Lab 6(a) - Logistic Regression

Lab 7 Logistic Regression

Objective 1 - Perform Logistic Regression with and without preproccessing and compare teh results.

Objective 2 - Perform various data normalization operations using “caret” package and compare results

Objective 3 - Compute sensitivity, specificity and AUC. draw ROC curve for one of teh chosen result

Getting the dataset

fileURL <- "http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data"

download.file(fileURL, destfile="breast-cancer-wisconsin.data", method="curl")

reading the data

df <- read.table("breast-cancer-wisconsin.data", na.strings = "?", sep=",")

str(df)

## 'data.frame':    699 obs. of  11 variables:
##  $ V1 : int  1000025 1002945 1015425 1016277 1017023 1017122 1018099 1018561 1033078 1033078 ...
##  $ V2 : int  5 5 3 6 4 8 1 2 2 4 ...
##  $ V3 : int  1 4 1 8 1 10 1 1 1 2 ...
##  $ V4 : int  1 4 1 8 1 10 1 2 1 1 ...
##  $ V5 : int  1 5 1 1 3 8 1 1 1 1 ...
##  $ V6 : int  2 7 2 3 2 7 2 2 2 2 ...
##  $ V7 : int  1 10 2 4 1 10 10 1 1 1 ...
##  $ V8 : int  3 3 3 3 3 9 3 3 1 2 ...
##  $ V9 : int  1 2 1 7 1 7 1 1 1 1 ...
##  $ V10: int  1 1 1 1 1 1 1 1 5 1 ...
##  $ V11: int  2 2 2 2 2 4 2 2 2 2 ...

Wisconsin dataset has 699 observations and 11 variables

All variables in the dataset are integers

The columns can be named by the following line of code

names(data) <- c(“ClumpThickness”,

##“UniformityCellSize”, ##“UniformityCellShape”, ##“MarginalAdhesion”, ##“SingleEpithelialCellSize”, ##“BareNuclei”, ##“BlandChromatin”, ##“NormalNucleoli”, ##“Mitoses”, ##“Class”) # These names are displayed in the tree to facilitate semantic interpretation ## Installing Dataexplorer, ggplot2 and data.table libraries

library(DataExplorer)

library(ggplot2)

library(data.table)

Eliminating the first column on IDs as it is irrelevant in the next steps of the code

df <- df [ ,-1]

Viewing the current state of the table, we run the code below:

df

##     V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
## 1    5  1  1  1  2  1  3  1   1   2
## 2    5  4  4  5  7 10  3  2   1   2
## 3    3  1  1  1  2  2  3  1   1   2
## 4    6  8  8  1  3  4  3  7   1   2
## 5    4  1  1  3  2  1  3  1   1   2
## 6    8 10 10  8  7 10  9  7   1   4
## 7    1  1  1  1  2 10  3  1   1   2
## 8    2  1  2  1  2  1  3  1   1   2
## 9    2  1  1  1  2  1  1  1   5   2
## 10   4  2  1  1  2  1  2  1   1   2
## 11   1  1  1  1  1  1  3  1   1   2
## 12   2  1  1  1  2  1  2  1   1   2
## 13   5  3  3  3  2  3  4  4   1   4
## 14   1  1  1  1  2  3  3  1   1   2
## 15   8  7  5 10  7  9  5  5   4   4
## 16   7  4  6  4  6  1  4  3   1   4
## 17   4  1  1  1  2  1  2  1   1   2
## 18   4  1  1  1  2  1  3  1   1   2
## 19  10  7  7  6  4 10  4  1   2   4
## 20   6  1  1  1  2  1  3  1   1   2
## 21   7  3  2 10  5 10  5  4   4   4
## 22  10  5  5  3  6  7  7 10   1   4
## 23   3  1  1  1  2  1  2  1   1   2
## 24   8  4  5  1  2 NA  7  3   1   4
## 25   1  1  1  1  2  1  3  1   1   2
## 26   5  2  3  4  2  7  3  6   1   4
## 27   3  2  1  1  1  1  2  1   1   2
## 28   5  1  1  1  2  1  2  1   1   2
## 29   2  1  1  1  2  1  2  1   1   2
## 30   1  1  3  1  2  1  1  1   1   2
## 31   3  1  1  1  1  1  2  1   1   2
## 32   2  1  1  1  2  1  3  1   1   2
## 33  10  7  7  3  8  5  7  4   3   4
## 34   2  1  1  2  2  1  3  1   1   2
## 35   3  1  2  1  2  1  2  1   1   2
## 36   2  1  1  1  2  1  2  1   1   2
## 37  10 10 10  8  6  1  8  9   1   4
## 38   6  2  1  1  1  1  7  1   1   2
## 39   5  4  4  9  2 10  5  6   1   4
## 40   2  5  3  3  6  7  7  5   1   4
## 41   6  6  6  9  6 NA  7  8   1   2
## 42  10  4  3  1  3  3  6  5   2   4
## 43   6 10 10  2  8 10  7  3   3   4
## 44   5  6  5  6 10  1  3  1   1   4
## 45  10 10 10  4  8  1  8 10   1   4
## 46   1  1  1  1  2  1  2  1   2   2
## 47   3  7  7  4  4  9  4  8   1   4
## 48   1  1  1  1  2  1  2  1   1   2
## 49   4  1  1  3  2  1  3  1   1   2
## 50   7  8  7  2  4  8  3  8   2   4
## 51   9  5  8  1  2  3  2  1   5   4
## 52   5  3  3  4  2  4  3  4   1   4
## 53  10  3  6  2  3  5  4 10   2   4
## 54   5  5  5  8 10  8  7  3   7   4
## 55  10  5  5  6  8  8  7  1   1   4
## 56  10  6  6  3  4  5  3  6   1   4
## 57   8 10 10  1  3  6  3  9   1   4
## 58   8  2  4  1  5  1  5  4   4   4
## 59   5  2  3  1  6 10  5  1   1   4
## 60   9  5  5  2  2  2  5  1   1   4
## 61   5  3  5  5  3  3  4 10   1   4
## 62   1  1  1  1  2  2  2  1   1   2
## 63   9 10 10  1 10  8  3  3   1   4
## 64   6  3  4  1  5  2  3  9   1   4
## 65   1  1  1  1  2  1  2  1   1   2
## 66  10  4  2  1  3  2  4  3  10   4
## 67   4  1  1  1  2  1  3  1   1   2
## 68   5  3  4  1  8 10  4  9   1   4
## 69   8  3  8  3  4  9  8  9   8   4
## 70   1  1  1  1  2  1  3  2   1   2
## 71   5  1  3  1  2  1  2  1   1   2
## 72   6 10  2  8 10  2  7  8  10   4
## 73   1  3  3  2  2  1  7  2   1   2
## 74   9  4  5 10  6 10  4  8   1   4
## 75  10  6  4  1  3  4  3  2   3   4
## 76   1  1  2  1  2  2  4  2   1   2
## 77   1  1  4  1  2  1  2  1   1   2
## 78   5  3  1  2  2  1  2  1   1   2
## 79   3  1  1  1  2  3  3  1   1   2
## 80   2  1  1  1  3  1  2  1   1   2
## 81   2  2  2  1  1  1  7  1   1   2
## 82   4  1  1  2  2  1  2  1   1   2
## 83   5  2  1  1  2  1  3  1   1   2
## 84   3  1  1  1  2  2  7  1   1   2
## 85   3  5  7  8  8  9  7 10   7   4
## 86   5 10  6  1 10  4  4 10  10   4
## 87   3  3  6  4  5  8  4  4   1   4
## 88   3  6  6  6  5 10  6  8   3   4
## 89   4  1  1  1  2  1  3  1   1   2
## 90   2  1  1  2  3  1  2  1   1   2
## 91   1  1  1  1  2  1  3  1   1   2
## 92   3  1  1  2  2  1  1  1   1   2
## 93   4  1  1  1  2  1  3  1   1   2
## 94   1  1  1  1  2  1  2  1   1   2
## 95   2  1  1  1  2  1  3  1   1   2
## 96   1  1  1  1  2  1  3  1   1   2
## 97   2  1  1  2  2  1  1  1   1   2
## 98   5  1  1  1  2  1  3  1   1   2
## 99   9  6  9  2 10  6  2  9  10   4
## 100  7  5  6 10  5 10  7  9   4   4
## 101 10  3  5  1 10  5  3 10   2   4
## 102  2  3  4  4  2  5  2  5   1   4
## 103  4  1  2  1  2  1  3  1   1   2
## 104  8  2  3  1  6  3  7  1   1   4
## 105 10 10 10 10 10  1  8  8   8   4
## 106  7  3  4  4  3  3  3  2   7   4
## 107 10 10 10  8  2 10  4  1   1   4
## 108  1  6  8 10  8 10  5  7   1   4
## 109  1  1  1  1  2  1  2  3   1   2
## 110  6  5  4  4  3  9  7  8   3   4
## 111  1  3  1  2  2  2  5  3   2   2
## 112  8  6  4  3  5  9  3  1   1   4
## 113 10  3  3 10  2 10  7  3   3   4
## 114 10 10 10  3 10  8  8  1   1   4
## 115  3  3  2  1  2  3  3  1   1   2
## 116  1  1  1  1  2  5  1  1   1   2
## 117  8  3  3  1  2  2  3  2   1   2
## 118  4  5  5 10  4 10  7  5   8   4
## 119  1  1  1  1  4  3  1  1   1   2
## 120  3  2  1  1  2  2  3  1   1   2
## 121  1  1  2  2  2  1  3  1   1   2
## 122  4  2  1  1  2  2  3  1   1   2
## 123 10 10 10  2 10 10  5  3   3   4
## 124  5  3  5  1  8 10  5  3   1   4
## 125  5  4  6  7  9  7  8 10   1   4
## 126  1  1  1  1  2  1  2  1   1   2
## 127  7  5  3  7  4 10  7  5   5   4
## 128  3  1  1  1  2  1  3  1   1   2
## 129  8  3  5  4  5 10  1  6   2   4
## 130  1  1  1  1 10  1  1  1   1   2
## 131  5  1  3  1  2  1  2  1   1   2
## 132  2  1  1  1  2  1  3  1   1   2
## 133  5 10  8 10  8 10  3  6   3   4
## 134  3  1  1  1  2  1  2  2   1   2
## 135  3  1  1  1  3  1  2  1   1   2
## 136  5  1  1  1  2  2  3  3   1   2
## 137  4  1  1  1  2  1  2  1   1   2
## 138  3  1  1  1  2  1  1  1   1   2
## 139  4  1  2  1  2  1  2  1   1   2
## 140  1  1  1  1  1 NA  2  1   1   2
## 141  3  1  1  1  2  1  1  1   1   2
## 142  2  1  1  1  2  1  1  1   1   2
## 143  9  5  5  4  4  5  4  3   3   4
## 144  1  1  1  1  2  5  1  1   1   2
## 145  2  1  1  1  2  1  2  1   1   2
## 146  1  1  3  1  2 NA  2  1   1   2
## 147  3  4  5  2  6  8  4  1   1   4
## 148  1  1  1  1  3  2  2  1   1   2
## 149  3  1  1  3  8  1  5  8   1   2
## 150  8  8  7  4 10 10  7  8   7   4
## 151  1  1  1  1  1  1  3  1   1   2
## 152  7  2  4  1  6 10  5  4   3   4
## 153 10 10  8  6  4  5  8 10   1   4
## 154  4  1  1  1  2  3  1  1   1   2
## 155  1  1  1  1  2  1  1  1   1   2
## 156  5  5  5  6  3 10  3  1   1   4
## 157  1  2  2  1  2  1  2  1   1   2
## 158  2  1  1  1  2  1  3  1   1   2
## 159  1  1  2  1  3 NA  1  1   1   2
## 160  9  9 10  3  6 10  7 10   6   4
## 161 10  7  7  4  5 10  5  7   2   4
## 162  4  1  1  1  2  1  3  2   1   2
## 163  3  1  1  1  2  1  3  1   1   2
## 164  1  1  1  2  1  3  1  1   7   2
## 165  5  1  1  1  2 NA  3  1   1   2
## 166  4  1  1  1  2  2  3  2   1   2
## 167  5  6  7  8  8 10  3 10   3   4
## 168 10  8 10 10  6  1  3  1  10   4
## 169  3  1  1  1  2  1  3  1   1   2
## 170  1  1  1  2  1  1  1  1   1   2
## 171  3  1  1  1  2  1  1  1   1   2
## 172  1  1  1  1  2  1  3  1   1   2
## 173  1  1  1  1  2  1  2  1   1   2
## 174  6 10 10 10  8 10 10 10   7   4
## 175  8  6  5  4  3 10  6  1   1   4
## 176  5  8  7  7 10 10  5  7   1   4
## 177  2  1  1  1  2  1  3  1   1   2
## 178  5 10 10  3  8  1  5 10   3   4
## 179  4  1  1  1  2  1  3  1   1   2
## 180  5  3  3  3  6 10  3  1   1   4
## 181  1  1  1  1  1  1  3  1   1   2
## 182  1  1  1  1  2  1  1  1   1   2
## 183  6  1  1  1  2  1  3  1   1   2
## 184  5  8  8  8  5 10  7  8   1   4
## 185  8  7  6  4  4 10  5  1   1   4
## 186  2  1  1  1  1  1  3  1   1   2
## 187  1  5  8  6  5  8  7 10   1   4
## 188 10  5  6 10  6 10  7  7  10   4
## 189  5  8  4 10  5  8  9 10   1   4
## 190  1  2  3  1  2  1  3  1   1   2
## 191 10 10 10  8  6  8  7 10   1   4
## 192  7  5 10 10 10 10  4 10   3   4
## 193  5  1  1  1  2  1  2  1   1   2
## 194  1  1  1  1  2  1  3  1   1   2
## 195  3  1  1  1  2  1  3  1   1   2
## 196  4  1  1  1  2  1  3  1   1   2
## 197  8  4  4  5  4  7  7  8   2   2
## 198  5  1  1  4  2  1  3  1   1   2
## 199  1  1  1  1  2  1  1  1   1   2
## 200  3  1  1  1  2  1  2  1   1   2
## 201  9  7  7  5  5 10  7  8   3   4
## 202 10  8  8  4 10 10  8  1   1   4
## 203  1  1  1  1  2  1  3  1   1   2
## 204  5  1  1  1  2  1  3  1   1   2
## 205  1  1  1  1  2  1  3  1   1   2
## 206  5 10 10  9  6 10  7 10   5   4
## 207 10 10  9  3  7  5  3  5   1   4
## 208  1  1  1  1  1  1  3  1   1   2
## 209  1  1  1  1  1  1  3  1   1   2
## 210  5  1  1  1  1  1  3  1   1   2
## 211  8 10 10 10  5 10  8 10   6   4
## 212  8 10  8  8  4  8  7  7   1   4
## 213  1  1  1  1  2  1  3  1   1   2
## 214 10 10 10 10  7 10  7 10   4   4
## 215 10 10 10 10  3 10 10  6   1   4
## 216  8  7  8  7  5  5  5 10   2   4
## 217  1  1  1  1  2  1  2  1   1   2
## 218  1  1  1  1  2  1  3  1   1   2
## 219  6 10  7  7  6  4  8 10   2   4
## 220  6  1  3  1  2  1  3  1   1   2
## 221  1  1  1  2  2  1  3  1   1   2
## 222 10  6  4  3 10 10  9 10   1   4
## 223  4  1  1  3  1  5  2  1   1   4
## 224  7  5  6  3  3  8  7  4   1   4
## 225 10  5  5  6  3 10  7  9   2   4
## 226  1  1  1  1  2  1  2  1   1   2
## 227 10  5  7  4  4 10  8  9   1   4
## 228  8  9  9  5  3  5  7  7   1   4
## 229  1  1  1  1  1  1  3  1   1   2
## 230 10 10 10  3 10 10  9 10   1   4
## 231  7  4  7  4  3  7  7  6   1   4
## 232  6  8  7  5  6  8  8  9   2   4
## 233  8  4  6  3  3  1  4  3   1   2
## 234 10  4  5  5  5 10  4  1   1   4
## 235  3  3  2  1  3  1  3  6   1   2
## 236  3  1  4  1  2 NA  3  1   1   2
## 237 10  8  8  2  8 10  4  8  10   4
## 238  9  8  8  5  6  2  4 10   4   4
## 239  8 10 10  8  6  9  3 10  10   4
## 240 10  4  3  2  3 10  5  3   2   4
## 241  5  1  3  3  2  2  2  3   1   2
## 242  3  1  1  3  1  1  3  1   1   2
## 243  2  1  1  1  2  1  3  1   1   2
## 244  1  1  1  1  2  5  5  1   1   2
## 245  1  1  1  1  2  1  3  1   1   2
## 246  5  1  1  2  2  2  3  1   1   2
## 247  8 10 10  8  5 10  7  8   1   4
## 248  8  4  4  1  2  9  3  3   1   4
## 249  4  1  1  1  2  1  3  6   1   2
## 250  3  1  1  1  2 NA  3  1   1   2
## 251  1  2  2  1  2  1  1  1   1   2
## 252 10  4  4 10  2 10  5  3   3   4
## 253  6  3  3  5  3 10  3  5   3   2
## 254  6 10 10  2  8 10  7  3   3   4
## 255  9 10 10  1 10  8  3  3   1   4
## 256  5  6  6  2  4 10  3  6   1   4
## 257  3  1  1  1  2  1  1  1   1   2
## 258  3  1  1  1  2  1  2  1   1   2
## 259  3  1  1  1  2  1  3  1   1   2
## 260  5  7  7  1  5  8  3  4   1   2
## 261 10  5  8 10  3 10  5  1   3   4
## 262  5 10 10  6 10 10 10  6   5   4
## 263  8  8  9  4  5 10  7  8   1   4
## 264 10  4  4 10  6 10  5  5   1   4
## 265  7  9  4 10 10  3  5  3   3   4
## 266  5  1  4  1  2  1  3  2   1   2
## 267 10 10  6  3  3 10  4  3   2   4
## 268  3  3  5  2  3 10  7  1   1   4
## 269 10  8  8  2  3  4  8  7   8   4
## 270  1  1  1  1  2  1  3  1   1   2
## 271  8  4  7  1  3 10  3  9   2   4
## 272  5  1  1  1  2  1  3  1   1   2
## 273  3  3  5  2  3 10  7  1   1   4
## 274  7  2  4  1  3  4  3  3   1   4
## 275  3  1  1  1  2  1  3  2   1   2
## 276  3  1  3  1  2 NA  2  1   1   2
## 277  3  1  1  1  2  1  2  1   1   2
## 278  1  1  1  1  2  1  2  1   1   2
## 279  1  1  1  1  2  1  3  1   1   2
## 280 10  5  7  3  3  7  3  3   8   4
## 281  3  1  1  1  2  1  3  1   1   2
## 282  2  1  1  2  2  1  3  1   1   2
## 283  1  4  3 10  4 10  5  6   1   4
## 284 10  4  6  1  2 10  5  3   1   4
## 285  7  4  5 10  2 10  3  8   2   4
## 286  8 10 10 10  8 10 10  7   3   4
## 287 10 10 10 10 10 10  4 10  10   4
## 288  3  1  1  1  3  1  2  1   1   2
## 289  6  1  3  1  4  5  5 10   1   4
## 290  5  6  6  8  6 10  4 10   4   4
## 291  1  1  1  1  2  1  1  1   1   2
## 292  1  1  1  1  2  1  3  1   1   2
## 293  8  8  8  1  2 NA  6 10   1   4
## 294 10  4  4  6  2 10  2  3   1   4
## 295  1  1  1  1  2 NA  2  1   1   2
## 296  5  5  7  8  6 10  7  4   1   4
## 297  5  3  4  3  4  5  4  7   1   2
## 298  5  4  3  1  2 NA  2  3   1   2
## 299  8  2  1  1  5  1  1  1   1   2
## 300  9  1  2  6  4 10  7  7   2   4
## 301  8  4 10  5  4  4  7 10   1   4
## 302  1  1  1  1  2  1  3  1   1   2
## 303 10 10 10  7  9 10  7 10  10   4
## 304  1  1  1  1  2  1  3  1   1   2
## 305  8  3  4  9  3 10  3  3   1   4
## 306 10  8  4  4  4 10  3 10   4   4
## 307  1  1  1  1  2  1  3  1   1   2
## 308  1  1  1  1  2  1  3  1   1   2
## 309  7  8  7  6  4  3  8  8   4   4
## 310  3  1  1  1  2  5  5  1   1   2
## 311  2  1  1  1  3  1  2  1   1   2
## 312  1  1  1  1  2  1  1  1   1   2
## 313  8  6  4 10 10  1  3  5   1   4
## 314  1  1  1  1  2  1  1  1   1   2
## 315  1  1  1  1  1  1  2  1   1   2
## 316  4  6  5  6  7 NA  4  9   1   2
## 317  5  5  5  2  5 10  4  3   1   4
## 318  6  8  7  8  6  8  8  9   1   4
## 319  1  1  1  1  5  1  3  1   1   2
## 320  4  4  4  4  6  5  7  3   1   2
## 321  7  6  3  2  5 10  7  4   6   4
## 322  3  1  1  1  2 NA  3  1   1   2
## 323  3  1  1  1  2  1  3  1   1   2
## 324  5  4  6 10  2 10  4  1   1   4
## 325  1  1  1  1  2  1  3  1   1   2
## 326  3  2  2  1  2  1  2  3   1   2
## 327 10  1  1  1  2 10  5  4   1   4
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## 330 10  4  6  4  5 10  7  1   1   4
## 331 10  4  7  2  2  8  6  1   1   4
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## 334  5  4  6  6  4 10  4  3   1   4
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## 337  6  5  5  8  4 10  3  4   1   4
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## 339  1  1  1  1  1  1  2  1   1   2
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## 342  1  1  1  1  2  1  3  1   1   2
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## 347  5  2  2  2  3  1  1  3   1   2
## 348  1  1  1  1  1  1  1  3   1   2
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## 357  5  3  3  1  3  3  3  3   3   4
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## 360 10  3  5  4  3  7  3  5   3   4
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## 364  4  4  4  2  2  3  2  1   1   2
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## 366  2  1  1  1  2  1  2  1   1   2
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## 368  5  8  8 10  5 10  8 10   3   4
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## 370  1  1  3  1  1  1  2  1   1   2
## 371  4  3  2  1  3  1  2  1   1   2
## 372  1  1  3  1  2  1  1  1   1   2
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## 376  1  1  1  1  2  1  1  1   1   2
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## 378  1  1  1  1  1  1  2  1   1   2
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## 380  5  3  4  1  4  1  3  1   1   2
## 381  1  1  1  1  2  1  1  1   1   2
## 382 10  6  3  6  4 10  7  8   4   4
## 383  3  2  2  2  2  1  3  2   1   2
## 384  2  1  1  1  2  1  1  1   1   2
## 385  2  1  1  1  2  1  1  1   1   2
## 386  3  3  2  2  3  1  1  2   3   2
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## 389  2  1  1  1  2  1  2  2   1   2
## 390  5  1  1  1  3  2  2  2   1   2
## 391  1  1  1  2  2  1  2  1   1   2
## 392 10  8  7  4  3 10  7  9   1   4
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## 396  3  1  1  1  2  1  2  1   1   2
## 397  3  1  1  1  2  1  3  1   1   2
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## 402  3  1  1  1  2  1  1  1   1   2
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## 404  3  1  1  1  2  4  1  1   1   2
## 405  1  2  1  3  2  1  1  2   1   2
## 406  1  1  1  1  2  1  2  1   1   2
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## 408  1  1  1  1  2  1  2  1   1   2
## 409  2  3  2  2  2  2  3  1   1   2
## 410  3  1  2  1  2  1  2  1   1   2
## 411  1  1  1  1  2  1  2  1   1   2
## 412  1  1  1  1  1 NA  2  1   1   2
## 413 10 10 10  6  8  4  8  5   1   4
## 414  5  1  2  1  2  1  3  1   1   2
## 415  8  5  6  2  3 10  6  6   1   4
## 416  3  3  2  6  3  3  3  5   1   2
## 417  8  7  8  5 10 10  7  2   1   4
## 418  1  1  1  1  2  1  2  1   1   2
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## 420  2  3  1  1  5  1  1  1   1   2
## 421  3  2  2  3  2  3  3  1   1   2
## 422 10 10 10  7 10 10  8  2   1   4
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## 425  3  1  1  1  2  1  1  1   1   2
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## 427  5  3  6  1  2  1  1  1   1   2
## 428  8  7  8  2  4  2  5 10   1   4
## 429  1  1  1  1  2  1  2  1   1   2
## 430  2  1  1  1  2  1  2  1   1   2
## 431  1  3  1  1  2  1  2  2   1   2
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## 434  3  2  2  3  2  1  1  1   1   2
## 435  6  9  7  5  5  8  4  2   1   2
## 436 10  8 10  1  3 10  5  1   1   4
## 437 10 10 10  1  6  1  2  8   1   4
## 438  4  1  1  1  2  1  1  1   1   2
## 439  4  1  3  3  2  1  1  1   1   2
## 440  5  1  1  1  2  1  1  1   1   2
## 441 10  4  3 10  4 10 10  1   1   4
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## 444  1  1  1  1  2  2  1  1   1   2
## 445  5  1  1  6  3  1  2  1   1   2
## 446  2  1  1  1  2  1  1  1   1   2
## 447  1  1  1  1  2  1  1  1   1   2
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## 449  1  1  1  1  1  1  1  1   1   2
## 450  5  7  9  8  6 10  8 10   1   4
## 451  4  1  1  3  1  1  2  1   1   2
## 452  5  1  1  1  2  1  1  1   1   2
## 453  3  1  1  3  2  1  1  1   1   2
## 454  4  5  5  8  6 10 10  7   1   4
## 455  2  3  1  1  3  1  1  1   1   2
## 456 10  2  2  1  2  6  1  1   2   4
## 457 10  6  5  8  5 10  8  6   1   4
## 458  8  8  9  6  6  3 10 10   1   4
## 459  5  1  2  1  2  1  1  1   1   2
## 460  5  1  3  1  2  1  1  1   1   2
## 461  5  1  1  3  2  1  1  1   1   2
## 462  3  1  1  1  2  5  1  1   1   2
## 463  6  1  1  3  2  1  1  1   1   2
## 464  4  1  1  1  2  1  1  2   1   2
## 465  4  1  1  1  2  1  1  1   1   2
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## 467 10  6  6  2  4 10  9  7   1   4
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## 471  3  1  1  1  1  1  2  1   1   2
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## 473  6  1  1  1  1  1  1  1   1   2
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## 478  4  1  1  1  2  1  1  1   1   2
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## 481  5  1  1  1  1  1  1  1   1   2
## 482  5  3  2  4  2  1  1  1   1   2
## 483  9 10 10 10 10  5 10 10  10   4
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## 486  1  1  1  3  1  3  1  1   1   2
## 487  3  1  1  1  1  1  2  1   1   2
## 488 10 10 10 10  6 10  8  1   5   4
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## 494  5 10 10 10  6 10  6  5   2   4
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## 503  4  1  1  2  2  1  2  1   1   2
## 504  4  1  1  1  2  1  3  1   1   2
## 505  1  1  1  1  2  1  1  1   1   2
## 506  3  3  1  1  2  1  1  1   1   2
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## 508  1  1  1  1  2  4  1  1   1   2
## 509  5  1  1  1  2  1  1  1   1   2
## 510  2  1  1  1  2  1  1  1   1   2
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## 513  5  1  1  1  2  1  1  1   1   2
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## 515  6  6  7 10  3 10  8 10   2   4
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## 518  1  1  1  1  1  1  2  1   1   2
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## 522  4  1  1  1  3  1  1  1   1   2
## 523 10  4  5  4  3  5  7  3   1   4
## 524  7  5  6 10  4 10  5  3   1   4
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## 571  8 10  4  4  8 10  8  2   1   4
## 572  7  6 10  5  3 10  9 10   2   4
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## 579  1  1  1  1  2  1  2  1   1   2
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## 581  5  1  2  1  2  1  2  1   1   2
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## 584  3  1  1  1  2  1  1  1   1   2
## 585  5  1  1  6  3  1  1  1   1   2
## 586  1  1  1  1  2  1  1  1   1   2
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## 606 10  5 10  3  5  8  7  8   3   4
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## 666  1  1  1  1  2  1  1  1   1   2
## 667  5  2  2  2  2  1  1  1   2   2
## 668  3  1  1  1  2  1  3  1   1   2
## 669  5  7  4  1  6  1  7 10   3   4
## 670  5 10 10  8  5  5  7 10   1   4
## 671  3 10  7  8  5  8  7  4   1   4
## 672  3  2  1  2  2  1  3  1   1   2
## 673  2  1  1  1  2  1  3  1   1   2
## 674  5  3  2  1  3  1  1  1   1   2
## 675  1  1  1  1  2  1  2  1   1   2
## 676  4  1  4  1  2  1  1  1   1   2
## 677  1  1  2  1  2  1  2  1   1   2
## 678  5  1  1  1  2  1  1  1   1   2
## 679  1  1  1  1  2  1  1  1   1   2
## 680  2  1  1  1  2  1  1  1   1   2
## 681 10 10 10 10  5 10 10 10   7   4
## 682  5 10 10 10  4 10  5  6   3   4
## 683  5  1  1  1  2  1  3  2   1   2
## 684  1  1  1  1  2  1  1  1   1   2
## 685  1  1  1  1  2  1  1  1   1   2
## 686  1  1  1  1  2  1  1  1   1   2
## 687  1  1  1  1  2  1  1  1   1   2
## 688  3  1  1  1  2  1  2  3   1   2
## 689  4  1  1  1  2  1  1  1   1   2
## 690  1  1  1  1  2  1  1  1   8   2
## 691  1  1  1  3  2  1  1  1   1   2
## 692  5 10 10  5  4  5  4  4   1   4
## 693  3  1  1  1  2  1  1  1   1   2
## 694  3  1  1  1  2  1  2  1   2   2
## 695  3  1  1  1  3  2  1  1   1   2
## 696  2  1  1  1  2  1  1  1   1   2
## 697  5 10 10  3  7  3  8 10   2   4
## 698  4  8  6  4  3  4 10  6   1   4
## 699  4  8  8  5  4  5 10  4   1   4

Converting the numeric variables into labels

df$V11 <- factor(df$V11, levels=c(2,4), labels=c("1", "2"))

str(df)

## 'data.frame':    699 obs. of  10 variables:
##  $ V2 : int  5 5 3 6 4 8 1 2 2 4 ...
##  $ V3 : int  1 4 1 8 1 10 1 1 1 2 ...
##  $ V4 : int  1 4 1 8 1 10 1 2 1 1 ...
##  $ V5 : int  1 5 1 1 3 8 1 1 1 1 ...
##  $ V6 : int  2 7 2 3 2 7 2 2 2 2 ...
##  $ V7 : int  1 10 2 4 1 10 10 1 1 1 ...
##  $ V8 : int  3 3 3 3 3 9 3 3 1 2 ...
##  $ V9 : int  1 2 1 7 1 7 1 1 1 1 ...
##  $ V10: int  1 1 1 1 1 1 1 1 5 1 ...
##  $ V11: Factor w/ 2 levels "1","2": 1 1 1 1 1 2 1 1 1 1 ...

Splitting the dataset into the Training set and Test set

install.packages(‘caTools’)

library(caTools)

set.seed(123)

set.seed(123)

split = sample.split(df$V11, SplitRatio = 0.7)

training_set = subset(df, split == TRUE)

test_set = subset(df, split == FALSE)

Splitting the dataset into the Training set and Test set

The dataset is split into train and test datasets.

Train now has 490 observations

Test now has 209 observations

Checking Class distribution

We use prop.table()

prop.table() helps in the creation of frequency and contingency tables from categorical variables, along with tests of independence, measures of association, and methods for graphically displaying results.

prop.table(table(df$V11))

## 
##         1         2 
## 0.6552217 0.3447783

The frequency of 1’s is 65% while the frequency of 2’s is 34%

prop.table(table(training_set$V11))

## 
##        1        2 
## 0.655102 0.344898

prop.table(table(test_set$V11))

## 
##         1         2 
## 0.6555024 0.3444976

Building a classifier

The classifier is built using a GLM (Generalized Linear Models)

GLM is an extension of linear regression models that allow the dependent variable to be non-normal.

classifier = glm(V11 ~., training_set, family = binomial)

summary(classifier)

## 
## Call:
## glm(formula = V11 ~ ., family = binomial, data = training_set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.2762  -0.0940  -0.0552   0.0284   2.0749  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -10.076354   1.424300  -7.075  1.5e-12 ***
## V2            0.505034   0.188574   2.678 0.007402 ** 
## V3            0.004358   0.219328   0.020 0.984146    
## V4            0.487276   0.255273   1.909 0.056282 .  
## V5            0.180709   0.155224   1.164 0.244350    
## V6            0.051222   0.186649   0.274 0.783754    
## V7            0.400580   0.114917   3.486 0.000491 ***
## V8            0.477829   0.207467   2.303 0.021270 *  
## V9            0.204022   0.127727   1.597 0.110192    
## V10           0.270990   0.301128   0.900 0.368166    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 619.45  on 478  degrees of freedom
## Residual deviance:  67.17  on 469  degrees of freedom
##   (11 observations deleted due to missingness)
## AIC: 87.17
## 
## Number of Fisher Scoring iterations: 8

Predicting the Test set results

prob_pred = predict(classifier, type = 'response', test_set[ ,-10] )

prob_pred

##            2            4            5            9           12           15 
## 0.8576330951 0.8761263735 0.0098446429 0.0028598601 0.0015619624 0.9987642960 
##           23           29           30           31           34           36 
## 0.0025855848 0.0015619624 0.0015490546 0.0024567972 0.0030132690 0.0015619624 
##           39           42           44           49           55           58 
## 0.9826086040 0.9182216319 0.2344952006 0.0098446429 0.9974025923 0.7404543476 
##           62           64           65           66           67           73 
## 0.0014072577 0.4242578120 0.0009432046 0.9117175063 0.0068791895 0.0388604957 
##           75           88           92           95          108          109 
## 0.8235282745 0.9936113791 0.0019222500 0.0025163647 0.9906592301 0.0014177853 
##          111          114          121          126          127          128 
## 0.0138877921 0.9997854944 0.0029603874 0.0009432046 0.9978454338 0.0041628410 
##          130          132          133          135          148          154 
## 0.0008812090 0.0025163647 0.9977258082 0.0027211051 0.0014811091 0.0059002091 
##          155          157          160          167          169          174 
## 0.0005851177 0.0015412035 0.9999869558 0.9976093913 0.0041628410 0.9999972620 
##          178          181          183          184          186          187 
## 0.9812930184 0.0014443114 0.0186646573 0.9993497035 0.0023910167 0.9895400421 
##          191          195          198          199          201          204 
## 0.9999725737 0.0041628410 0.0193562972 0.0005851177 0.9998588843 0.0113478194 
##          206          207          212          214          220          223 
## 0.9999565838 0.9935115472 0.9995924131 0.9999963862 0.0479832631 0.0282592745 
##          233          234          236          237          242          245 
## 0.6890652598 0.9931700185           NA 0.9999516716 0.0056682460 0.0015201045 
##          246          248          249          254          256          259 
## 0.0201138268 0.8942936184 0.0188494248 0.9993994249 0.9478133806 0.0041628410 
##          263          271          273          274          275          276 
## 0.9998190261 0.9961048417 0.9028145419 0.4182266320 0.0051001893           NA 
##          283          287          294          301          306          308 
## 0.8593587694 0.9999974435 0.9815076259 0.9992693698 0.9984206184 0.0015201045 
##          316          319          326          327          330          332 
##           NA 0.0017721499 0.0063335725 0.9619767778 0.9987944745 0.0148275879 
##          336          341          346          347          349          350 
## 0.0005851177 0.9962332262 0.0005851177 0.0135014336 0.1401076556 0.9252624378 
##          352          354          355          357          359          360 
## 0.0025163647 0.9989309214 0.0009432046 0.1568778786 0.9773039611 0.9875138101 
##          361          370          374          385          387          389 
## 0.9999971496 0.0023712741 0.0084555803 0.0009691923 0.9924518145 0.0019147960 
##          390          393          394          395          400          402 
## 0.0135286812 0.0025855848 0.0005559175 0.0025064627 0.0015558101 0.0016049710 
##          410          412          413          415          421          424 
## 0.0042021893           NA 0.9996966771 0.9969584458 0.0213907151 0.0185130373 
##          425          427          434          436          437          440 
## 0.0016049710 0.0484353642 0.0037584171 0.9991639147 0.9743637252 0.0043946006 
##          441          442          443          445          453          456 
## 0.9995582481 0.0396397585 0.0018688970 0.0181569021 0.0023021057 0.4669781032 
##          457          461          462          463          468          470 
## 0.9997886629 0.0062957972 0.0079175431 0.0103894276 0.9978255357 0.0015345114 
##          486          487          488          489          491          493 
## 0.0017757439 0.0024567972 0.9999887164 0.2884459967 0.0005851177 0.0040644568 
##          494          497          498          500          501          507 
## 0.9996347036 0.0005559175 0.0026682769 0.0042771581 0.0186646573 0.9997943688 
##          511          514          515          517          521          522 
## 0.0005851177 0.0024567972 0.9998435015 0.0005559175 0.0006158506 0.0027959414 
##          524          527          530          531          534          537 
## 0.9966462040 0.0026567039 0.0040644568 0.9942477256 0.0025855848 0.0113478194 
##          538          541          544          553          558          562 
## 0.0183421540 0.0105130821 0.0042771581 0.0159347053 0.0062957972 0.0113478194 
##          567          570          574          578          588          593 
## 0.0067589227 0.9998325135 0.0009432046 0.0009432046 0.0086532957 0.9876966129 
##          596          597          600          602          607          610 
## 0.0070675717 0.0069440344 0.0178452746 0.0008961503 0.0031812324 0.0043946006 
##          611          612          613          618          620          621 
## 0.9985146253 0.9952424105 0.9999995100           NA 0.0070675717 0.0025855848 
##          628          629          631          636          642          647 
## 0.0047931644 0.0009691923 0.0190953686 0.0068869572 0.0025855848 0.0009563040 
##          656          662          663          666          678          680 
## 0.0025855848 0.0068791895 0.0024955897 0.0005851177 0.0043946006 0.0009691923 
##          683          684          694          695          696 
## 0.0138804613 0.0005851177 0.0033876519 0.0025193256 0.0009691923

y_pred = ifelse(prob_pred > 0.5, 1, 0)

y_pred

##   2   4   5   9  12  15  23  29  30  31  34  36  39  42  44  49  55  58  62  64 
##   1   1   0   0   0   1   0   0   0   0   0   0   1   1   0   0   1   1   0   0 
##  65  66  67  73  75  88  92  95 108 109 111 114 121 126 127 128 130 132 133 135 
##   0   1   0   0   1   1   0   0   1   0   0   1   0   0   1   0   0   0   1   0 
## 148 154 155 157 160 167 169 174 178 181 183 184 186 187 191 195 198 199 201 204 
##   0   0   0   0   1   1   0   1   1   0   0   1   0   1   1   0   0   0   1   0 
## 206 207 212 214 220 223 233 234 236 237 242 245 246 248 249 254 256 259 263 271 
##   1   1   1   1   0   0   1   1  NA   1   0   0   0   1   0   1   1   0   1   1 
## 273 274 275 276 283 287 294 301 306 308 316 319 326 327 330 332 336 341 346 347 
##   1   0   0  NA   1   1   1   1   1   0  NA   0   0   1   1   0   0   1   0   0 
## 349 350 352 354 355 357 359 360 361 370 374 385 387 389 390 393 394 395 400 402 
##   0   1   0   1   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0 
## 410 412 413 415 421 424 425 427 434 436 437 440 441 442 443 445 453 456 457 461 
##   0  NA   1   1   0   0   0   0   0   1   1   0   1   0   0   0   0   0   1   0 
## 462 463 468 470 486 487 488 489 491 493 494 497 498 500 501 507 511 514 515 517 
##   0   0   1   0   0   0   1   0   0   0   1   0   0   0   0   1   0   0   1   0 
## 521 522 524 527 530 531 534 537 538 541 544 553 558 562 567 570 574 578 588 593 
##   0   0   1   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   1 
## 596 597 600 602 607 610 611 612 613 618 620 621 628 629 631 636 642 647 656 662 
##   0   0   0   0   0   0   1   1   1  NA   0   0   0   0   0   0   0   0   0   0 
## 663 666 678 680 683 684 694 695 696 
##   0   0   0   0   0   0   0   0   0

cm = table(test_set$V11, y_pred)

cm

##    y_pred
##       0   1
##   1 129   3
##   2   8  64

Variation 1 - Run the above by removing the variable with missing values

Checking for missing values

sum(is.na(df))

## [1] 16

Missing values are 16

colSums(is.na(df))

##  V2  V3  V4  V5  V6  V7  V8  V9 V10 V11 
##   0   0   0   0   0  16   0   0   0   0

the missing values are in variable v7

df$V7 <- NULL

df

##     V2 V3 V4 V5 V6 V8 V9 V10 V11
## 1    5  1  1  1  2  3  1   1   1
## 2    5  4  4  5  7  3  2   1   1
## 3    3  1  1  1  2  3  1   1   1
## 4    6  8  8  1  3  3  7   1   1
## 5    4  1  1  3  2  3  1   1   1
## 6    8 10 10  8  7  9  7   1   2
## 7    1  1  1  1  2  3  1   1   1
## 8    2  1  2  1  2  3  1   1   1
## 9    2  1  1  1  2  1  1   5   1
## 10   4  2  1  1  2  2  1   1   1
## 11   1  1  1  1  1  3  1   1   1
## 12   2  1  1  1  2  2  1   1   1
## 13   5  3  3  3  2  4  4   1   2
## 14   1  1  1  1  2  3  1   1   1
## 15   8  7  5 10  7  5  5   4   2
## 16   7  4  6  4  6  4  3   1   2
## 17   4  1  1  1  2  2  1   1   1
## 18   4  1  1  1  2  3  1   1   1
## 19  10  7  7  6  4  4  1   2   2
## 20   6  1  1  1  2  3  1   1   1
## 21   7  3  2 10  5  5  4   4   2
## 22  10  5  5  3  6  7 10   1   2
## 23   3  1  1  1  2  2  1   1   1
## 24   8  4  5  1  2  7  3   1   2
## 25   1  1  1  1  2  3  1   1   1
## 26   5  2  3  4  2  3  6   1   2
## 27   3  2  1  1  1  2  1   1   1
## 28   5  1  1  1  2  2  1   1   1
## 29   2  1  1  1  2  2  1   1   1
## 30   1  1  3  1  2  1  1   1   1
## 31   3  1  1  1  1  2  1   1   1
## 32   2  1  1  1  2  3  1   1   1
## 33  10  7  7  3  8  7  4   3   2
## 34   2  1  1  2  2  3  1   1   1
## 35   3  1  2  1  2  2  1   1   1
## 36   2  1  1  1  2  2  1   1   1
## 37  10 10 10  8  6  8  9   1   2
## 38   6  2  1  1  1  7  1   1   1
## 39   5  4  4  9  2  5  6   1   2
## 40   2  5  3  3  6  7  5   1   2
## 41   6  6  6  9  6  7  8   1   1
## 42  10  4  3  1  3  6  5   2   2
## 43   6 10 10  2  8  7  3   3   2
## 44   5  6  5  6 10  3  1   1   2
## 45  10 10 10  4  8  8 10   1   2
## 46   1  1  1  1  2  2  1   2   1
## 47   3  7  7  4  4  4  8   1   2
## 48   1  1  1  1  2  2  1   1   1
## 49   4  1  1  3  2  3  1   1   1
## 50   7  8  7  2  4  3  8   2   2
## 51   9  5  8  1  2  2  1   5   2
## 52   5  3  3  4  2  3  4   1   2
## 53  10  3  6  2  3  4 10   2   2
## 54   5  5  5  8 10  7  3   7   2
## 55  10  5  5  6  8  7  1   1   2
## 56  10  6  6  3  4  3  6   1   2
## 57   8 10 10  1  3  3  9   1   2
## 58   8  2  4  1  5  5  4   4   2
## 59   5  2  3  1  6  5  1   1   2
## 60   9  5  5  2  2  5  1   1   2
## 61   5  3  5  5  3  4 10   1   2
## 62   1  1  1  1  2  2  1   1   1
## 63   9 10 10  1 10  3  3   1   2
## 64   6  3  4  1  5  3  9   1   2
## 65   1  1  1  1  2  2  1   1   1
## 66  10  4  2  1  3  4  3  10   2
## 67   4  1  1  1  2  3  1   1   1
## 68   5  3  4  1  8  4  9   1   2
## 69   8  3  8  3  4  8  9   8   2
## 70   1  1  1  1  2  3  2   1   1
## 71   5  1  3  1  2  2  1   1   1
## 72   6 10  2  8 10  7  8  10   2
## 73   1  3  3  2  2  7  2   1   1
## 74   9  4  5 10  6  4  8   1   2
## 75  10  6  4  1  3  3  2   3   2
## 76   1  1  2  1  2  4  2   1   1
## 77   1  1  4  1  2  2  1   1   1
## 78   5  3  1  2  2  2  1   1   1
## 79   3  1  1  1  2  3  1   1   1
## 80   2  1  1  1  3  2  1   1   1
## 81   2  2  2  1  1  7  1   1   1
## 82   4  1  1  2  2  2  1   1   1
## 83   5  2  1  1  2  3  1   1   1
## 84   3  1  1  1  2  7  1   1   1
## 85   3  5  7  8  8  7 10   7   2
## 86   5 10  6  1 10  4 10  10   2
## 87   3  3  6  4  5  4  4   1   2
## 88   3  6  6  6  5  6  8   3   2
## 89   4  1  1  1  2  3  1   1   1
## 90   2  1  1  2  3  2  1   1   1
## 91   1  1  1  1  2  3  1   1   1
## 92   3  1  1  2  2  1  1   1   1
## 93   4  1  1  1  2  3  1   1   1
## 94   1  1  1  1  2  2  1   1   1
## 95   2  1  1  1  2  3  1   1   1
## 96   1  1  1  1  2  3  1   1   1
## 97   2  1  1  2  2  1  1   1   1
## 98   5  1  1  1  2  3  1   1   1
## 99   9  6  9  2 10  2  9  10   2
## 100  7  5  6 10  5  7  9   4   2
## 101 10  3  5  1 10  3 10   2   2
## 102  2  3  4  4  2  2  5   1   2
## 103  4  1  2  1  2  3  1   1   1
## 104  8  2  3  1  6  7  1   1   2
## 105 10 10 10 10 10  8  8   8   2
## 106  7  3  4  4  3  3  2   7   2
## 107 10 10 10  8  2  4  1   1   2
## 108  1  6  8 10  8  5  7   1   2
## 109  1  1  1  1  2  2  3   1   1
## 110  6  5  4  4  3  7  8   3   2
## 111  1  3  1  2  2  5  3   2   1
## 112  8  6  4  3  5  3  1   1   2
## 113 10  3  3 10  2  7  3   3   2
## 114 10 10 10  3 10  8  1   1   2
## 115  3  3  2  1  2  3  1   1   1
## 116  1  1  1  1  2  1  1   1   1
## 117  8  3  3  1  2  3  2   1   1
## 118  4  5  5 10  4  7  5   8   2
## 119  1  1  1  1  4  1  1   1   1
## 120  3  2  1  1  2  3  1   1   1
## 121  1  1  2  2  2  3  1   1   1
## 122  4  2  1  1  2  3  1   1   1
## 123 10 10 10  2 10  5  3   3   2
## 124  5  3  5  1  8  5  3   1   2
## 125  5  4  6  7  9  8 10   1   2
## 126  1  1  1  1  2  2  1   1   1
## 127  7  5  3  7  4  7  5   5   2
## 128  3  1  1  1  2  3  1   1   1
## 129  8  3  5  4  5  1  6   2   2
## 130  1  1  1  1 10  1  1   1   1
## 131  5  1  3  1  2  2  1   1   1
## 132  2  1  1  1  2  3  1   1   1
## 133  5 10  8 10  8  3  6   3   2
## 134  3  1  1  1  2  2  2   1   1
## 135  3  1  1  1  3  2  1   1   1
## 136  5  1  1  1  2  3  3   1   1
## 137  4  1  1  1  2  2  1   1   1
## 138  3  1  1  1  2  1  1   1   1
## 139  4  1  2  1  2  2  1   1   1
## 140  1  1  1  1  1  2  1   1   1
## 141  3  1  1  1  2  1  1   1   1
## 142  2  1  1  1  2  1  1   1   1
## 143  9  5  5  4  4  4  3   3   2
## 144  1  1  1  1  2  1  1   1   1
## 145  2  1  1  1  2  2  1   1   1
## 146  1  1  3  1  2  2  1   1   1
## 147  3  4  5  2  6  4  1   1   2
## 148  1  1  1  1  3  2  1   1   1
## 149  3  1  1  3  8  5  8   1   1
## 150  8  8  7  4 10  7  8   7   2
## 151  1  1  1  1  1  3  1   1   1
## 152  7  2  4  1  6  5  4   3   2
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## 606 10  5 10  3  5  7  8   3   2
## 607  4  1  1  2  2  1  1   1   1
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## 609  5 10 10 10 10 10  1   1   2
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## 622  6  3  3  3  3  6  1   1   1
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## 670  5 10 10  8  5  7 10   1   2
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## 673  2  1  1  1  2  3  1   1   1
## 674  5  3  2  1  3  1  1   1   1
## 675  1  1  1  1  2  2  1   1   1
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## 678  5  1  1  1  2  1  1   1   1
## 679  1  1  1  1  2  1  1   1   1
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## 681 10 10 10 10  5 10 10   7   2
## 682  5 10 10 10  4  5  6   3   2
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## 696  2  1  1  1  2  1  1   1   1
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## 698  4  8  6  4  3 10  6   1   2
## 699  4  8  8  5  4 10  4   1   2

Column v7 has been dropped

set.seed(123)

split = sample.split(df$V11, SplitRatio = 0.7)

training_set = subset(df, split == TRUE)

test_set = subset(df, split == FALSE)

classifier = glm(V11 ~., training_set, family = binomial)

summary(classifier)

## 
## Call:
## glm(formula = V11 ~ ., family = binomial, data = training_set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.3476  -0.1292  -0.0772   0.0302   2.2627  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -9.59512    1.16741  -8.219  < 2e-16 ***
## V2           0.47900    0.15688   3.053  0.00226 ** 
## V3           0.04879    0.18747   0.260  0.79469    
## V4           0.72113    0.22617   3.188  0.00143 ** 
## V5           0.20877    0.13195   1.582  0.11360    
## V6           0.18009    0.17400   1.035  0.30067    
## V8           0.49784    0.17388   2.863  0.00420 ** 
## V9           0.10696    0.11438   0.935  0.34973    
## V10          0.40112    0.36497   1.099  0.27175    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 631.346  on 489  degrees of freedom
## Residual deviance:  93.381  on 481  degrees of freedom
## AIC: 111.38
## 
## Number of Fisher Scoring iterations: 8

Predicting the Test set results

prob_pred = predict(classifier, type = 'response', test_set[ ,-9] )

y_pred = ifelse(prob_pred > 0.5, 1, 0)

cm = table(test_set$V11, y_pred)

cm

##    y_pred
##       0   1
##   1 133   4
##   2   7  65

Q2: Variation 2 - Run the Expt by imputing the missing values. comment on this experiment

Varaition 3 - Run the experiment after normalising the values

Above variations shall be run and commented upon once I get to research the exact meaning of the expected results

training_set[ ,1:8] = scale(training_set[ , 1:8])

test_set[ ,1:8] = scale(test_set[ , 1:8])

classifier = glm(V11 ~., training_set, family = binomial)

summary(classifier)

## 
## Call:
## glm(formula = V11 ~ ., family = binomial, data = training_set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.3476  -0.1292  -0.0772   0.0302   2.2627  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -1.1352     0.3444  -3.296 0.000982 ***
## V2            1.3243     0.4337   3.053 0.002263 ** 
## V3            0.1495     0.5747   0.260 0.794685    
## V4            2.1332     0.6690   3.188 0.001430 ** 
## V5            0.5847     0.3696   1.582 0.113603    
## V6            0.4069     0.3931   1.035 0.300669    
## V8            1.2518     0.4372   2.863 0.004196 ** 
## V9            0.3318     0.3548   0.935 0.349731    
## V10           0.6942     0.6316   1.099 0.271749    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 631.346  on 489  degrees of freedom
## Residual deviance:  93.381  on 481  degrees of freedom
## AIC: 111.38
## 
## Number of Fisher Scoring iterations: 8

Predicting the Test set results

Predicting the Test set results

prob_pred = predict(classifier, type = 'response', test_set[ ,-9] )

y_pred = ifelse(prob_pred > 0.5, 1, 0)

cm = table(test_set$V11, y_pred)

cm

##    y_pred
##       0   1
##   1 133   4
##   2   5  67

Check this - Q3: Perform scaling with “preProcess_normalized” command in caret.

Q4: Choose 2 different options of normalization and observe the output

Q5: Compute sensitivity, specificity and AUC. draw ROC curve for one of the chosen result

Q6: Compare performance with Naive Bayes

Above shall be done once I finalize on researching more on Linear regression