what the data structure model has to reference
+#For example, we use model_unscaled@b to get the intercept and model_unscaled@coef to get the coefficients
+#Those references (b and coef) can be found listed in the console by using attributes(model_unscaled)
+
+attributes(model_unscaled)
+
+# Console output for attributes(model_unscaled) is left out since it is a long output
+
+#model lists some high level information about the model data structure
+
+model_unscaled
+
+# Console output for model_unscaled
+##
+## Support Vector Machine object of class "ksvm" 
+## SV type: C-svc  (classification) 
+## parameter : cost C = 100 
+## Linear (vanilla) kernel function. 
+## Number of Support Vectors : 186 
+## Objective Function Value : -2213.731 
+## Training error : 0.278287 
+
+# -------------------------- Calculating the a coefficients ------------------------------------
+#
+#Classification is done using linear kernel, a*unscaled(x) + a0 = a*x + a0. 
+# Unfortunately, the model does not output a directly, but we can use the model output to find a.
+# calculate a1 to am using the stored data point values in the model data structure and corresponding coefficients
+# multiplying the xmatrix by the coef gives the linear combination of data points that define a1,...,am
+# we use the xmatrix attribute since the model stores these data points as unscaled
+
+a_unscaled <- colSums(model_unscaled@xmatrix[[1]] * model_unscaled@coef[[1]])
+
+#
+# a0 is just -model_unscaled@b
+
+a0_unscaled <- -model_unscaled@b
+
+#
+
+a_unscaled
+a0_unscaled
+
+#Console output for a_unscaled
+## V1            V2            V3            V4            V5            
+## -0.0483050561 -0.0083148473 -0.0836550114  0.1751121271  1.8254844547   
+## V6           V7            V8            V9           V10 
+## 0.2763673361 0.0654782414 -0.1108211169 -0.0047229653 -0.0007764962 
+
+#Console output for a0_unscaled
+## 0.5255393
+
+# -------------------------- Calculating the predicted values ------------------------------------
+#
+#The ksvm package provides a predict() function that implements this for us, but we also
+#show how to get the predicted values using the a coefficients
+
+# Calculate the predicted values using the a's we got above and our data set
+# The coefficients for this model are based on the UNSCALED data points, so we do not need to 
+# scale our data points to get the correct predictions.
+
+#Create predicted vector (to hold our calculated predicted values)
+
+predicted_unscaled<-rep(0,nrow(data))
+
+#For each data point, calculate a*(data point)+a0, 
+#and predict value of data point based on the resulting value
+
+for (i in 1:nrow(data)){
+
+  #If the data point is above the classifier, predicted value = 1
+
+  if (sum(a_unscaled*data[i,1:10]) + a0_unscaled >= 0){
+    predicted_unscaled[i] <- 1
+  }
+
+  #If the data point is below the classifier, predicted value = 0
+
+  if (sum(a_unscaled*data[i,1:10]) + a0_unscaled < 0){
+    predicted_unscaled[i] <- 0
+  }
+}
+predicted_unscaled
+
+# Output from predicted_unscaled
+## [1] 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1
+## [42] 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1
+## [83] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1
+## [124] 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1
+## [165] 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
+## [206] 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0
+## [247] 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [288] 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
+## [329] 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
+## [370] 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
+## [411] 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
+## [452] 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
+## [493] 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0
+## [534] 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1
+## [575] 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
+## [616] 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
+
+# Get prediction from ksvm model we created
+#
+
+pred_unscaled <- predict(model_unscaled,data[,1:10])
+pred_unscaled
+
+#Output from pred_unscaled
+## [1] 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1
+## [42] 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1
+## [83] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1
+## [124] 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1
+## [165] 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
+## [206] 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0
+## [247] 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+## [288] 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
+## [329] 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
+## [370] 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
+## [411] 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
+## [452] 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
+## [493] 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0
+## [534] 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1
+## [575] 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
+## [616] 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
+
+# typing "pred_unscaled" will give the sequence of 1s and 0s showing the model's classification
+# As you can see in the outputs, pred and predicted have the same predicted values
+# so we know that our a coefficients are correct for the SCALED data version of the model
+
+# -------------------------- Calculating the model's accuracy ------------------------------------
+#
+# I will use a simple accuracy measure that outputs the
+# percent of testing observations that are correctly classified.
+
+sum(pred_unscaled == data$V11) / nrow(data)
+sum(predicted_unscaled == data$V11) / nrow(data)
+
+#Output from sum(pred_unscaled == data$V11) / nrow(data)
+## [1] 0.7217125
+#
+#Output from sum(predicted_unscaled == data$V11) / nrow(data)
+## [1] 0.7217125