library("AER")
## Warning: package 'AER' was built under R version 4.2.3
## Loading required package: car
## Loading required package: carData
## Loading required package: lmtest
## Warning: package 'lmtest' was built under R version 4.2.3
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.2.3
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: sandwich
## Warning: package 'sandwich' was built under R version 4.2.3
## Loading required package: survival
library(ggplot2)

Part 1

First Data Set

data("HousePrices")
library(datasets)
HousePrices
##      price lotsize bedrooms bathrooms stories driveway recreation fullbase
## 1    42000    5850        3         1       2      yes         no      yes
## 2    38500    4000        2         1       1      yes         no       no
## 3    49500    3060        3         1       1      yes         no       no
## 4    60500    6650        3         1       2      yes        yes       no
## 5    61000    6360        2         1       1      yes         no       no
## 6    66000    4160        3         1       1      yes        yes      yes
## 7    66000    3880        3         2       2      yes         no      yes
## 8    69000    4160        3         1       3      yes         no       no
## 9    83800    4800        3         1       1      yes        yes      yes
## 10   88500    5500        3         2       4      yes        yes       no
## 11   90000    7200        3         2       1      yes         no      yes
## 12   30500    3000        2         1       1       no         no       no
## 13   27000    1700        3         1       2      yes         no       no
## 14   36000    2880        3         1       1       no         no       no
## 15   37000    3600        2         1       1      yes         no       no
## 16   37900    3185        2         1       1      yes         no       no
## 17   40500    3300        3         1       2       no         no       no
## 18   40750    5200        4         1       3      yes         no       no
## 19   45000    3450        1         1       1      yes         no       no
## 20   45000    3986        2         2       1       no        yes      yes
## 21   48500    4785        3         1       2      yes        yes      yes
## 22   65900    4510        4         2       2      yes         no      yes
## 23   37900    4000        3         1       2      yes         no       no
## 24   38000    3934        2         1       1      yes         no       no
## 25   42000    4960        2         1       1      yes         no       no
## 26   42300    3000        2         1       2      yes         no       no
## 27   43500    3800        2         1       1      yes         no       no
## 28   44000    4960        2         1       1      yes         no      yes
## 29   44500    3000        3         1       1       no         no       no
## 30   44900    4500        3         1       2      yes         no       no
## 31   45000    3500        2         1       1       no         no      yes
## 32   48000    3500        4         1       2      yes         no       no
## 33   49000    4000        2         1       1      yes         no       no
## 34   51500    4500        2         1       1      yes         no       no
## 35   61000    6360        2         1       2      yes         no       no
## 36   61000    4500        2         1       1      yes         no       no
## 37   61700    4032        2         1       1      yes         no      yes
## 38   67000    5170        3         1       4      yes         no       no
## 39   82000    5400        4         2       2      yes         no       no
## 40   54500    3150        2         2       1       no         no      yes
## 41   66500    3745        3         1       2      yes         no      yes
## 42   70000    4520        3         1       2      yes         no      yes
## 43   82000    4640        4         1       2      yes         no       no
## 44   92000    8580        5         3       2      yes         no       no
## 45   38000    2000        2         1       2      yes         no       no
## 46   44000    2160        3         1       2       no         no      yes
## 47   41000    3040        2         1       1       no         no       no
## 48   43000    3090        3         1       2       no         no       no
## 49   48000    4960        4         1       3       no         no       no
## 50   54800    3350        3         1       2      yes         no       no
## 51   55000    5300        5         2       2      yes         no       no
## 52   57000    4100        4         1       1       no         no      yes
## 53   68000    9166        2         1       1      yes         no      yes
## 54   95000    4040        3         1       2      yes         no      yes
## 55   38000    3630        3         3       2       no        yes       no
## 56   25000    3620        2         1       1      yes         no       no
## 57   25245    2400        3         1       1       no         no       no
## 58   56000    7260        3         2       1      yes        yes      yes
## 59   35500    4400        3         1       2      yes         no       no
## 60   30000    2400        3         1       2      yes         no       no
## 61   48000    4120        2         1       2      yes         no       no
## 62   48000    4750        2         1       1      yes         no       no
## 63   52000    4280        2         1       1      yes         no       no
## 64   54000    4820        3         1       2      yes         no       no
## 65   56000    5500        4         1       2      yes        yes      yes
## 66   60000    5500        3         1       2      yes         no       no
## 67   60000    5040        3         1       2      yes         no      yes
## 68   67000    6000        2         1       1      yes         no      yes
## 69   47000    2500        2         1       1       no         no       no
## 70   70000    4095        3         1       2       no        yes      yes
## 71   45000    4095        2         1       1      yes         no       no
## 72   51000    3150        3         1       2      yes         no      yes
## 73   32500    1836        2         1       1       no         no      yes
## 74   34000    2475        3         1       2      yes         no       no
## 75   35000    3210        3         1       2      yes         no      yes
## 76   36000    3180        3         1       1       no         no       no
## 77   45000    1650        3         1       2       no         no      yes
## 78   47000    3180        4         1       2      yes         no      yes
## 79   55000    3180        2         2       1      yes         no      yes
## 80   63900    6360        2         1       1      yes         no      yes
## 81   50000    4240        3         1       2      yes         no       no
## 82   35000    3240        2         1       1       no        yes       no
## 83   50000    3650        3         1       2      yes         no       no
## 84   43000    3240        3         1       2      yes         no       no
## 85   55500    3780        2         1       2      yes        yes      yes
## 86   57000    6480        3         1       2       no         no       no
## 87   60000    5850        2         1       1      yes        yes      yes
## 88   78000    3150        3         2       1      yes        yes      yes
## 89   35000    3000        2         1       1      yes         no       no
## 90   44000    3090        2         1       1      yes        yes      yes
## 91   47000    6060        3         1       1      yes        yes      yes
## 92   58000    5900        4         2       2       no         no      yes
## 93  163000    7420        4         1       2      yes        yes      yes
## 94  128000    8500        3         2       4      yes         no       no
## 95  123500    8050        3         1       1      yes        yes      yes
## 96   39000    6800        2         1       1      yes         no       no
## 97   53900    8250        3         1       1      yes         no       no
## 98   59900    8250        3         1       1      yes         no      yes
## 99   35000    3500        2         1       1      yes        yes       no
## 100  43000    2835        2         1       1      yes         no       no
## 101  57000    4500        3         2       2       no         no      yes
## 102  79000    3300        3         3       2      yes         no      yes
## 103 125000    4320        3         1       2      yes         no      yes
## 104 132000    3500        4         2       2      yes         no       no
## 105  58000    4992        3         2       2      yes         no       no
## 106  43000    4600        2         1       1      yes         no       no
## 107  48000    3720        2         1       1       no         no       no
## 108  58500    3680        3         2       2      yes         no       no
## 109  73000    3000        3         2       2      yes        yes      yes
## 110  63500    3750        2         1       1      yes        yes      yes
## 111  43000    5076        3         1       1       no         no       no
## 112  46500    4500        2         1       1       no         no       no
## 113  92000    5000        3         1       2      yes         no       no
## 114  75000    4260        4         1       2      yes         no      yes
## 115  75000    6540        4         2       2       no         no       no
## 116  85000    3700        4         1       2      yes        yes       no
## 117  93000    3760        3         1       2      yes         no       no
## 118  94500    4000        3         2       2      yes         no      yes
## 119 106500    4300        3         2       2      yes         no      yes
## 120 116000    6840        5         1       2      yes        yes      yes
## 121  61500    4400        2         1       1      yes         no       no
## 122  80000   10500        4         2       2      yes         no       no
## 123  37000    4400        2         1       1      yes         no       no
## 124  59500    4840        3         1       2      yes         no       no
## 125  70000    4120        2         1       1      yes         no      yes
## 126  95000    4260        4         2       2      yes         no       no
## 127 117000    5960        3         3       2      yes        yes      yes
## 128 122500    8800        3         2       2      yes         no       no
## 129 123500    4560        3         2       2      yes        yes      yes
## 130 127000    4600        3         2       2      yes        yes       no
## 131  35000    4840        2         1       2      yes         no       no
## 132  44500    3850        3         1       2      yes         no       no
## 133  49900    4900        3         1       2       no         no       no
## 134  50500    3850        3         1       1      yes         no       no
## 135  65000    3760        3         1       1      yes         no       no
## 136  90000    6000        4         2       4      yes         no       no
## 137  46000    4370        3         1       2      yes         no       no
## 138  35000    7700        2         1       1      yes         no       no
## 139  26500    2990        2         1       1       no         no       no
## 140  43000    3750        3         1       2      yes         no       no
## 141  56000    3000        3         1       2      yes         no       no
## 142  40000    2650        3         1       2      yes         no      yes
## 143  51000    4500        4         2       2      yes         no      yes
## 144  51000    4500        2         1       1       no         no       no
## 145  57250    4500        3         1       2       no         no      yes
## 146  44000    4500        2         1       2      yes         no       no
## 147  61000    2175        3         1       2       no        yes      yes
## 148  62000    4500        3         2       3      yes         no       no
## 149  80000    4800        5         2       3       no         no      yes
## 150  50000    4600        4         1       2      yes         no       no
## 151  59900    3450        3         1       2      yes         no       no
## 152  35500    3000        3         1       2       no         no       no
## 153  37000    3600        2         2       2      yes         no      yes
## 154  42000    3600        3         1       2       no         no       no
## 155  48000    3750        3         1       1      yes         no       no
## 156  60000    2610        4         3       2       no         no       no
## 157  60000    2953        3         1       2      yes         no      yes
## 158  60000    2747        4         2       2       no         no       no
## 159  62000    1905        5         1       2       no         no      yes
## 160  63000    3968        3         1       2       no         no       no
## 161  63900    3162        3         1       2      yes         no       no
## 162 130000    6000        4         1       2      yes         no      yes
## 163  25000    2910        3         1       1       no         no       no
## 164  50000    2135        3         2       2       no         no       no
## 165  52900    3120        3         1       2       no         no      yes
## 166  62000    4075        3         1       1      yes        yes      yes
## 167  73500    3410        3         1       2       no         no       no
## 168  38000    2800        3         1       1      yes         no       no
## 169  46000    2684        2         1       1      yes         no       no
## 170  48000    3100        3         1       2       no         no      yes
## 171  52500    3630        2         1       1      yes         no      yes
## 172  32000    1950        3         1       1       no         no       no
## 173  38000    2430        3         1       1       no         no       no
## 174  46000    4320        3         1       1       no         no       no
## 175  50000    3036        3         1       2      yes         no      yes
## 176  57500    3630        3         2       2      yes         no       no
## 177  70000    5400        4         1       2      yes         no       no
## 178  69900    3420        4         2       2      yes         no      yes
## 179  74500    3180        3         2       2      yes         no       no
## 180  42000    3660        4         1       2       no         no       no
## 181  60000    4410        2         1       1       no         no       no
## 182  50000    3990        3         1       2      yes         no       no
## 183  58000    4340        3         1       1      yes         no       no
## 184  63900    3510        3         1       2      yes         no       no
## 185  28000    3420        5         1       2       no         no       no
## 186  54000    3420        2         1       2      yes         no       no
## 187  44700    5495        3         1       1      yes         no      yes
## 188  47000    3480        4         1       2       no         no       no
## 189  50000    7424        3         1       1       no         no       no
## 190  57250    3460        4         1       2      yes         no       no
## 191  67000    3630        3         1       2      yes         no       no
## 192  52500    3630        2         1       1      yes         no       no
## 193  42000    3480        3         1       2       no         no       no
## 194  57500    3460        3         2       1      yes         no      yes
## 195  33000    3180        2         1       1      yes         no       no
## 196  34400    3635        2         1       1       no         no       no
## 197  40000    3960        3         1       1      yes         no       no
## 198  40500    4350        3         1       2       no         no       no
## 199  46500    3930        2         1       1       no         no       no
## 200  52000    3570        3         1       2      yes         no      yes
## 201  53000    3600        3         1       1      yes         no       no
## 202  53900    2520        5         2       1       no         no      yes
## 203  50000    3480        3         1       1       no         no       no
## 204  55500    3180        4         2       2      yes         no       no
## 205  56000    3290        2         1       1      yes         no       no
## 206  60000    4000        4         2       2       no         no       no
## 207  60000    2325        3         1       2       no         no       no
## 208  69500    4350        2         1       1      yes         no      yes
## 209  72000    3540        2         1       1       no        yes      yes
## 210  92500    3960        3         1       1      yes         no      yes
## 211  40500    2640        2         1       1       no         no       no
## 212  42000    2700        2         1       1       no         no       no
## 213  47900    2700        3         1       1       no         no       no
## 214  52000    3180        3         1       2       no         no      yes
## 215  62000    3500        4         1       2      yes         no       no
## 216  41000    3630        2         1       1      yes         no       no
## 217 138300    6000        4         3       2      yes        yes      yes
## 218  42000    3150        3         1       2       no         no       no
## 219  47000    3792        4         1       2      yes         no       no
## 220  64500    3510        3         1       3      yes         no       no
## 221  46000    3120        3         1       2       no         no       no
## 222  58000    3000        4         1       3      yes         no      yes
## 223  70100    4200        3         1       2      yes         no       no
## 224  78500    2817        4         2       2       no        yes      yes
## 225  87250    3240        4         1       3      yes         no       no
## 226  70800    2800        3         2       2       no         no      yes
## 227  56000    3816        2         1       1      yes         no      yes
## 228  48000    3185        2         1       1      yes         no      yes
## 229  68000    6321        3         1       2      yes         no      yes
## 230  79000    3650        3         2       2      yes         no       no
## 231  80000    4700        4         1       2      yes        yes      yes
## 232  87000    6615        4         2       2      yes        yes       no
## 233  25000    3850        3         1       2      yes         no       no
## 234  32500    3970        1         1       1       no         no       no
## 235  36000    3000        2         1       2      yes         no       no
## 236  42500    4352        4         1       2       no         no       no
## 237  43000    3630        4         1       2      yes         no       no
## 238  50000    3600        6         1       2      yes         no       no
## 239  26000    3000        2         1       1      yes         no      yes
## 240  30000    3000        4         1       2      yes         no       no
## 241  34000    2787        4         2       2      yes         no       no
## 242  52000    3000        2         1       2      yes         no       no
## 243  70000    4770        3         1       1      yes        yes      yes
## 244  27000    3649        2         1       1      yes         no       no
## 245  32500    3970        3         1       2      yes         no      yes
## 246  37200    2910        2         1       1       no         no       no
## 247  38000    3480        2         1       1      yes         no       no
## 248  42000    6615        3         1       2      yes         no       no
## 249  44500    3500        2         1       1      yes         no       no
## 250  45000    3450        3         1       2      yes         no      yes
## 251  48500    3450        3         1       1      yes         no      yes
## 252  52000    3520        2         2       1      yes         no      yes
## 253  53900    6930        4         1       2       no         no       no
## 254  60000    4600        3         2       2      yes         no       no
## 255  61000    4360        4         1       2      yes         no       no
## 256  64500    3450        3         1       2      yes         no      yes
## 257  71000    4410        4         3       2      yes         no      yes
## 258  75500    4600        2         2       1      yes         no       no
## 259  33500    3640        2         1       1      yes         no       no
## 260  41000    6000        2         1       1      yes         no       no
## 261  41000    5400        4         1       2      yes         no       no
## 262  46200    3640        4         1       2      yes         no      yes
## 263  48500    3640        2         1       1      yes         no       no
## 264  48900    4040        2         1       1      yes         no       no
## 265  50000    3640        2         1       1      yes         no       no
## 266  51000    3640        2         1       1      yes         no       no
## 267  52500    5640        2         1       1       no         no       no
## 268  52500    3600        2         1       1      yes         no       no
## 269  54000    3600        2         1       1      yes         no       no
## 270  59000    4632        4         1       2      yes         no       no
## 271  60000    3640        3         2       2      yes         no      yes
## 272  63000    4900        2         1       2      yes         no      yes
## 273  64000    4510        4         1       2      yes         no       no
## 274  64900    4100        2         2       1      yes        yes      yes
## 275  65000    3640        3         1       2      yes         no       no
## 276  66000    5680        3         1       2      yes        yes       no
## 277  70000    6300        3         1       1      yes         no       no
## 278  65500    4000        3         1       2      yes         no       no
## 279  57000    3960        3         1       2      yes         no       no
## 280  52000    5960        3         1       2      yes        yes      yes
## 281  54000    5830        2         1       1      yes         no       no
## 282  74500    4500        4         2       1       no         no      yes
## 283  90000    4100        3         2       3      yes         no       no
## 284  45000    6750        2         1       1      yes         no       no
## 285  45000    9000        3         1       2      yes         no       no
## 286  65000    2550        3         1       2      yes         no      yes
## 287  55000    7152        3         1       2      yes         no       no
## 288  62000    6450        4         1       2      yes         no       no
## 289  30000    3360        2         1       1      yes         no       no
## 290  34000    3264        2         1       1      yes         no       no
## 291  38000    4000        3         1       1      yes         no       no
## 292  39000    4000        3         1       2      yes         no       no
## 293  45000    3069        2         1       1      yes         no       no
## 294  47000    4040        2         1       1      yes         no       no
## 295  47500    4040        2         1       1      yes         no       no
## 296  49000    3185        2         1       1      yes         no       no
## 297  50000    5900        2         1       1      yes         no       no
## 298  50000    3120        3         1       2      yes         no       no
## 299  52900    5450        2         1       1      yes         no       no
## 300  53000    4040        2         1       1      yes         no       no
## 301  55000    4080        2         1       1      yes         no       no
## 302  56000    8080        3         1       1      yes         no       no
## 303  58500    4040        2         1       2      yes         no       no
## 304  59500    4080        3         1       2      yes         no       no
## 305  60000    5800        3         1       1      yes         no       no
## 306  64000    5885        2         1       1      yes         no       no
## 307  67000    9667        4         2       2      yes        yes      yes
## 308  68100    3420        4         2       2      yes         no       no
## 309  70000    5800        2         1       1      yes        yes      yes
## 310  72000    7600        4         1       2      yes         no       no
## 311  57500    5400        3         1       1      yes         no       no
## 312  69900    4995        4         2       1      yes         no      yes
## 313  70000    3000        3         1       2      yes         no      yes
## 314  75000    5500        3         2       1      yes         no      yes
## 315  76900    6450        3         2       1      yes        yes      yes
## 316  78000    6210        4         1       4      yes        yes       no
## 317  80000    5000        3         1       4      yes         no       no
## 318  82000    5000        3         1       3      yes         no       no
## 319  83000    5828        4         1       4      yes        yes       no
## 320  83000    5200        3         1       3      yes         no       no
## 321  83900    5500        3         1       3      yes        yes       no
## 322  88500    6350        3         2       3      yes        yes       no
## 323  93000    8250        3         2       3      yes         no       no
## 324  98000    6000        3         1       1      yes         no       no
## 325  98500    7700        3         2       1      yes         no       no
## 326  99000    8880        3         2       2      yes         no      yes
## 327 101000    8880        2         1       1      yes         no       no
## 328 110000    6480        3         2       4      yes         no       no
## 329 115442    7000        3         2       4      yes         no       no
## 330 120000    8875        3         1       1      yes         no       no
## 331 124000    7155        3         2       1      yes        yes      yes
## 332 175000    8960        4         4       4      yes         no       no
## 333  50000    7350        2         1       1      yes         no       no
## 334  55000    3850        2         1       1      yes         no       no
## 335  60000    7000        3         1       1      yes         no       no
## 336  61000    7770        2         1       1      yes         no       no
## 337 106000    7440        3         2       1      yes        yes      yes
## 338 155000    7500        3         3       1      yes         no      yes
## 339 141000    8100        4         1       2      yes        yes      yes
## 340  62500    3900        3         1       2      yes         no       no
## 341  70000    2970        3         1       3      yes         no       no
## 342  73000    3000        3         1       2      yes         no      yes
## 343  80000   10500        2         1       1      yes         no       no
## 344  80000    5500        3         2       2      yes         no       no
## 345  88000    4500        3         1       4      yes         no       no
## 346  49000    3850        3         1       1      yes         no       no
## 347  52000    4130        3         2       2      yes         no       no
## 348  59500    4046        3         1       2      yes         no      yes
## 349  60000    4079        3         1       3      yes         no       no
## 350  64000    4000        3         1       2      yes         no       no
## 351  64500    9860        3         1       1      yes         no       no
## 352  68500    7000        3         1       2      yes         no      yes
## 353  78500    7980        3         1       1      yes         no       no
## 354  86000    6800        2         1       1      yes        yes      yes
## 355  86900    4300        6         2       2      yes         no       no
## 356  75000   10269        3         1       1      yes         no       no
## 357  78000    6100        3         1       3      yes        yes       no
## 358  95000    6420        3         2       3      yes         no       no
## 359  97000   12090        4         2       2      yes         no       no
## 360 107000    6600        3         1       4      yes         no       no
## 361 130000    6600        4         2       2      yes        yes      yes
## 362 145000    8580        4         3       4      yes         no       no
## 363 175000    9960        3         2       2      yes         no      yes
## 364  72000   10700        3         1       2      yes        yes      yes
## 365  84900   15600        3         1       1      yes         no       no
## 366  99000   13200        2         1       1      yes         no      yes
## 367 114000    9000        4         2       4      yes         no       no
## 368 120000    7950        5         2       2      yes         no      yes
## 369 145000   16200        5         3       2      yes         no       no
## 370  79000    6100        3         2       1      yes         no      yes
## 371  82000    6360        3         1       1      yes        yes      yes
## 372  85000    6420        3         1       1      yes         no      yes
## 373 100500    6360        4         2       3      yes         no       no
## 374 122000    6540        4         2       2      yes        yes      yes
## 375 126500    6420        3         2       2      yes         no       no
## 376 133000    6550        4         2       2      yes         no       no
## 377 140000    5750        3         2       4      yes        yes       no
## 378 190000    7420        4         2       3      yes         no       no
## 379  84000    7160        3         1       1      yes         no      yes
## 380  97000    4000        3         2       2      yes         no      yes
## 381 103500    9000        4         2       4      yes        yes       no
## 382 112500    6550        3         1       2      yes         no      yes
## 383 140000   13200        3         1       2      yes         no      yes
## 384  74700    7085        3         1       1      yes        yes      yes
## 385  78000    6600        4         2       2      yes        yes      yes
## 386  78900    6900        3         1       1      yes        yes      yes
## 387  83900   11460        3         1       3      yes         no       no
## 388  85000    7020        3         1       1      yes         no      yes
## 389  85000    6540        3         1       1      yes        yes      yes
## 390  86000    8000        3         1       1      yes        yes      yes
## 391  86900    9620        3         1       1      yes         no      yes
## 392  94500   10500        3         2       1      yes         no      yes
## 393  96000    5020        3         1       4      yes         no       no
## 394 106000    7440        3         2       4      yes         no       no
## 395  72000    6600        3         1       1      yes        yes      yes
## 396  74500    7200        3         1       2      yes        yes      yes
## 397  77000    6710        3         2       2      yes        yes      yes
## 398  80750    6660        4         2       2      yes        yes      yes
## 399  82900    7000        3         1       1      yes         no      yes
## 400  85000    7231        3         1       2      yes        yes      yes
## 401  92500    7410        3         1       1      yes        yes      yes
## 402  76000    7800        3         1       1      yes         no      yes
## 403  77500    6825        3         1       1      yes        yes      yes
## 404  80000    6360        3         1       3      yes         no       no
## 405  80000    6600        4         2       1      yes         no      yes
## 406  86000    6900        3         2       1      yes        yes      yes
## 407  87000    6600        3         1       1      yes        yes      yes
## 408  87500    6420        3         1       3      yes         no      yes
## 409  89000    6600        3         2       1      yes         no      yes
## 410  89900    6600        3         2       3      yes         no       no
## 411  90000    9000        3         1       1      yes         no      yes
## 412  95000    6500        3         2       3      yes         no       no
## 413 112000    6360        3         2       4      yes         no       no
## 414  31900    5300        3         1       1       no         no       no
## 415  52000    2850        3         2       2       no         no      yes
## 416  90000    6400        3         1       1      yes        yes      yes
## 417 100000   11175        3         1       1      yes         no      yes
## 418  91700    6750        2         1       1      yes        yes      yes
## 419 174500    7500        4         2       2      yes         no      yes
## 420  94700    6000        3         1       2      yes         no       no
## 421  68000   10240        2         1       1      yes         no       no
## 422  80000    5136        3         1       2      yes        yes      yes
## 423  61100    3400        3         1       2      yes         no      yes
## 424  62900    2880        3         1       2      yes         no       no
## 425  65500    3840        3         1       2      yes         no       no
## 426  66000    2870        2         1       2      yes        yes      yes
## 427  49500    5320        2         1       1      yes         no       no
## 428  50000    3512        2         1       1      yes         no       no
## 429  53500    3480        2         1       1      yes         no       no
## 430  58550    3600        3         1       1      yes         no      yes
## 431  64500    3520        2         1       2      yes         no       no
## 432  65000    5320        3         1       2      yes        yes      yes
## 433  69000    6040        3         1       1      yes         no       no
## 434  73000   11410        2         1       2      yes         no       no
## 435  75000    8400        3         1       2      yes        yes      yes
## 436  75000    5300        4         2       1      yes         no       no
## 437 132000    7800        3         2       2      yes         no       no
## 438  60000    3520        3         1       2      yes         no       no
## 439  65000    5360        3         1       2      yes         no       no
## 440  69000    6862        3         1       2      yes         no       no
## 441  51900    3520        3         1       1      yes         no       no
## 442  57000    4050        2         1       2      yes        yes      yes
## 443  65000    3520        3         1       1      yes         no       no
## 444  79500    4400        4         1       2      yes         no       no
## 445  72500    5720        2         1       2      yes         no       no
## 446 104900   11440        4         1       2      yes         no      yes
## 447 114900    7482        3         2       3      yes         no       no
## 448 120000    5500        4         2       2      yes         no      yes
## 449  58000    4320        3         1       2      yes         no       no
## 450  67000    5400        2         1       2      yes         no       no
## 451  67000    4320        3         1       1      yes         no       no
## 452  69000    4815        2         1       1      yes         no       no
## 453  73000    6100        3         1       1      yes         no      yes
## 454  73500    7980        3         1       1      yes         no       no
## 455  74900    6050        3         1       1      yes         no      yes
## 456  75000    3800        3         1       2      yes        yes      yes
## 457  79500    5400        5         1       2      yes        yes      yes
## 458 120900    6000        3         2       4      yes        yes      yes
## 459  44555    2398        3         1       1      yes         no       no
## 460  47000    2145        3         1       2      yes         no      yes
## 461  47600    2145        3         1       2      yes         no      yes
## 462  49000    2145        3         1       3      yes         no       no
## 463  49000    2610        3         1       2      yes         no      yes
## 464  49000    1950        3         2       2      yes         no      yes
## 465  49500    2145        3         1       3      yes         no       no
## 466  52000    2275        3         1       3      yes         no       no
## 467  54000    2856        3         1       3      yes         no       no
## 468  55000    2015        3         1       2      yes         no      yes
## 469  55000    2176        2         1       2      yes        yes       no
## 470  56000    2145        4         2       1      yes         no      yes
## 471  60000    2145        3         1       3      yes         no       no
## 472  60500    2787        3         1       1      yes         no      yes
## 473  50000    9500        3         1       2      yes         no       no
## 474  64900    4990        4         2       2      yes        yes      yes
## 475  93000    6670        3         1       3      yes         no      yes
## 476  85000    6254        4         2       1      yes         no      yes
## 477  61500   10360        2         1       1      yes         no       no
## 478  88500    5500        3         2       1      yes        yes      yes
## 479  88000    5450        4         2       1      yes         no      yes
## 480  89000    5500        3         1       3      yes         no       no
## 481  89500    6000        4         1       3      yes        yes      yes
## 482  95000    5700        3         1       1      yes        yes      yes
## 483  95500    6600        2         2       4      yes         no      yes
## 484  51500    4000        2         1       1      yes         no       no
## 485  62900    4880        3         1       1      yes         no       no
## 486 118500    4880        4         2       2      yes         no       no
## 487  42900    8050        2         1       1      yes         no       no
## 488  44100    8100        2         1       1      yes         no       no
## 489  47000    5880        3         1       1      yes         no       no
## 490  50000    5880        2         1       1      yes         no       no
## 491  50000   12944        3         1       1      yes         no       no
## 492  53000    6020        3         1       1      yes         no       no
## 493  53000    4050        2         1       1      yes         no       no
## 494  54000    8400        2         1       1      yes         no       no
## 495  58500    5600        2         1       1      yes         no       no
## 496  59000    5985        3         1       1      yes         no      yes
## 497  60000    4500        3         1       1      yes         no      yes
## 498  62900    4920        3         1       2      yes         no       no
## 499  64000    8250        3         1       1      yes         no       no
## 500  65000    8400        4         1       4      yes         no       no
## 501  67900    6440        2         1       1      yes         no       no
## 502  68500    8100        4         1       4      yes         no      yes
## 503  70000    6720        3         1       1      yes         no       no
## 504  70500    5948        3         1       2      yes         no       no
## 505  71500    8150        3         2       1      yes        yes      yes
## 506  71900    4800        2         1       1      yes        yes      yes
## 507  75000    9800        4         2       2      yes        yes       no
## 508  75000    8520        3         1       1      yes         no       no
## 509  87000    8372        3         1       3      yes         no       no
## 510  64000    4040        3         1       2      yes         no       no
## 511  70000    4646        3         1       2      yes        yes      yes
## 512  47500    4775        4         1       2      yes         no       no
## 513  62600    4950        4         1       2      yes         no       no
## 514  66000    5010        3         1       2      yes         no      yes
## 515  58900    6060        2         1       1      yes         no      yes
## 516  53000    3584        2         1       1      yes         no       no
## 517  95000    6000        3         2       3      yes        yes       no
## 518  96500    6000        4         2       4      yes         no       no
## 519 101000    6240        4         2       2      yes         no       no
## 520 102000    6000        3         2       2      yes        yes       no
## 521 103000    7680        4         2       4      yes        yes       no
## 522 105000    6000        4         2       4      yes        yes       no
## 523 108000    6000        4         2       4      yes         no       no
## 524 110000    6000        4         2       4      yes         no       no
## 525 113000    6000        4         2       4      yes         no       no
## 526 120000    7475        3         2       4      yes         no       no
## 527 105000    5150        3         2       4      yes         no       no
## 528 106000    6325        3         1       4      yes         no       no
## 529 107500    6000        3         2       4      yes         no       no
## 530 108000    6000        3         2       3      yes         no       no
## 531 113750    6000        3         1       4      yes        yes       no
## 532 120000    7000        3         1       4      yes         no       no
## 533  70000   12900        3         1       1      yes         no       no
## 534  71000    7686        3         1       1      yes        yes      yes
## 535  82000    5000        3         1       3      yes         no       no
## 536  82000    5800        3         2       4      yes         no       no
## 537  82500    6000        3         2       4      yes         no       no
## 538  83000    4800        3         1       3      yes         no       no
## 539  84000    6500        3         2       3      yes         no       no
## 540  85000    7320        4         2       2      yes         no       no
## 541  85000    6525        3         2       4      yes         no       no
## 542  91500    4800        3         2       4      yes        yes       no
## 543  94000    6000        3         2       4      yes         no       no
## 544 103000    6000        3         2       4      yes        yes       no
## 545 105000    6000        3         2       2      yes        yes       no
## 546 105000    6000        3         1       2      yes         no       no
##     gasheat aircon garage prefer
## 1        no     no      1     no
## 2        no     no      0     no
## 3        no     no      0     no
## 4        no     no      0     no
## 5        no     no      0     no
## 6        no    yes      0     no
## 7        no     no      2     no
## 8        no     no      0     no
## 9        no     no      0     no
## 10       no    yes      1     no
## 11       no    yes      3     no
## 12       no     no      0     no
## 13       no     no      0     no
## 14       no     no      0     no
## 15       no     no      0     no
## 16       no    yes      0     no
## 17       no     no      1     no
## 18       no     no      0     no
## 19       no     no      0     no
## 20       no     no      1     no
## 21       no    yes      1     no
## 22       no     no      0     no
## 23       no    yes      0     no
## 24       no     no      0     no
## 25       no     no      0     no
## 26       no     no      0     no
## 27       no     no      0     no
## 28       no    yes      0     no
## 29       no    yes      0     no
## 30       no    yes      0     no
## 31       no     no      0     no
## 32       no    yes      2     no
## 33       no     no      0     no
## 34       no     no      0     no
## 35       no     no      0     no
## 36       no    yes      2     no
## 37       no     no      0     no
## 38       no    yes      0     no
## 39       no    yes      2     no
## 40       no     no      0     no
## 41       no     no      0     no
## 42       no    yes      0     no
## 43       no     no      1     no
## 44       no     no      2     no
## 45       no     no      0     no
## 46       no     no      0     no
## 47       no     no      0     no
## 48       no     no      0     no
## 49       no     no      0     no
## 50       no     no      0     no
## 51       no     no      0     no
## 52       no     no      0     no
## 53       no    yes      2     no
## 54      yes     no      1     no
## 55       no     no      0     no
## 56       no     no      0     no
## 57       no     no      0     no
## 58       no     no      3     no
## 59       no     no      0     no
## 60       no     no      0     no
## 61       no     no      0     no
## 62       no     no      0     no
## 63       no    yes      2     no
## 64       no     no      0     no
## 65       no     no      0     no
## 66       no    yes      0     no
## 67       no    yes      0     no
## 68       no    yes      1     no
## 69       no    yes      0     no
## 70       no    yes      0     no
## 71       no     no      2     no
## 72       no     no      0     no
## 73       no     no      0     no
## 74       no     no      0     no
## 75       no     no      0     no
## 76       no     no      0     no
## 77       no     no      0     no
## 78       no    yes      0     no
## 79       no     no      2     no
## 80       no    yes      1     no
## 81       no    yes      0     no
## 82       no     no      1     no
## 83       no     no      0     no
## 84       no     no      2     no
## 85       no     no      0     no
## 86       no    yes      1     no
## 87       no     no      2     no
## 88       no    yes      0     no
## 89       no     no      1     no
## 90       no     no      0     no
## 91       no     no      0     no
## 92       no     no      1     no
## 93       no    yes      2     no
## 94       no    yes      2     no
## 95       no    yes      1     no
## 96       no     no      0     no
## 97       no     no      2     no
## 98       no     no      3     no
## 99       no     no      0     no
## 100      no     no      0     no
## 101      no    yes      0     no
## 102      no     no      0     no
## 103     yes     no      2     no
## 104     yes     no      2     no
## 105      no     no      2     no
## 106      no     no      0     no
## 107      no    yes      0     no
## 108      no     no      0     no
## 109      no     no      0     no
## 110      no     no      0     no
## 111      no     no      0     no
## 112      no     no      0     no
## 113      no    yes      0     no
## 114      no    yes      0     no
## 115      no    yes      0     no
## 116      no    yes      0     no
## 117     yes     no      2     no
## 118      no    yes      1     no
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## 120      no    yes      1     no
## 121      no     no      1     no
## 122      no     no      1     no
## 123      no     no      0     no
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## 126     yes     no      0     no
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## 129      no    yes      1     no
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## 131      no     no      0     no
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## 144      no     no      0     no
## 145      no    yes      0     no
## 146     yes     no      1     no
## 147      no    yes      0     no
## 148     yes     no      1     no
## 149     yes     no      0     no
## 150      no     no      0     no
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## 152      no     no      0     no
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## 155      no     no      0     no
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## 157      no    yes      0     no
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## 163      no     no      0     no
## 164      no     no      0     no
## 165     yes     no      0     no
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## 167      no    yes      0     no
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## 170      no     no      0     no
## 171      no     no      0     no
## 172     yes     no      0     no
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## 192      no    yes      0     no
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## 194      no    yes      1     no
## 195      no     no      0     no
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## 212      no     no      0     no
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## 214      no     no      0     no
## 215      no     no      2     no
## 216      no     no      0     no
## 217     yes     no      2     no
## 218      no     no      0     no
## 219      no     no      0     no
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## 221      no     no      0     no
## 222      no    yes      2     no
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## 229      no    yes      1     no
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## 231      no    yes      1     no
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## 235      no     no      0     no
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## 238      no     no      1     no
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## 240      no     no      0     no
## 241      no     no      0     no
## 242      no    yes      0     no
## 243      no     no      0     no
## 244      no     no      0     no
## 245      no     no      0     no
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## 250      no     no      0     no
## 251      no     no      2     no
## 252      no     no      0     no
## 253      no     no      1     no
## 254      no    yes      1     no
## 255      no     no      0     no
## 256      no     no      1     no
## 257      no     no      2     no
## 258      no    yes      2     no
## 259      no     no      0     no
## 260      no     no      0     no
## 261      no     no      0     no
## 262      no     no      0     no
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## 266      no     no      0     no
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## 269      no     no      0     no
## 270      no    yes      0     no
## 271      no     no      0     no
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## 274      no     no      0     no
## 275      no    yes      0     no
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## 279      no     no      0     no
## 280      no     no      0     no
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## 282      no    yes      2     no
## 283      no    yes      2     no
## 284      no     no      0     no
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## 286      no     no      0     no
## 287      no    yes      0     no
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## 289      no     no      1     no
## 290      no     no      0     no
## 291      no     no      0     no
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## 298      no     no      1     no
## 299      no     no      0     no
## 300      no     no      0     no
## 301      no     no      0     no
## 302      no    yes      2     no
## 303      no     no      1     no
## 304      no     no      2     no
## 305     yes     no      2     no
## 306      no    yes      1     no
## 307      no     no      1     no
## 308      no     no      0     no
## 309      no    yes      0     no
## 310      no    yes      2     no
## 311      no     no      3     no
## 312      no     no      0     no
## 313      no    yes      0     no
## 314      no     no      0     no
## 315     yes     no      0     no
## 316      no    yes      0     no
## 317      no     no      0     no
## 318      no    yes      0     no
## 319      no     no      0     no
## 320      no    yes      0     no
## 321      no    yes      1     no
## 322      no    yes      0     no
## 323      no    yes      0     no
## 324      no    yes      1     no
## 325      no     no      2     no
## 326      no    yes      1     no
## 327      no    yes      1     no
## 328      no    yes      2     no
## 329      no    yes      2     no
## 330      no     no      1     no
## 331      no    yes      2     no
## 332      no    yes      3     no
## 333      no     no      1     no
## 334      no     no      0     no
## 335      no     no      3     no
## 336      no     no      1     no
## 337      no    yes      0    yes
## 338      no    yes      2    yes
## 339      no    yes      2    yes
## 340      no     no      0     no
## 341      no     no      0     no
## 342      no     no      0     no
## 343      no     no      1     no
## 344      no     no      1     no
## 345      no    yes      0     no
## 346      no     no      0     no
## 347      no     no      2     no
## 348      no     no      1     no
## 349      no     no      0     no
## 350      no     no      2     no
## 351      no     no      0     no
## 352      no     no      0     no
## 353      no     no      2     no
## 354      no     no      2     no
## 355      no     no      0     no
## 356      no     no      1    yes
## 357      no    yes      0    yes
## 358      no    yes      0    yes
## 359      no     no      2    yes
## 360      no    yes      3    yes
## 361      no    yes      1    yes
## 362      no    yes      2    yes
## 363      no     no      2    yes
## 364      no     no      0     no
## 365      no    yes      2     no
## 366     yes     no      1     no
## 367      no    yes      2     no
## 368     yes     no      2     no
## 369      no     no      0     no
## 370      no     no      2    yes
## 371      no    yes      2    yes
## 372      no    yes      0    yes
## 373      no    yes      2    yes
## 374      no    yes      2    yes
## 375      no    yes      1    yes
## 376      no    yes      1    yes
## 377      no    yes      1    yes
## 378      no    yes      2    yes
## 379      no     no      2    yes
## 380      no    yes      0    yes
## 381      no    yes      1    yes
## 382      no    yes      0    yes
## 383      no    yes      2    yes
## 384      no     no      2    yes
## 385      no     no      0    yes
## 386      no     no      0    yes
## 387      no     no      2    yes
## 388      no    yes      2    yes
## 389      no     no      2    yes
## 390      no    yes      2    yes
## 391      no     no      2    yes
## 392      no    yes      1    yes
## 393      no    yes      0    yes
## 394      no     no      1    yes
## 395      no     no      0    yes
## 396      no     no      1    yes
## 397      no     no      1    yes
## 398      no     no      1    yes
## 399      no     no      2    yes
## 400      no    yes      0    yes
## 401      no    yes      2    yes
## 402      no    yes      2    yes
## 403      no    yes      0    yes
## 404      no     no      0    yes
## 405      no     no      0    yes
## 406      no     no      0    yes
## 407      no     no      2    yes
## 408      no     no      0    yes
## 409      no    yes      0    yes
## 410      no    yes      0    yes
## 411      no     no      1    yes
## 412      no    yes      0    yes
## 413      no    yes      0    yes
## 414      no    yes      0    yes
## 415      no     no      0    yes
## 416      no    yes      1    yes
## 417      no    yes      1    yes
## 418      no     no      2    yes
## 419      no    yes      3    yes
## 420     yes     no      1    yes
## 421      no    yes      2    yes
## 422      no    yes      0    yes
## 423      no     no      2    yes
## 424      no     no      0    yes
## 425      no     no      1    yes
## 426      no     no      0    yes
## 427      no     no      1    yes
## 428      no     no      1    yes
## 429      no     no      0    yes
## 430      no    yes      0    yes
## 431      no     no      0    yes
## 432      no     no      0    yes
## 433      no     no      2    yes
## 434      no     no      0    yes
## 435      no    yes      2    yes
## 436      no    yes      0    yes
## 437      no     no      0    yes
## 438      no     no      0    yes
## 439      no     no      2    yes
## 440      no    yes      2    yes
## 441      no     no      2    yes
## 442      no     no      0    yes
## 443      no     no      0    yes
## 444      no    yes      2    yes
## 445      no    yes      0    yes
## 446      no     no      1    yes
## 447     yes     no      1    yes
## 448      no    yes      1    yes
## 449      no     no      2    yes
## 450      no     no      0    yes
## 451      no     no      0    yes
## 452      no    yes      0    yes
## 453      no    yes      0    yes
## 454      no     no      1    yes
## 455      no     no      0    yes
## 456      no     no      1    yes
## 457      no    yes      0    yes
## 458      no    yes      0    yes
## 459      no     no      0    yes
## 460      no     no      0    yes
## 461      no     no      0    yes
## 462      no     no      0    yes
## 463      no     no      0    yes
## 464      no     no      0    yes
## 465      no     no      0    yes
## 466     yes    yes      0    yes
## 467      no     no      0    yes
## 468      no     no      0    yes
## 469      no     no      0    yes
## 470      no     no      0    yes
## 471      no     no      1    yes
## 472      no     no      0    yes
## 473      no     no      3    yes
## 474      no     no      0    yes
## 475      no     no      0    yes
## 476      no     no      1    yes
## 477      no     no      1    yes
## 478      no     no      2    yes
## 479      no    yes      0    yes
## 480      no     no      1    yes
## 481      no     no      0    yes
## 482      no    yes      2    yes
## 483      no     no      0    yes
## 484      no     no      0    yes
## 485      no     no      2    yes
## 486      no    yes      1    yes
## 487      no     no      0     no
## 488      no     no      1     no
## 489      no     no      1     no
## 490      no     no      0     no
## 491      no     no      0     no
## 492      no     no      0     no
## 493      no     no      0     no
## 494      no     no      1     no
## 495      no    yes      0     no
## 496      no     no      0     no
## 497      no     no      0     no
## 498      no     no      1     no
## 499      no     no      0     no
## 500      no     no      3     no
## 501      no    yes      3     no
## 502      no    yes      2     no
## 503      no     no      0     no
## 504      no    yes      0     no
## 505      no     no      0     no
## 506      no     no      0     no
## 507      no     no      2     no
## 508      no    yes      2     no
## 509      no    yes      2     no
## 510      no     no      1     no
## 511      no     no      2     no
## 512      no     no      0     no
## 513      no    yes      0     no
## 514      no     no      0     no
## 515      no     no      1     no
## 516     yes     no      0     no
## 517      no    yes      0     no
## 518      no    yes      0     no
## 519      no    yes      1     no
## 520      no     no      1     no
## 521      no    yes      1     no
## 522      no    yes      1     no
## 523      no    yes      1     no
## 524      no     no      2     no
## 525      no    yes      1     no
## 526      no    yes      2     no
## 527      no    yes      2     no
## 528      no    yes      1     no
## 529      no    yes      1     no
## 530      no    yes      0     no
## 531      no    yes      2     no
## 532      no    yes      2     no
## 533      no     no      2     no
## 534     yes     no      0     no
## 535      no    yes      0     no
## 536      no    yes      0     no
## 537      no    yes      0     no
## 538      no    yes      0     no
## 539      no    yes      0     no
## 540      no     no      0     no
## 541      no     no      1     no
## 542      no    yes      0     no
## 543      no    yes      0     no
## 544      no    yes      1     no
## 545      no    yes      1     no
## 546      no    yes      1     no

Second Data Set

data("CigarettesSW")
CigarettesSW
##    state year   cpi population     packs    income      tax     price      taxs
## 1     AL 1985 1.076    3973000 116.48628  46014968 32.50000 102.18167  33.34834
## 2     AR 1985 1.076    2327000 128.53459  26210736 37.00000 101.47500  37.00000
## 3     AZ 1985 1.076    3184000 104.52261  43956936 31.00000 108.57875  36.17042
## 4     CA 1985 1.076   26444000 100.36304 447102816 26.00000 107.83734  32.10400
## 5     CO 1985 1.076    3209000 112.96354  49466672 31.00000  94.26666  31.00000
## 6     CT 1985 1.076    3201000 109.27835  60063368 42.00000 128.02499  51.48333
## 7     DE 1985 1.076     618000 143.85114   9927301 30.00000 102.49166  30.00000
## 8     FL 1985 1.076   11352000 122.18112 166919248 37.00000 115.29000  42.49000
## 9     GA 1985 1.076    5963000 127.23462  78364336 28.00000  97.02517  28.84183
## 10    IA 1985 1.076    2830000 113.74558  37902896 34.00000 101.84200  37.91700
## 11    ID 1985 1.076     994000 103.01811  11577261 25.10000 102.89933  29.05767
## 12    IL 1985 1.076   11401000 123.20848 176786352 28.00001 104.44025  28.91526
## 13    IN 1985 1.076    5460000 137.63737  71751616 26.50000  96.18000  31.08000
## 14    KS 1985 1.076    2428000 116.68040  34784360 32.00000  98.92291  34.88125
## 15    KY 1985 1.076    3695000 186.03519  42703144 19.00000  87.00125  23.14292
## 16    LA 1985 1.076    4409000 127.55727  53431900 32.00000 108.39400  36.16900
## 17    MA 1985 1.076    5881000 115.67760  98328688 42.00000 112.20834  42.00000
## 18    MD 1985 1.076    4414000 120.97871  74851664 29.00000  91.96667  29.00000
## 19    ME 1985 1.076    1163000 128.11694  14575292 36.00000 107.04750  41.09750
## 20    MI 1985 1.076    9077000 128.00485 133728040 37.00000 104.91417  37.83083
## 21    MN 1985 1.076    4185000 112.90323  63152360 34.00000 113.64967  40.43300
## 22    MO 1985 1.076    5001000 130.37393  69341920 29.00000  99.33817  29.85484
## 23    MS 1985 1.076    2588000 117.04018  25678534 27.58333 105.29333  33.54333
## 24    MT 1985 1.076     822000 104.25790   9785230 32.00000  99.29166  32.00000
## 25    NC 1985 1.076    6255000 155.28377  79104656 18.00000  84.96799  21.26800
## 26    ND 1985 1.076     677000 105.46529   8672948 34.00000 106.80800  38.10800
## 27    NE 1985 1.076    1585000 107.38171  21778072 34.00000 104.60667  38.02333
## 28    NH 1985 1.076     997000 197.99399  15767469 33.00000  95.50000  33.00000
## 29    NJ 1985 1.076    7566000 116.52128 133549208 41.00000 110.41666  41.00000
## 30    NM 1985 1.076    1439000  88.74218  17258916 28.00000 102.77800  31.95300
## 31    NV 1985 1.076     951000 141.95584  14581495 31.00000 114.18850  37.46350
## 32    NY 1985 1.076   17794000 116.66292 297728512 37.00000 109.99783  37.88117
## 33    OH 1985 1.076   10736000 127.59874 153455776 30.00000 100.42374  34.78208
## 34    OK 1985 1.076    3272000 127.13937  43395580 34.00000 101.46808  34.82642
## 35    OR 1985 1.076    2673000 119.45380  36205164 35.00000  97.03333  35.00000
## 36    PA 1985 1.076   11772000 117.70303 170033840 34.00000 109.07401  40.17400
## 37    RI 1985 1.076     967000 132.78178  14229156 39.00000 100.94167  39.00000
## 38    SC 1985 1.076    3304000 127.20944  38536176 23.00000  90.64125  27.31625
## 39    SD 1985 1.076     698000 106.59026   8340000 31.00000  97.08334  31.00000
## 40    TN 1985 1.076    4716000 129.83459  57749668 29.00000 101.94550  34.77050
## 41    TX 1985 1.076   16275000 115.10293 231003152 35.25000 107.38000  39.38000
## 42    UT 1985 1.076    1643000  68.04626  19462380 28.00000 110.19584  34.23750
## 43    VA 1985 1.076    5716000 134.00980  87361632 18.50000  91.61533  22.02367
## 44    VT 1985 1.076     530000 145.28302   6887097 33.00000 100.98334  33.00000
## 45    WA 1985 1.076    4401000  96.22813  64846548 39.00000 129.46109  47.46942
## 46    WI 1985 1.076    4748000 107.87700  65732720 41.00000 114.59000  46.45667
## 47    WV 1985 1.076    1907000 112.84740  20852964 33.00000 108.91125  38.18625
## 48    WY 1985 1.076     500000 129.39999   7116756 24.00000  93.46667  24.00000
## 49    AL 1995 1.524    4262731 101.08543  83903280 40.50000 158.37134  41.90467
## 50    AR 1995 1.524    2480121 111.04297  45995496 55.50000 175.54251  63.85917
## 51    AZ 1995 1.524    4306908  71.95417  88870496 65.33333 198.60750  74.79082
## 52    CA 1995 1.524   31493524  56.85931 771470144 61.00000 210.50467  74.77133
## 53    CO 1995 1.524    3738061  82.58292  92946544 44.00000 167.35001  44.00000
## 54    CT 1995 1.524    3265293  79.47219 104315120 74.00000 218.28050  86.35550
## 55    DE 1995 1.524     718265 124.46660  18237436 48.00000 165.60001  48.00000
## 56    FL 1995 1.524   14185403  93.07455 333525344 57.90000 187.71718  68.52551
## 57    GA 1995 1.524    7188538  97.47462 159800448 36.00000 156.57307  37.43142
## 58    IA 1995 1.524    2840860  92.40160  60170928 60.00000 190.89000  69.09000
## 59    ID 1995 1.524    1165000  74.84978  22868920 52.00000 179.63751  60.55417
## 60    IL 1995 1.524   11884935  83.26508 304767456 68.00001 198.47617  79.23450
## 61    IN 1995 1.524    5791819 134.25835 126525008 39.50000 154.53375  46.85875
## 62    KS 1995 1.524    2586942  88.75344  56626672 48.00000 175.21001  56.34333
## 63    KY 1995 1.524    3855248 172.64778  74079712 27.00000 145.97968  35.26300
## 64    LA 1995 1.524    4327978 105.17613  84572688 44.00000 167.79535  50.45367
## 65    MA 1995 1.524    6062335  76.62064 170051568 75.00000 217.10501  85.33833
## 66    MD 1995 1.524    5023650  77.47355 135115456 60.00000 186.03375  68.85875
## 67    ME 1995 1.524    1237438 102.46978  25045934 61.00000 197.23065  72.16400
## 68    MI 1995 1.524    9659871  81.38825 231594240 99.00000 240.84967 112.63300
## 69    MN 1995 1.524    4605445  82.94530 113216856 72.00000 220.34866  86.41534
## 70    MO 1995 1.524    5324610 122.45028 117639672 41.00000 157.23009  42.38842
## 71    MS 1995 1.524    2690788 105.58245  46241956 42.00000 169.22940  53.07108
## 72    MT 1995 1.524     868522  87.15957  16296835 42.00000 156.21667  42.00000
## 73    NC 1995 1.524    7185403 121.53806 157633568 29.00000 149.99400  34.76900
## 74    ND 1995 1.524     641548  79.80697  12243384 68.00000 192.24867  78.88200
## 75    NE 1995 1.524    1635142  87.27071  36293064 58.00000 182.17500  66.67500
## 76    NH 1995 1.524    1145604 156.33675  28649564 49.00000 166.64166  49.00000
## 77    NJ 1995 1.524    7965523  80.37137 233208576 64.00000 203.08717  75.49550
## 78    NM 1995 1.524    1682417  64.66887  31716160 45.00000 176.14624  53.38792
## 79    NV 1995 1.524    1525777  93.52612  39377292 59.00000 206.59917  72.51583
## 80    NY 1995 1.524   18150928  70.81732 503163328 80.00000 221.85800  88.53300
## 81    OH 1995 1.524   11155493 111.38010 255312928 48.00000 165.89125  55.89958
## 82    OK 1995 1.524    3265547 108.68011  63333300 47.00000 170.13499  55.10167
## 83    OR 1995 1.524    3141421  92.15575  71209312 62.00000 190.30000  62.00000
## 84    PA 1995 1.524   12044780  95.64309 285923232 55.00000 176.16316  64.97150
## 85    RI 1995 1.524     989203  92.59980  23786644 80.00000 224.45924  94.68425
## 86    SC 1995 1.524    3699943 108.08275  72050072 31.00000 152.81874  38.27708
## 87    SD 1995 1.524     728251  97.21923  14454129 47.00000 168.03799  53.46300
## 88    TN 1995 1.524    5241168 122.32005 114259984 37.00000 167.06700  49.37533
## 89    TX 1995 1.524   18679706  73.07931 402096768 65.00000 198.20233  76.21900
## 90    UT 1995 1.524    1976774  49.27220  37278220 50.50000 180.97626  59.11792
## 91    VA 1995 1.524    6601392 105.38687 161441792 26.50001 166.66125  34.43626
## 92    VT 1995 1.524     582827 122.33475  12448607 44.00000 175.63875  52.36375
## 93    WA 1995 1.524    5431024  65.53092 129680832 80.50000 239.10934  96.14267
## 94    WI 1995 1.524    5137004  92.46635 115959680 62.00000 201.38126  71.58958
## 95    WV 1995 1.524    1820560 115.56883  32611268 41.00000 166.51718  50.42550
## 96    WY 1995 1.524     478447 112.23814  10293195 36.00000 158.54166  36.00000

Descriptions for Data sets

1.HousePrices:

  • Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987. A data fame containing 546 observations on 12 variables. We can see, based on the graph and table below, that this data set is cross sectional.
str(HousePrices)
## 'data.frame':    546 obs. of  12 variables:
##  $ price     : num  42000 38500 49500 60500 61000 66000 66000 69000 83800 88500 ...
##  $ lotsize   : num  5850 4000 3060 6650 6360 4160 3880 4160 4800 5500 ...
##  $ bedrooms  : num  3 2 3 3 2 3 3 3 3 3 ...
##  $ bathrooms : num  1 1 1 1 1 1 2 1 1 2 ...
##  $ stories   : num  2 1 1 2 1 1 2 3 1 4 ...
##  $ driveway  : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
##  $ recreation: Factor w/ 2 levels "no","yes": 1 1 1 2 1 2 1 1 2 2 ...
##  $ fullbase  : Factor w/ 2 levels "no","yes": 2 1 1 1 1 2 2 1 2 1 ...
##  $ gasheat   : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ aircon    : Factor w/ 2 levels "no","yes": 1 1 1 1 1 2 1 1 1 2 ...
##  $ garage    : num  1 0 0 0 0 0 2 0 0 1 ...
##  $ prefer    : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...

Price: Sale price of a house

lotsize: lot size of a property in square feet

bedrooms: number of bedrooms

stories: number of stories excluding basement

driveway: does the house have a driveway

recreation: does the house have a rec room

fullbase: is the basement fully finished

gasheat: gas or hotwater heating?

aircon: is there AC?

garage: number of garage places

prefer: is it located in a preferred neighborhood of the city?

price_na <- any(is.na(HousePrices$price))
price_na
## [1] FALSE
lotsize_na <- any(is.na(HousePrices$lotsize))
lotsize_na
## [1] FALSE
bedroom_na <- any(is.na(HousePrices$bedrooms))
bedroom_na
## [1] FALSE
bathroom_na <- any(is.na(HousePrices$bathrooms))
bathroom_na
## [1] FALSE
stories_na <- any(is.na(HousePrices$stories))
stories_na
## [1] FALSE
driveway_na <- any(is.na(HousePrices$driveway))
driveway_na
## [1] FALSE
recreation_na <- any(is.na(HousePrices$recreation))
recreation_na
## [1] FALSE
fullbase_na <- any(is.na(HousePrices$fullbase))
fullbase_na
## [1] FALSE
gasheat_na <- any(is.na(HousePrices$gasheat))
gasheat_na
## [1] FALSE
aircon_na <- any(is.na(HousePrices$aircon))
aircon_na
## [1] FALSE
garage_na <- any(is.na(HousePrices$garage))
garage_na
## [1] FALSE
prefer_na <- any(is.na(HousePrices$prefer))
prefer_na
## [1] FALSE

No values missing in the data set.

g1 <- plot(HousePrices$price ~ HousePrices$lotsize,main = 'Price of House Sold Based on Lot Size', xlab= 'Lot Size (Sq. Feet)', ylab= 'Sale Price')

g1
## NULL

2. CigarettesSW :

  • This data set consists of panel data on cigarette consumption for the 48 continental US States from 1985-1995. This data set contains 48 observations on 7 variables for 2 periods. We can tell by the graph, the summary of the data set in the library, and the table that this is a panel data set.
str(CigarettesSW)
## 'data.frame':    96 obs. of  9 variables:
##  $ state     : Factor w/ 48 levels "AL","AR","AZ",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ year      : Factor w/ 2 levels "1985","1995": 1 1 1 1 1 1 1 1 1 1 ...
##  $ cpi       : num  1.08 1.08 1.08 1.08 1.08 ...
##  $ population: num  3973000 2327000 3184000 26444000 3209000 ...
##  $ packs     : num  116 129 105 100 113 ...
##  $ income    : num  4.60e+07 2.62e+07 4.40e+07 4.47e+08 4.95e+07 ...
##  $ tax       : num  32.5 37 31 26 31 ...
##  $ price     : num  102.2 101.5 108.6 107.8 94.3 ...
##  $ taxs      : num  33.3 37 36.2 32.1 31 ...

State:(1-48) factor indicating which state is being analyzed out of the 48 states observed

Year: a factor indicating the year (1985 or 1995)

CPI: consumer price index

Population: state population

Packs: number of packs per capita

Income: state personal income (total, nominal)

Tax: average state, federal and average local excise taxes for fiscal year

Price: average price during fiscal year, including sales tax

Taxs: Average excise taxes for fiscal year, including sales tax

state_na <- any(is.na(CigarettesSW$state))
state_na
## [1] FALSE
year_na <- any(is.na(CigarettesSW$year))
year_na
## [1] FALSE
cpi_na <- any(is.na(CigarettesSW$cpi))
cpi_na
## [1] FALSE
population_na <- any(is.na(CigarettesSW$population))
population_na
## [1] FALSE
packs_na <- any(is.na(CigarettesSW$packs))
packs_na
## [1] FALSE
income_na <- any(is.na(CigarettesSW$income))
income_na
## [1] FALSE
tax_na <- any(is.na(CigarettesSW$tax))
tax_na
## [1] FALSE
price_na <- any(is.na(CigarettesSW$price))
price_na
## [1] FALSE
taxs_na <- any(is.na(CigarettesSW$taxs))
taxs_na
## [1] FALSE

No values missing in observations.

CigarettesMatrix <- matrix((CigarettesSW$packs), ncol=48)
CigarettesMatrix
##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
## [1,] 116.4863 104.5226 112.9635 143.8511 127.2346 103.0181 137.6374 186.0352
## [2,] 128.5346 100.3630 109.2784 122.1811 113.7456 123.2085 116.6804 127.5573
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]     [,15]    [,16]
## [1,] 115.6776 128.1169 112.9032 117.0402 155.2838 107.3817 116.52128 141.9558
## [2,] 120.9787 128.0049 130.3739 104.2579 105.4653 197.9940  88.74218 116.6629
##         [,17]    [,18]    [,19]    [,20]     [,21]    [,22]     [,23]    [,24]
## [1,] 127.5987 119.4538 132.7818 106.5903 115.10293 134.0098  96.22813 112.8474
## [2,] 127.1394 117.7030 127.2094 129.8346  68.04626 145.2830 107.87700 129.4000
##         [,25]    [,26]    [,27]     [,28]    [,29]    [,30]     [,31]    [,32]
## [1,] 101.0854 71.95417 82.58292 124.46660 97.47462 74.84978 134.25835 172.6478
## [2,] 111.0430 56.85931 79.47219  93.07455 92.40160 83.26508  88.75344 105.1761
##         [,33]     [,34]    [,35]     [,36]     [,37]     [,38]    [,39]
## [1,] 76.62064 102.46978  82.9453 105.58245 121.53806  87.27071 80.37137
## [2,] 77.47355  81.38825 122.4503  87.15957  79.80697 156.33675 64.66887
##         [,40]    [,41]    [,42]    [,43]     [,44]    [,45]    [,46]    [,47]
## [1,] 93.52612 111.3801 92.15575  92.5998  97.21923 73.07931 105.3869 65.53092
## [2,] 70.81732 108.6801 95.64309 108.0827 122.32005 49.27220 122.3348 92.46635
##         [,48]
## [1,] 115.5688
## [2,] 112.2381
barplot(CigarettesMatrix, legend=TRUE, beside=TRUE, main='Packs Per Capita by State', xlab='State', ylab='Number of Packs Per Capita' , ylim = c(0,200))

CigarettesSW$"1985" = (CigarettesSW$year==1985)
CigarettesSW$"1995" = (CigarettesSW$year==1995)
data1 <- matrix(CigarettesSW$packs, ncol=48)
margin.table(data1, margin=1)
## [1] 5333.807 5147.706
sum(CigarettesSW$packs)
## [1] 10481.51
g2 <- table(CigarettesSW$year, CigarettesSW$state)
g2
##       
##        AL AR AZ CA CO CT DE FL GA IA ID IL IN KS KY LA MA MD ME MI MN MO MS MT
##   1985  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
##   1995  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
##       
##        NC ND NE NH NJ NM NV NY OH OK OR PA RI SC SD TN TX UT VA VT WA WI WV WY
##   1985  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
##   1995  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1

Part 2.