Assignment 7
Jose Miguel Botero C, Karen Sofía Guerrero B, Juan José Gutierrez L, Juan Felipe Peña O, Marcela Mejía M
2022-06-16
DATASET: wage1
pacman::p_load(tidyverse,Lock5Data,ISLR,nycflights13,wooldridge,expss,hablar,rio,rstatix,ggpubr,lmtest)
wooldridge::wage1## wage educ exper tenure nonwhite female married numdep smsa northcen south
## 1 3.10 11 2 0 0 1 0 2 1 0 0
## 2 3.24 12 22 2 0 1 1 3 1 0 0
## 3 3.00 11 2 0 0 0 0 2 0 0 0
## 4 6.00 8 44 28 0 0 1 0 1 0 0
## 5 5.30 12 7 2 0 0 1 1 0 0 0
## 6 8.75 16 9 8 0 0 1 0 1 0 0
## 7 11.25 18 15 7 0 0 0 0 1 0 0
## 8 5.00 12 5 3 0 1 0 0 1 0 0
## 9 3.60 12 26 4 0 1 0 2 1 0 0
## 10 18.18 17 22 21 0 0 1 0 1 0 0
## 11 6.25 16 8 2 0 1 0 0 1 0 0
## 12 8.13 13 3 0 0 1 0 0 1 0 0
## 13 8.77 12 15 0 0 0 1 2 1 0 0
## 14 5.50 12 18 3 0 0 0 0 1 0 0
## 15 22.20 12 31 15 0 0 1 1 1 0 0
## 16 17.33 16 14 0 0 0 1 1 1 0 0
## 17 7.50 12 10 0 0 1 1 0 1 0 0
## 18 10.63 13 16 10 0 1 0 0 1 0 0
## 19 3.60 12 13 0 0 1 1 3 1 0 0
## 20 4.50 12 36 6 0 1 1 0 1 0 0
## 21 6.88 12 11 4 0 1 0 0 1 0 0
## 22 8.48 12 29 13 0 0 1 3 1 0 0
## 23 6.33 16 9 9 0 1 0 0 1 0 0
## 24 0.53 12 3 1 0 1 0 0 1 0 0
## 25 6.00 11 37 8 1 1 0 0 1 0 0
## 26 9.56 16 3 3 1 0 1 1 1 0 0
## 27 7.78 16 11 10 0 0 1 1 1 0 0
## 28 12.50 16 31 0 0 0 1 0 1 0 0
## 29 12.50 15 30 0 0 0 1 2 1 0 0
## 30 3.25 8 9 1 0 1 1 2 1 0 0
## 31 13.00 14 23 5 0 0 1 2 1 0 0
## 32 4.50 14 2 5 0 1 0 2 1 0 0
## 33 9.68 13 16 16 0 1 0 0 1 0 0
## 34 5.00 12 7 3 0 1 0 0 1 0 0
## 35 4.68 12 3 0 0 1 0 0 1 0 0
## 36 4.27 16 22 4 1 1 1 1 1 0 0
## 37 6.15 12 15 6 1 1 1 1 1 0 0
## 38 3.51 4 39 15 0 0 1 5 1 0 0
## 39 3.00 14 3 3 0 1 1 0 1 0 0
## 40 6.25 12 11 0 0 1 0 0 1 0 0
## 41 7.81 12 3 0 0 1 1 0 1 0 0
## 42 10.00 12 20 5 1 1 1 4 1 0 0
## 43 4.50 14 16 0 0 1 1 1 1 0 0
## 44 4.00 11 45 12 0 1 1 0 1 0 0
## 45 6.38 13 11 4 0 1 0 0 1 0 0
## 46 13.70 15 20 13 0 0 1 2 1 0 0
## 47 1.67 10 1 0 0 0 0 1 1 0 0
## 48 2.93 12 36 2 0 1 1 1 1 0 0
## 49 3.65 14 9 2 0 0 0 0 1 0 0
## 50 2.90 12 15 1 0 1 1 2 1 0 0
## 51 1.63 12 18 0 0 1 0 2 0 0 0
## 52 8.60 16 3 2 0 1 0 0 1 0 0
## 53 5.00 12 15 5 0 0 1 1 1 0 0
## 54 6.00 12 7 7 0 0 1 0 1 0 0
## 55 2.50 12 2 0 0 0 0 2 0 0 0
## 56 3.25 15 3 0 0 0 0 1 0 0 0
## 57 3.40 16 1 1 0 1 0 1 0 0 0
## 58 10.00 8 13 0 1 0 0 0 1 0 0
## 59 21.63 18 8 8 0 1 0 0 1 0 0
## 60 4.38 16 7 0 0 0 0 0 1 0 0
## 61 11.71 13 40 20 0 1 0 0 1 0 0
## 62 12.39 14 42 5 0 0 0 0 1 0 0
## 63 6.25 10 36 8 0 0 0 0 1 0 0
## 64 3.71 10 13 0 1 1 0 4 1 0 0
## 65 7.78 14 9 3 0 0 0 0 1 0 0
## 66 19.98 14 26 23 0 0 1 2 1 0 0
## 67 6.25 16 7 4 1 1 1 3 1 0 0
## 68 10.00 12 25 3 0 0 1 3 1 0 0
## 69 5.71 16 10 5 0 0 1 1 1 0 0
## 70 2.00 12 3 2 0 1 0 4 1 0 0
## 71 5.71 16 3 0 0 1 0 0 1 0 0
## 72 13.08 17 17 2 1 0 1 3 1 0 0
## 73 4.91 12 17 8 0 0 1 2 1 0 0
## 74 2.91 12 20 34 0 1 1 2 1 0 0
## 75 3.75 12 7 0 0 1 1 0 1 0 0
## 76 11.90 13 24 19 0 0 1 2 1 0 0
## 77 4.00 12 28 0 0 1 1 1 1 0 0
## 78 3.10 12 2 1 0 1 0 1 1 0 0
## 79 8.45 12 19 13 0 0 1 4 1 0 0
## 80 7.14 18 13 0 0 0 1 2 1 0 0
## 81 4.50 9 22 5 0 0 1 4 1 0 0
## 82 4.65 16 3 1 0 0 0 0 1 0 0
## 83 2.90 10 4 0 0 1 0 1 1 0 0
## 84 6.67 12 7 5 0 0 0 0 1 0 0
## 85 3.50 12 6 2 1 1 0 1 1 0 0
## 86 3.26 12 13 3 0 1 1 1 1 0 0
## 87 3.25 12 14 0 0 1 1 1 1 0 0
## 88 8.00 12 14 4 0 1 0 1 1 0 0
## 89 9.85 8 40 24 1 0 1 2 1 0 0
## 90 7.50 12 11 7 0 0 1 1 1 0 0
## 91 5.91 12 14 6 0 0 1 2 0 0 0
## 92 11.76 14 40 39 0 0 1 0 1 0 0
## 93 3.00 12 1 0 0 1 0 2 1 0 0
## 94 4.81 12 2 0 0 1 0 0 1 0 0
## 95 6.50 12 4 1 0 1 0 0 1 0 0
## 96 4.00 9 19 1 0 1 1 1 1 0 0
## 97 3.50 13 1 0 0 0 0 1 1 0 0
## 98 13.16 12 34 22 0 0 1 0 1 0 0
## 99 4.25 14 5 2 0 0 1 2 1 0 0
## 100 3.50 12 3 0 0 0 0 0 1 0 0
## 101 5.13 15 6 6 0 1 0 0 1 0 0
## 102 3.75 12 14 0 0 1 1 3 1 0 0
## 103 4.50 12 35 12 0 1 1 0 1 0 0
## 104 7.63 12 8 4 0 1 0 0 1 0 0
## 105 15.00 14 7 7 1 0 1 1 1 0 0
## 106 6.85 15 11 3 0 1 1 2 1 0 0
## 107 13.33 12 14 11 0 0 1 2 1 0 0
## 108 6.67 12 35 10 0 0 0 0 1 0 0
## 109 2.53 12 46 0 0 1 0 0 1 0 0
## 110 9.80 17 7 0 0 0 1 0 1 0 0
## 111 3.37 11 45 12 0 0 1 0 1 0 0
## 112 24.98 18 29 25 0 0 1 0 1 0 0
## 113 5.40 12 6 3 0 0 1 0 1 0 0
## 114 6.11 14 15 0 0 0 1 2 1 0 0
## 115 4.20 14 33 16 0 1 1 0 1 0 0
## 116 3.75 10 15 0 0 0 0 0 1 0 0
## 117 3.50 14 5 0 0 1 1 0 0 0 1
## 118 3.64 12 7 2 0 0 0 0 1 0 1
## 119 3.80 15 6 1 0 0 1 1 1 0 1
## 120 3.00 8 33 12 0 1 1 3 0 0 1
## 121 5.00 16 2 1 0 1 1 0 0 0 1
## 122 4.63 14 4 0 0 1 1 2 1 0 1
## 123 3.00 15 1 0 0 0 0 0 1 0 1
## 124 3.20 12 29 0 0 1 0 1 1 0 1
## 125 3.91 18 17 3 0 0 1 2 0 0 1
## 126 6.43 16 17 3 0 1 1 2 0 0 1
## 127 5.48 10 36 3 0 1 1 0 1 0 1
## 128 1.50 8 31 30 0 0 0 0 0 0 1
## 129 2.90 10 23 2 0 1 0 2 0 0 1
## 130 5.00 11 13 1 0 0 1 0 0 0 1
## 131 8.92 18 3 3 0 0 1 0 1 0 1
## 132 5.00 15 15 0 0 0 0 0 1 0 1
## 133 3.52 12 48 1 0 0 1 0 0 0 1
## 134 2.90 11 6 0 0 1 0 1 0 0 1
## 135 4.50 12 12 0 0 0 1 3 1 0 1
## 136 2.25 12 5 0 0 1 0 2 1 0 1
## 137 5.00 14 19 5 0 0 1 4 1 0 1
## 138 10.00 16 9 3 1 0 1 2 1 0 1
## 139 3.75 2 39 13 0 0 1 0 1 0 1
## 140 10.00 14 28 11 0 1 1 0 1 0 1
## 141 10.95 16 23 20 0 0 1 4 1 0 1
## 142 7.90 12 2 0 0 0 0 0 1 0 1
## 143 4.72 12 15 1 0 1 0 0 1 0 1
## 144 5.84 13 5 0 0 1 1 1 1 0 1
## 145 3.83 12 18 2 0 1 0 3 1 0 1
## 146 3.20 15 2 2 0 1 0 2 1 0 1
## 147 2.00 10 3 0 1 1 0 5 1 0 1
## 148 4.50 12 31 4 0 1 1 3 1 0 1
## 149 11.55 16 20 5 0 1 1 3 1 0 1
## 150 2.14 13 34 15 1 1 1 0 1 0 1
## 151 2.38 9 5 0 1 0 0 5 1 0 1
## 152 3.75 12 11 0 0 0 0 1 1 0 1
## 153 5.52 13 31 3 0 0 0 0 1 0 1
## 154 6.50 12 8 5 0 1 1 0 1 0 1
## 155 3.10 12 2 2 0 1 0 1 1 0 1
## 156 10.00 14 18 5 0 0 1 2 1 0 1
## 157 6.63 16 3 0 0 0 1 0 1 0 1
## 158 10.00 16 3 2 0 0 1 0 1 0 1
## 159 2.31 9 4 1 0 1 0 5 0 1 0
## 160 6.88 18 4 4 0 0 0 0 1 1 0
## 161 2.83 10 1 0 0 0 0 4 1 1 0
## 162 3.13 10 1 0 0 1 0 1 1 1 0
## 163 8.00 13 28 5 0 0 1 1 1 1 0
## 164 4.50 12 47 4 0 1 1 0 1 1 0
## 165 8.65 18 13 1 0 1 0 0 1 1 0
## 166 2.00 13 2 6 0 1 0 0 1 1 0
## 167 4.75 12 48 2 0 1 1 0 1 1 0
## 168 6.25 13 6 5 0 1 1 1 1 1 0
## 169 6.00 13 8 0 0 0 1 2 1 1 0
## 170 15.38 13 25 21 0 0 1 2 1 1 0
## 171 14.58 18 13 7 0 1 0 0 1 1 0
## 172 12.50 12 8 1 0 0 0 0 1 1 0
## 173 5.25 12 19 10 0 1 1 2 1 1 0
## 174 2.17 13 1 4 0 1 0 1 1 1 0
## 175 7.14 12 43 5 0 1 0 0 1 1 0
## 176 6.22 12 19 9 0 1 1 1 1 1 0
## 177 9.00 12 11 5 0 1 1 0 1 1 0
## 178 10.00 14 43 4 0 0 1 0 1 1 0
## 179 5.77 10 44 3 0 0 1 0 1 1 0
## 180 4.00 12 22 11 0 1 1 2 1 1 0
## 181 8.75 16 3 2 0 0 1 1 1 1 0
## 182 6.53 16 3 2 0 1 0 0 1 1 0
## 183 7.60 12 41 11 0 1 0 0 1 1 0
## 184 5.00 14 5 0 0 0 0 0 1 1 0
## 185 5.00 12 14 11 0 1 0 0 1 1 0
## 186 21.86 12 24 16 0 0 1 3 1 1 0
## 187 8.64 12 28 8 0 0 1 0 1 1 0
## 188 3.30 12 25 8 0 0 1 1 1 1 0
## 189 4.44 12 3 0 0 0 0 0 1 1 0
## 190 4.55 12 11 0 0 0 1 0 0 1 0
## 191 3.50 12 7 6 1 1 1 0 0 1 0
## 192 6.25 16 9 2 0 0 1 1 0 1 0
## 193 3.85 16 5 0 0 0 1 0 1 1 0
## 194 6.18 14 9 3 0 1 1 0 1 1 0
## 195 2.91 11 1 0 0 1 0 3 1 1 0
## 196 6.25 16 2 1 1 1 0 0 1 1 0
## 197 6.25 12 13 0 0 1 1 0 1 1 0
## 198 9.05 12 10 2 0 0 1 3 1 1 0
## 199 10.00 17 5 3 0 0 1 0 1 1 0
## 200 11.11 12 30 8 0 0 1 0 1 1 0
## 201 6.88 12 31 19 0 0 1 3 1 1 0
## 202 8.75 16 1 2 1 0 0 0 1 1 0
## 203 10.00 8 9 0 0 0 1 0 1 1 0
## 204 3.05 12 10 0 0 1 1 2 1 1 0
## 205 3.00 12 38 0 0 1 1 0 0 1 0
## 206 5.80 12 19 6 0 1 1 2 0 1 0
## 207 4.10 16 5 0 0 1 1 0 1 1 0
## 208 8.00 12 26 2 0 0 1 1 1 1 0
## 209 6.15 12 35 12 0 1 0 0 1 1 0
## 210 2.70 9 2 0 0 1 0 1 1 1 0
## 211 2.75 13 1 2 0 1 0 1 1 1 0
## 212 3.00 16 19 10 0 1 1 0 1 1 0
## 213 3.00 14 3 2 0 1 0 0 1 1 0
## 214 7.36 8 36 24 0 0 1 3 1 1 0
## 215 7.50 14 29 24 0 0 1 1 1 1 0
## 216 3.50 13 1 2 0 0 0 3 1 1 0
## 217 8.10 12 38 3 0 1 1 1 1 1 0
## 218 3.75 18 1 2 0 0 0 1 1 1 0
## 219 3.25 9 29 0 1 0 1 1 1 1 0
## 220 5.83 8 36 15 0 1 1 0 0 0 0
## 221 3.50 8 4 0 0 0 0 3 1 0 0
## 222 3.33 12 45 4 0 1 1 0 0 0 0
## 223 4.00 14 22 3 0 1 0 0 1 0 0
## 224 3.50 12 20 4 0 1 1 2 0 0 0
## 225 6.25 16 5 0 0 0 1 0 1 0 0
## 226 2.95 8 15 2 1 1 1 1 1 0 0
## 227 5.71 13 10 2 0 1 1 0 1 0 0
## 228 3.00 9 3 0 0 1 0 0 1 0 0
## 229 22.86 16 16 7 0 0 1 2 1 0 0
## 230 9.00 12 38 1 0 0 1 0 1 0 0
## 231 8.33 15 33 26 0 0 1 1 1 0 0
## 232 3.00 11 2 0 0 0 0 0 1 0 0
## 233 5.75 14 6 5 0 0 1 0 1 0 0
## 234 6.76 12 19 3 1 0 1 2 1 0 0
## 235 10.00 12 29 0 0 0 1 2 1 0 0
## 236 3.00 12 2 0 0 0 0 0 1 0 0
## 237 3.50 18 3 1 0 1 0 0 1 0 0
## 238 3.25 12 4 0 0 0 0 0 1 0 0
## 239 4.00 12 10 1 1 1 0 0 1 0 0
## 240 2.92 12 4 0 0 1 0 1 0 0 1
## 241 3.06 12 14 10 1 1 0 3 0 0 1
## 242 3.20 12 15 5 0 1 1 1 0 0 1
## 243 4.75 12 19 0 0 0 1 3 0 0 1
## 244 3.00 14 17 0 0 1 1 4 1 0 1
## 245 18.16 16 29 7 0 0 1 1 1 0 1
## 246 3.50 12 2 0 0 1 0 2 1 0 1
## 247 4.11 14 5 0 0 0 0 0 0 0 1
## 248 1.96 11 38 3 1 1 0 0 0 0 1
## 249 4.29 12 3 0 0 1 0 0 0 0 1
## 250 3.00 10 47 0 0 0 0 0 0 0 1
## 251 6.45 12 7 6 0 0 1 0 0 0 1
## 252 5.20 6 47 13 1 0 1 0 1 0 1
## 253 4.50 13 23 2 1 1 0 0 1 0 1
## 254 3.88 12 12 3 0 0 1 3 1 0 1
## 255 3.45 10 11 0 0 1 0 2 1 0 1
## 256 10.91 12 25 23 0 0 0 0 1 0 1
## 257 4.10 14 6 0 0 1 1 0 1 0 1
## 258 3.00 13 3 1 0 0 0 0 1 0 1
## 259 5.90 12 14 7 1 0 1 2 1 0 1
## 260 18.00 18 13 0 0 1 0 0 1 0 1
## 261 4.00 12 9 0 0 0 0 0 1 0 1
## 262 3.00 12 1 0 1 0 0 0 1 0 1
## 263 3.55 12 6 0 0 1 1 1 0 0 0
## 264 3.00 12 11 1 0 1 1 2 0 0 0
## 265 8.75 12 47 44 0 0 1 0 0 0 0
## 266 2.90 8 49 6 0 1 0 1 0 0 0
## 267 6.26 13 37 17 0 1 1 0 1 0 0
## 268 3.50 13 2 0 0 1 0 0 1 0 0
## 269 4.60 14 7 0 0 1 1 0 1 0 0
## 270 6.00 12 22 8 0 0 0 2 1 0 0
## 271 2.89 10 8 0 0 1 0 1 1 0 0
## 272 5.58 16 1 1 0 0 1 0 1 0 0
## 273 4.00 12 43 6 0 1 1 0 0 0 0
## 274 6.00 16 2 2 0 0 0 0 1 0 0
## 275 4.50 12 2 1 0 1 0 2 1 0 0
## 276 2.92 14 1 3 0 0 0 0 1 0 0
## 277 4.33 18 1 0 0 0 0 0 1 0 0
## 278 18.89 17 26 20 0 0 1 2 1 0 0
## 279 4.28 13 1 1 0 1 0 2 1 0 0
## 280 4.57 14 37 7 0 1 1 0 1 0 0
## 281 6.25 15 12 4 0 1 1 2 1 0 0
## 282 2.95 14 41 23 1 0 1 0 0 1 0
## 283 8.75 12 24 1 0 0 0 0 1 1 0
## 284 8.50 8 38 26 0 0 0 0 1 1 0
## 285 3.75 12 18 0 0 1 1 4 1 1 0
## 286 3.15 12 26 1 0 0 1 0 1 1 0
## 287 5.00 8 45 2 0 0 0 0 0 1 0
## 288 6.46 12 27 0 0 0 1 3 0 1 0
## 289 2.00 9 2 0 0 0 0 3 0 1 0
## 290 4.79 12 41 8 0 0 1 0 1 1 0
## 291 5.78 16 11 4 0 0 1 2 1 1 0
## 292 3.18 12 5 0 0 1 1 0 1 1 0
## 293 4.68 16 3 1 0 1 0 0 1 1 0
## 294 4.10 12 3 2 0 1 0 0 1 1 0
## 295 2.91 12 4 0 0 0 1 0 1 0 1
## 296 6.00 13 21 13 0 0 1 4 0 0 1
## 297 3.60 10 34 26 0 1 1 0 0 0 1
## 298 3.95 6 49 6 0 0 1 6 0 0 1
## 299 7.00 12 6 5 1 0 1 1 0 0 1
## 300 3.00 12 26 9 0 1 1 0 0 0 1
## 301 6.08 16 9 0 0 0 0 0 0 0 1
## 302 8.63 12 23 9 0 0 1 1 0 0 1
## 303 3.00 8 33 2 0 0 1 0 0 0 1
## 304 3.75 12 5 2 0 1 1 1 0 0 1
## 305 2.90 6 49 7 0 0 1 0 0 0 1
## 306 3.00 4 48 0 1 0 1 0 0 0 1
## 307 6.25 11 35 31 0 0 1 0 1 0 1
## 308 3.50 11 23 2 1 1 0 2 0 0 1
## 309 3.00 7 26 1 0 1 0 3 0 0 1
## 310 3.24 12 16 0 0 1 1 2 1 0 1
## 311 8.02 18 23 3 0 1 1 1 1 0 1
## 312 3.33 12 36 8 0 1 1 1 1 0 1
## 313 5.25 16 4 0 0 0 0 0 1 0 1
## 314 6.25 12 10 0 0 0 1 3 1 0 1
## 315 3.50 14 18 2 0 0 1 1 0 1 0
## 316 2.95 12 3 1 0 0 0 1 0 1 0
## 317 3.00 10 7 0 0 1 1 2 0 1 0
## 318 4.69 10 7 7 0 0 0 0 0 1 0
## 319 3.73 9 33 2 0 1 0 1 0 1 0
## 320 4.00 10 34 12 0 0 1 0 0 1 0
## 321 4.00 12 8 0 0 1 1 2 0 1 0
## 322 2.90 12 17 1 0 1 1 2 0 1 0
## 323 3.05 12 2 0 0 1 0 1 0 1 0
## 324 5.05 10 5 0 0 1 0 0 1 1 0
## 325 13.95 16 41 16 0 0 1 0 1 1 0
## 326 18.16 16 35 28 0 0 1 1 1 1 0
## 327 6.25 16 11 4 0 0 0 0 1 1 0
## 328 5.25 12 4 0 1 0 0 0 1 1 0
## 329 4.79 12 12 3 0 1 1 3 1 1 0
## 330 3.35 7 35 0 0 1 0 1 1 0 1
## 331 3.00 8 33 0 0 0 1 1 1 0 1
## 332 8.43 16 8 6 0 0 1 0 1 0 1
## 333 5.70 16 2 0 0 0 0 0 1 0 1
## 334 11.98 18 8 10 0 0 1 2 1 0 1
## 335 3.50 13 29 1 0 1 1 0 0 0 1
## 336 4.24 10 14 5 1 0 1 1 0 0 1
## 337 7.00 16 26 3 0 1 1 1 1 0 1
## 338 6.00 14 11 3 0 1 1 2 1 0 1
## 339 12.22 16 10 2 0 0 0 0 1 0 1
## 340 4.50 12 13 0 0 0 1 0 1 0 1
## 341 3.00 9 23 20 0 1 1 2 0 0 1
## 342 2.90 11 1 2 1 0 0 2 0 0 1
## 343 15.00 11 35 31 0 0 1 0 0 0 1
## 344 4.00 12 5 2 0 0 1 0 0 0 1
## 345 5.25 11 13 11 0 0 1 2 0 0 1
## 346 4.00 12 22 3 0 0 1 3 0 0 1
## 347 3.30 12 21 9 0 1 1 2 0 0 1
## 348 5.05 12 19 0 0 1 1 3 0 0 1
## 349 3.58 12 13 0 0 0 0 0 1 0 1
## 350 5.00 14 15 5 0 0 1 2 0 0 1
## 351 4.57 14 3 0 0 0 1 0 0 0 1
## 352 12.50 18 6 2 0 0 0 0 1 0 1
## 353 3.45 12 6 5 0 1 1 0 1 0 1
## 354 4.63 12 16 1 0 1 0 0 1 0 1
## 355 10.00 12 31 2 0 0 1 0 1 0 1
## 356 2.92 11 1 0 0 1 0 1 0 1 0
## 357 4.51 12 5 2 0 0 0 0 1 1 0
## 358 6.50 17 3 0 0 0 1 0 1 1 0
## 359 7.50 16 11 0 0 0 1 0 1 1 0
## 360 3.54 13 6 7 0 1 1 0 0 1 0
## 361 4.20 13 11 3 0 1 1 2 1 1 0
## 362 3.51 12 7 2 0 1 1 0 1 1 0
## 363 4.50 14 5 0 0 0 1 0 1 1 0
## 364 3.35 14 5 4 0 1 1 0 1 1 0
## 365 2.91 11 2 2 0 0 0 2 1 1 0
## 366 5.25 10 44 7 0 0 1 1 1 1 0
## 367 4.05 8 44 25 0 0 1 0 1 1 0
## 368 3.75 14 13 0 0 1 1 3 1 1 0
## 369 3.40 12 26 15 0 1 1 1 1 1 0
## 370 3.00 10 2 1 0 1 0 1 1 0 1
## 371 6.29 17 10 3 0 0 1 1 1 0 1
## 372 2.54 9 2 0 0 1 0 1 1 0 1
## 373 4.50 12 35 0 0 1 1 1 1 0 1
## 374 3.13 12 6 5 0 1 1 1 1 0 1
## 375 6.36 14 8 1 0 0 1 0 1 0 1
## 376 4.68 16 1 0 0 0 0 0 1 0 1
## 377 6.80 12 14 10 0 0 1 2 0 0 1
## 378 8.53 10 14 6 0 0 1 0 0 0 1
## 379 4.17 0 22 10 0 1 0 0 0 0 1
## 380 3.75 14 8 4 0 1 1 0 0 0 1
## 381 11.10 15 1 4 0 1 0 2 0 0 1
## 382 3.26 16 15 5 1 1 1 2 1 0 1
## 383 9.13 12 14 12 0 0 1 3 1 0 1
## 384 4.50 11 37 10 0 0 1 2 1 0 1
## 385 3.00 11 1 1 0 1 0 1 1 0 1
## 386 8.75 12 4 4 0 0 1 0 1 0 1
## 387 4.14 13 29 0 0 1 1 0 1 0 1
## 388 2.87 12 45 8 0 1 1 0 0 1 0
## 389 3.35 13 22 0 0 1 0 2 0 1 0
## 390 6.08 16 42 10 0 0 0 0 0 1 0
## 391 3.00 15 9 0 1 0 0 0 0 1 0
## 392 4.20 16 8 0 0 1 1 1 1 1 0
## 393 5.60 15 31 15 0 1 0 2 1 1 0
## 394 10.00 12 24 24 0 0 1 0 1 1 0
## 395 12.50 18 16 5 0 0 1 1 1 1 0
## 396 3.76 6 6 0 0 0 0 4 0 0 1
## 397 3.10 6 14 0 1 1 0 5 1 0 1
## 398 4.29 12 47 25 0 1 1 2 1 0 1
## 399 10.92 12 34 5 0 0 1 0 0 0 1
## 400 7.50 16 6 2 0 1 1 1 1 0 1
## 401 4.05 9 7 4 0 1 1 1 1 0 1
## 402 4.65 12 27 2 0 0 1 3 1 0 1
## 403 5.00 11 24 5 0 0 1 0 1 0 1
## 404 2.90 10 18 0 0 1 1 2 0 0 1
## 405 8.00 12 12 3 1 1 0 1 0 0 1
## 406 8.43 8 27 3 0 0 1 3 1 0 1
## 407 2.92 9 49 0 0 1 0 0 1 0 1
## 408 6.25 17 4 0 0 1 0 0 1 0 0
## 409 6.25 16 24 2 0 1 1 2 1 0 0
## 410 5.11 11 3 0 0 0 0 0 1 0 0
## 411 4.00 10 2 0 0 1 0 1 1 0 0
## 412 4.44 8 29 11 0 0 1 3 0 0 1
## 413 6.88 13 34 21 0 0 1 0 0 0 1
## 414 5.43 14 10 3 1 0 1 1 1 0 1
## 415 3.00 13 5 0 0 1 0 1 1 0 1
## 416 2.90 11 2 0 0 1 0 2 1 0 1
## 417 6.25 7 39 21 1 0 1 0 1 0 1
## 418 4.34 16 5 2 1 1 0 0 1 0 1
## 419 3.25 12 14 2 0 1 1 2 0 0 1
## 420 7.26 13 8 2 0 0 0 0 1 0 1
## 421 6.35 14 10 1 0 1 1 2 1 0 1
## 422 5.63 16 2 2 0 0 1 0 1 0 0
## 423 8.75 14 9 3 0 0 1 1 1 0 0
## 424 3.20 11 1 0 0 0 0 0 0 0 0
## 425 3.00 8 45 1 0 1 1 0 0 0 0
## 426 3.00 14 33 3 0 1 1 0 1 0 0
## 427 12.50 17 21 18 0 0 1 3 1 0 0
## 428 2.88 10 2 0 0 1 0 3 1 0 0
## 429 3.35 12 9 1 0 0 1 0 1 1 0
## 430 6.50 12 33 2 0 0 1 0 0 1 0
## 431 10.38 18 16 2 1 0 1 1 1 1 0
## 432 4.50 14 10 0 0 0 1 0 1 1 0
## 433 10.00 18 9 8 0 0 0 0 0 1 0
## 434 3.81 12 8 1 0 1 1 2 0 1 0
## 435 8.80 16 9 1 0 0 1 0 0 0 1
## 436 9.42 14 23 0 0 1 1 2 0 0 1
## 437 6.33 12 23 8 0 0 1 2 0 0 1
## 438 4.00 9 22 18 1 0 0 0 0 0 1
## 439 2.90 12 37 0 0 1 1 0 0 0 1
## 440 20.00 12 22 4 0 0 1 1 0 0 1
## 441 11.25 17 28 25 0 0 1 1 1 0 1
## 442 3.50 12 14 0 1 1 0 2 1 0 1
## 443 6.00 15 19 4 0 1 1 2 1 0 1
## 444 14.38 17 10 9 1 0 1 1 0 0 1
## 445 6.36 16 25 0 0 0 1 1 1 0 1
## 446 3.55 12 21 0 0 1 1 1 0 0 1
## 447 3.00 15 32 0 0 0 1 0 1 0 1
## 448 4.50 16 21 10 0 0 1 1 1 0 1
## 449 6.63 12 36 0 0 1 0 0 1 0 1
## 450 9.30 15 2 2 0 0 1 0 1 0 1
## 451 3.00 12 11 0 0 1 1 2 1 0 1
## 452 3.25 12 40 2 0 1 0 0 0 1 0
## 453 1.50 12 11 1 0 1 1 2 0 1 0
## 454 5.90 12 9 7 0 1 1 1 1 1 0
## 455 8.00 16 23 4 0 0 0 0 1 1 0
## 456 2.90 11 1 0 0 1 0 1 1 1 0
## 457 3.29 14 30 13 0 0 0 0 1 1 0
## 458 6.50 14 41 33 0 0 1 0 1 1 0
## 459 4.00 13 6 0 0 1 0 1 1 1 0
## 460 6.00 14 11 0 0 0 1 0 0 1 0
## 461 4.08 12 43 17 0 1 1 0 1 1 0
## 462 3.75 12 39 2 0 1 1 0 1 1 0
## 463 3.05 8 50 24 0 1 0 0 0 0 1
## 464 3.50 12 26 20 0 1 1 0 0 0 1
## 465 2.92 3 51 30 1 0 0 0 1 0 1
## 466 4.50 11 3 9 0 0 0 0 1 0 1
## 467 3.35 15 3 1 0 1 1 2 1 0 1
## 468 5.95 11 15 9 1 0 1 1 0 0 1
## 469 8.00 12 17 6 0 0 1 2 0 0 1
## 470 3.00 4 36 0 0 0 1 1 0 0 1
## 471 5.00 9 31 9 1 0 1 6 0 0 1
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## 526 0 1.2527629 25 16 w1<- wage1- Using wage1 data set, estimate the model log(wage) = f(educ). Add exper, tenure, married, black, south, and urban sequentially, and comment on the changes in the coefficients of educ after each augmentation. Using linear hypothesis testing, conclude whether exper and tenure cancels the effect of each other? Test the regression assumptions.
# Log-level model
lm(log(wage) ~ educ, data=w1) %>% summary() # b1*100##
## Call:
## lm(formula = log(wage) ~ educ, data = w1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.21158 -0.36393 -0.07263 0.29712 1.52339
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.583773 0.097336 5.998 3.74e-09 ***
## educ 0.082744 0.007567 10.935 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4801 on 524 degrees of freedom
## Multiple R-squared: 0.1858, Adjusted R-squared: 0.1843
## F-statistic: 119.6 on 1 and 524 DF, p-value: < 2.2e-16w2 <- lm(log(wage) ~ educ+exper, data = w1)
summary(w2)##
## Call:
## lm(formula = log(wage) ~ educ + exper, data = w1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.05800 -0.30136 -0.04539 0.30601 1.44425
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.216854 0.108595 1.997 0.0464 *
## educ 0.097936 0.007622 12.848 < 2e-16 ***
## exper 0.010347 0.001555 6.653 7.24e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4614 on 523 degrees of freedom
## Multiple R-squared: 0.2493, Adjusted R-squared: 0.2465
## F-statistic: 86.86 on 2 and 523 DF, p-value: < 2.2e-16w3 <- lm(log(wage) ~ educ+exper+tenure, data = w1)
summary(w3)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure, data = w1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.05802 -0.29645 -0.03265 0.28788 1.42809
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.284360 0.104190 2.729 0.00656 **
## educ 0.092029 0.007330 12.555 < 2e-16 ***
## exper 0.004121 0.001723 2.391 0.01714 *
## tenure 0.022067 0.003094 7.133 3.29e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4409 on 522 degrees of freedom
## Multiple R-squared: 0.316, Adjusted R-squared: 0.3121
## F-statistic: 80.39 on 3 and 522 DF, p-value: < 2.2e-16wage1 <- w1 %>% dplyr::mutate(
marrmen = ifelse(female == 0 & married == 1,1,0),
marrfem = ifelse(female == 1 & married == 1,1,0),
)
w4 <- lm(log(wage) ~ marrmen + marrfem + educ + exper + tenure, data = wage1)
summary(w4)##
## Call:
## lm(formula = log(wage) ~ marrmen + marrfem + educ + exper + tenure,
## data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.99444 -0.24176 -0.04485 0.24534 1.26391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.328368 0.096206 3.413 0.000692 ***
## marrmen 0.348273 0.044287 7.864 2.16e-14 ***
## marrfem -0.063199 0.047143 -1.341 0.180638
## educ 0.083847 0.006870 12.204 < 2e-16 ***
## exper 0.003041 0.001656 1.836 0.066950 .
## tenure 0.015906 0.002923 5.441 8.15e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4065 on 520 degrees of freedom
## Multiple R-squared: 0.4207, Adjusted R-squared: 0.4151
## F-statistic: 75.52 on 5 and 520 DF, p-value: < 2.2e-16wage2 <- w1 %>% dplyr::mutate(
marrmen = ifelse(female == 0 & married == 1,1,0),
marrfem = ifelse(female == 1 & married == 1,1,0),
bmen = ifelse(female == 0 & nonwhite == 1,1,0),
bfem = ifelse(female == 1 & nonwhite == 1,1,0)
)
w5 <- lm(log(wage) ~ bmen + bfem + marrmen + marrfem + educ + exper + tenure, data = wage2,)
summary(w5)##
## Call:
## lm(formula = log(wage) ~ bmen + bfem + marrmen + marrfem + educ +
## exper + tenure, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.99929 -0.24369 -0.03954 0.24779 1.22205
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.327663 0.097410 3.364 0.000826 ***
## bmen 0.037529 0.079608 0.471 0.637534
## bfem -0.090279 0.084741 -1.065 0.287210
## marrmen 0.337644 0.045267 7.459 3.70e-13 ***
## marrfem -0.064434 0.047329 -1.361 0.173972
## educ 0.084289 0.006919 12.182 < 2e-16 ***
## exper 0.003156 0.001660 1.901 0.057895 .
## tenure 0.015812 0.002926 5.403 9.98e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4068 on 518 degrees of freedom
## Multiple R-squared: 0.4222, Adjusted R-squared: 0.4144
## F-statistic: 54.08 on 7 and 518 DF, p-value: < 2.2e-16wage3 <- w1 %>% dplyr::mutate(
marrmen = ifelse(female == 0 & married == 1,1,0),
marrfem = ifelse(female == 1 & married == 1,1,0),
bmen = ifelse(female == 0 & nonwhite == 1,1,0),
bfem = ifelse(female == 1 & nonwhite == 1,1,0),
smen = ifelse(female == 0 & south == 1,1,0),
sfem = ifelse(female == 1 & south == 1,1,0)
)
w6 <- lm(log(wage) ~ smen + sfem + bmen + bfem + marrmen + marrfem + educ + exper + tenure, data = wage3)
summary(w6)##
## Call:
## lm(formula = log(wage) ~ smen + sfem + bmen + bfem + marrmen +
## marrfem + educ + exper + tenure, data = wage3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.02008 -0.24979 -0.03848 0.22913 1.23594
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.367344 0.099444 3.694 0.000244 ***
## smen -0.085334 0.050200 -1.700 0.089758 .
## sfem -0.053757 0.052926 -1.016 0.310245
## bmen 0.054225 0.080376 0.675 0.500205
## bfem -0.086273 0.085443 -1.010 0.313104
## marrmen 0.353150 0.047874 7.377 6.52e-13 ***
## marrfem -0.064784 0.048385 -1.339 0.181185
## educ 0.082740 0.006956 11.895 < 2e-16 ***
## exper 0.003184 0.001659 1.920 0.055444 .
## tenure 0.015426 0.002928 5.268 2.03e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4061 on 516 degrees of freedom
## Multiple R-squared: 0.4263, Adjusted R-squared: 0.4163
## F-statistic: 42.61 on 9 and 516 DF, p-value: < 2.2e-16wage4 <- w1 %>% dplyr::mutate(
marrmen = ifelse(female == 0 & married == 1,1,0),
marrfem = ifelse(female == 1 & married == 1,1,0),
bmen = ifelse(female == 0 & nonwhite == 1,1,0),
bfem = ifelse(female == 1 & nonwhite == 1,1,0),
smen = ifelse(female == 0 & south == 1,1,0),
sfem = ifelse(female == 1 & south == 1,1,0),
umen = ifelse(female == 0 & smsa == 1,1,0),
ufem = ifelse(female == 1 & smsa == 1,1,0)
)
w7 <- lm(log(wage) ~ umen + ufem + smen + sfem + bmen + bfem + marrmen + marrfem + educ + exper + tenure, data = wage4)
summary(w7)##
## Call:
## lm(formula = log(wage) ~ umen + ufem + smen + sfem + bmen + bfem +
## marrmen + marrfem + educ + exper + tenure, data = wage4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.00373 -0.24410 -0.03511 0.23174 1.34327
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.319541 0.100425 3.182 0.001552 **
## umen 0.186720 0.049463 3.775 0.000179 ***
## ufem 0.093354 0.049818 1.874 0.061510 .
## smen -0.059712 0.050489 -1.183 0.237490
## sfem -0.024062 0.052897 -0.455 0.649385
## bmen 0.042926 0.079634 0.539 0.590096
## bfem -0.072161 0.085242 -0.847 0.397647
## marrmen 0.328023 0.051311 6.393 3.66e-10 ***
## marrfem -0.027657 0.049771 -0.556 0.578668
## educ 0.077584 0.007009 11.070 < 2e-16 ***
## exper 0.003379 0.001640 2.060 0.039867 *
## tenure 0.014814 0.002899 5.111 4.53e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4013 on 514 degrees of freedom
## Multiple R-squared: 0.442, Adjusted R-squared: 0.4301
## F-statistic: 37.02 on 11 and 514 DF, p-value: < 2.2e-16#1. In the first (lm) log-level model, wage increases by 8.27% when educ increases by one unit. By adding exper (w2), the coefficient of educ changes to 0.0979 indicating that wage increases by 9.79% when educ increases by one unit and exper is added. Add tenure (w3) and the coefficient of educ changes to 0.0920 so that wage increases by 9.20%. Add married (w4) and the coefficient educ changes 0.0838, wage increases by 8.38%. Black (w5) is added and the coefficient of educ changes to 0.0842 and wage increases by 8.42%. Add south (w6) and the coefficient of educ is 0.0827 and the wage increases by 8.27%. Finally, add urban (w7) and the coefficient of educ changes to 0.0775 so that the wage increases 7.75% when educ increases by one additional unit and all the variables are added.#ASSUMPTIONS
plot(w7)# Residual versus leverage plot
plot(w7,5)# Cooks distance
plot(w7,4)# Scale location plot, homocedasticity
plot(w7,3)#normality
plot(w7,2)#non-linear patterns
plot(w7,1)
# Testing homoskedasticity: Breusch-Pagan test
lmtest::bptest(w7)##
## studentized Breusch-Pagan test
##
## data: w7
## BP = 7.3365, df = 11, p-value = 0.7712# Outliers
car::outlierTest(w7) # If Bonferroni p-value < 5%, then that observation is an outlier.## rstudent unadjusted p-value Bonferroni p
## 24 -5.14409 3.8328e-07 0.0002016# Non-independence of errors
car::durbinWatsonTest(w7)## lag Autocorrelation D-W Statistic p-value
## 1 0.0887085 1.822043 0.034
## Alternative hypothesis: rho != 0# Global validation
gv1 <- gvlma::gvlma(w7)
gv1##
## Call:
## lm(formula = log(wage) ~ umen + ufem + smen + sfem + bmen + bfem +
## marrmen + marrfem + educ + exper + tenure, data = wage4)
##
## Coefficients:
## (Intercept) umen ufem smen sfem bmen
## 0.319541 0.186720 0.093354 -0.059712 -0.024062 0.042926
## bfem marrmen marrfem educ exper tenure
## -0.072161 0.328023 -0.027657 0.077584 0.003379 0.014814
##
##
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance = 0.05
##
## Call:
## gvlma::gvlma(x = w7)
##
## Value p-value Decision
## Global Stat 49.4432 4.719e-10 Assumptions NOT satisfied!
## Skewness 0.4823 4.874e-01 Assumptions acceptable.
## Kurtosis 39.1659 3.893e-10 Assumptions NOT satisfied!
## Link Function 5.6532 1.742e-02 Assumptions NOT satisfied!
## Heteroscedasticity 4.1418 4.184e-02 Assumptions NOT satisfied!#linear hypothesis
car::linearHypothesis(w7, c("exper - tenure = 0"), white.adjust = "hc1") ## Linear hypothesis test
##
## Hypothesis:
## exper - tenure = 0
##
## Model 1: restricted model
## Model 2: log(wage) ~ umen + ufem + smen + sfem + bmen + bfem + marrmen +
## marrfem + educ + exper + tenure
##
## Note: Coefficient covariance matrix supplied.
##
## Res.Df Df F Pr(>F)
## 1 515
## 2 514 1 7.2541 0.007305 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#2. Linear hypothesis: Do not reject H0 in the linear hypothesis so it is proved that exper and tenure cancel each other out.
#3. Assumptions: In the homoscedasticity test, do not reject the H0, so there is homoscedasticity in the model; in the outlier test, the value is less than 5%, so the observation is an outlier; in the independence test, do not reject H0, so the errors are independent; and in the global validation, the assumption is not fulfilledDATASET: marketing
pacman::p_load(tidyverse,car, wooldridge, jtools, hablar, broom, gvlma, datarium, MASS, forestmangr)
m1 <- datarium::marketing- Using the marketing data set, construct a categorical variable with 2 levels based on youtube variable. Interact the new variable with facebook and newspaper and interpret the coefficients. The dependent variable is sales. Plot the interaction plots for both interactions. Test the regression assumptions.
model <- lm(sales ~ youtube, data = m1)
mx<-max(m1$youtube)
med<-median(m1$youtube)
below <- m1[m1$youtube<med,]
below ## youtube facebook newspaper sales
## 2 53.40 47.16 54.12 12.48
## 3 20.64 55.08 83.16 11.16
## 6 10.44 58.68 90.00 8.64
## 7 69.00 39.36 28.20 14.16
## 8 144.24 23.52 13.92 15.84
## 9 10.32 2.52 1.20 5.76
## 11 79.32 6.96 29.04 10.32
## 13 28.56 42.12 79.08 11.04
## 14 117.00 9.12 8.64 11.64
## 17 81.36 43.92 136.80 15.00
## 19 83.04 24.60 21.96 13.56
## 20 176.76 28.68 22.92 17.52
## 23 15.84 19.08 59.52 6.72
## 25 74.76 15.12 21.96 11.64
## 27 171.48 35.16 15.12 18.00
## 30 84.72 19.20 48.96 12.60
## 32 135.48 20.88 46.32 14.28
## 33 116.64 1.80 36.00 11.52
## 35 114.84 1.68 8.88 11.40
## 38 89.64 59.28 54.84 17.64
## 39 51.72 32.04 42.12 12.12
## 45 30.12 30.84 51.96 10.20
## 47 107.64 11.88 42.84 12.72
## 50 80.28 14.04 44.16 11.64
## 52 120.48 11.52 4.32 12.84
## 57 8.76 33.72 49.68 6.60
## 58 163.44 23.04 19.92 15.84
## 61 64.20 2.40 25.68 9.72
## 64 123.24 35.52 10.08 16.80
## 65 157.32 51.36 34.68 21.60
## 66 82.80 11.16 1.08 11.16
## 67 37.80 29.52 2.64 11.40
## 68 167.16 17.40 12.24 16.08
## 72 131.76 17.16 38.04 14.88
## 73 32.16 39.60 23.16 10.56
## 74 155.28 6.84 37.56 13.20
## 76 20.28 52.44 107.28 10.44
## 77 33.00 1.92 24.84 8.28
## 78 144.60 34.20 17.04 17.04
## 79 6.48 35.88 11.28 6.36
## 80 139.20 9.24 27.72 13.20
## 81 91.68 32.04 26.76 14.16
## 83 90.36 24.36 39.00 13.56
## 84 82.08 53.40 42.72 16.32
## 87 91.56 33.00 19.20 14.40
## 88 132.84 48.72 75.84 19.20
## 89 105.96 30.60 88.08 15.48
## 90 131.76 57.36 61.68 20.04
## 91 161.16 5.88 11.16 13.44
## 92 34.32 1.80 39.60 8.76
## 95 128.88 16.80 13.08 13.80
## 100 162.24 50.04 55.08 20.64
## 106 165.48 55.68 70.80 23.04
## 107 30.00 13.20 35.64 8.64
## 108 108.48 0.36 27.84 10.44
## 109 15.72 0.48 30.72 6.36
## 115 93.84 56.16 41.40 17.52
## 116 90.12 42.00 63.24 15.12
## 117 167.04 17.16 30.72 14.64
## 118 91.68 0.96 17.76 11.28
## 119 150.84 44.28 95.04 19.08
## 120 23.28 19.20 26.76 7.92
## 121 169.56 32.16 55.44 18.60
## 122 22.56 26.04 60.48 8.40
## 124 147.72 41.52 14.88 18.24
## 126 104.64 14.16 31.08 12.72
## 127 9.36 46.68 60.72 7.92
## 128 96.24 0.00 11.04 10.56
## 130 71.52 14.40 51.72 11.64
## 131 0.84 47.52 10.44 1.92
## 133 10.08 32.64 2.52 6.84
## 135 44.28 46.32 78.72 12.96
## 136 57.96 56.40 10.20 13.92
## 137 30.72 46.80 11.16 11.40
## 139 51.60 31.08 24.60 11.52
## 141 88.08 20.40 15.48 13.08
## 144 125.52 6.84 41.28 12.48
## 145 115.44 17.76 46.68 13.68
## 146 168.36 2.28 10.80 12.36
## 149 45.60 48.36 14.28 13.08
## 150 53.64 30.96 24.72 12.12
## 152 145.20 10.08 58.44 13.92
## 156 4.92 13.92 6.84 3.84
## 157 112.68 52.20 60.60 18.36
## 159 14.04 44.28 54.24 8.76
## 160 158.04 22.08 41.52 15.48
## 162 102.84 42.96 59.16 15.96
## 165 140.64 17.64 6.48 14.28
## 167 21.48 45.12 25.92 9.60
## 171 60.00 13.92 22.08 10.08
## 173 23.52 24.12 20.40 9.12
## 183 67.44 6.84 35.64 10.44
## 187 167.40 2.52 31.92 12.36
## 190 22.44 14.52 28.08 8.04
## 191 47.40 49.32 6.96 12.96
## 192 90.60 12.96 7.20 11.88
## 193 20.64 4.92 37.92 7.08
## 195 179.64 42.72 7.20 20.76
## 196 45.84 4.44 16.56 9.12
## 197 113.04 5.88 9.72 11.64above <- m1[m1$youtube<med,]
above## youtube facebook newspaper sales
## 2 53.40 47.16 54.12 12.48
## 3 20.64 55.08 83.16 11.16
## 6 10.44 58.68 90.00 8.64
## 7 69.00 39.36 28.20 14.16
## 8 144.24 23.52 13.92 15.84
## 9 10.32 2.52 1.20 5.76
## 11 79.32 6.96 29.04 10.32
## 13 28.56 42.12 79.08 11.04
## 14 117.00 9.12 8.64 11.64
## 17 81.36 43.92 136.80 15.00
## 19 83.04 24.60 21.96 13.56
## 20 176.76 28.68 22.92 17.52
## 23 15.84 19.08 59.52 6.72
## 25 74.76 15.12 21.96 11.64
## 27 171.48 35.16 15.12 18.00
## 30 84.72 19.20 48.96 12.60
## 32 135.48 20.88 46.32 14.28
## 33 116.64 1.80 36.00 11.52
## 35 114.84 1.68 8.88 11.40
## 38 89.64 59.28 54.84 17.64
## 39 51.72 32.04 42.12 12.12
## 45 30.12 30.84 51.96 10.20
## 47 107.64 11.88 42.84 12.72
## 50 80.28 14.04 44.16 11.64
## 52 120.48 11.52 4.32 12.84
## 57 8.76 33.72 49.68 6.60
## 58 163.44 23.04 19.92 15.84
## 61 64.20 2.40 25.68 9.72
## 64 123.24 35.52 10.08 16.80
## 65 157.32 51.36 34.68 21.60
## 66 82.80 11.16 1.08 11.16
## 67 37.80 29.52 2.64 11.40
## 68 167.16 17.40 12.24 16.08
## 72 131.76 17.16 38.04 14.88
## 73 32.16 39.60 23.16 10.56
## 74 155.28 6.84 37.56 13.20
## 76 20.28 52.44 107.28 10.44
## 77 33.00 1.92 24.84 8.28
## 78 144.60 34.20 17.04 17.04
## 79 6.48 35.88 11.28 6.36
## 80 139.20 9.24 27.72 13.20
## 81 91.68 32.04 26.76 14.16
## 83 90.36 24.36 39.00 13.56
## 84 82.08 53.40 42.72 16.32
## 87 91.56 33.00 19.20 14.40
## 88 132.84 48.72 75.84 19.20
## 89 105.96 30.60 88.08 15.48
## 90 131.76 57.36 61.68 20.04
## 91 161.16 5.88 11.16 13.44
## 92 34.32 1.80 39.60 8.76
## 95 128.88 16.80 13.08 13.80
## 100 162.24 50.04 55.08 20.64
## 106 165.48 55.68 70.80 23.04
## 107 30.00 13.20 35.64 8.64
## 108 108.48 0.36 27.84 10.44
## 109 15.72 0.48 30.72 6.36
## 115 93.84 56.16 41.40 17.52
## 116 90.12 42.00 63.24 15.12
## 117 167.04 17.16 30.72 14.64
## 118 91.68 0.96 17.76 11.28
## 119 150.84 44.28 95.04 19.08
## 120 23.28 19.20 26.76 7.92
## 121 169.56 32.16 55.44 18.60
## 122 22.56 26.04 60.48 8.40
## 124 147.72 41.52 14.88 18.24
## 126 104.64 14.16 31.08 12.72
## 127 9.36 46.68 60.72 7.92
## 128 96.24 0.00 11.04 10.56
## 130 71.52 14.40 51.72 11.64
## 131 0.84 47.52 10.44 1.92
## 133 10.08 32.64 2.52 6.84
## 135 44.28 46.32 78.72 12.96
## 136 57.96 56.40 10.20 13.92
## 137 30.72 46.80 11.16 11.40
## 139 51.60 31.08 24.60 11.52
## 141 88.08 20.40 15.48 13.08
## 144 125.52 6.84 41.28 12.48
## 145 115.44 17.76 46.68 13.68
## 146 168.36 2.28 10.80 12.36
## 149 45.60 48.36 14.28 13.08
## 150 53.64 30.96 24.72 12.12
## 152 145.20 10.08 58.44 13.92
## 156 4.92 13.92 6.84 3.84
## 157 112.68 52.20 60.60 18.36
## 159 14.04 44.28 54.24 8.76
## 160 158.04 22.08 41.52 15.48
## 162 102.84 42.96 59.16 15.96
## 165 140.64 17.64 6.48 14.28
## 167 21.48 45.12 25.92 9.60
## 171 60.00 13.92 22.08 10.08
## 173 23.52 24.12 20.40 9.12
## 183 67.44 6.84 35.64 10.44
## 187 167.40 2.52 31.92 12.36
## 190 22.44 14.52 28.08 8.04
## 191 47.40 49.32 6.96 12.96
## 192 90.60 12.96 7.20 11.88
## 193 20.64 4.92 37.92 7.08
## 195 179.64 42.72 7.20 20.76
## 196 45.84 4.44 16.56 9.12
## 197 113.04 5.88 9.72 11.64#Dummy variable= youtube2
m1<- m1 %>% dplyr::mutate(youtube2=
ifelse(m1$youtube>= med, 1, 0))
regression <- lm(youtube2~facebook+newspaper, data = m1)
summary(regression)##
## Call:
## lm(formula = youtube2 ~ facebook + newspaper, data = m1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.59695 -0.49204 -0.00731 0.50100 0.56415
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4233608 0.0735516 5.756 3.26e-08 ***
## facebook 0.0018651 0.0021356 0.873 0.384
## newspaper 0.0006701 0.0014559 0.460 0.646
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.502 on 197 degrees of freedom
## Multiple R-squared: 0.007256, Adjusted R-squared: -0.002823
## F-statistic: 0.7199 on 2 and 197 DF, p-value: 0.4881# The adjusted r^2 is nearly 0 so this means that the two independent variables don't explain the dependent variable at all.
#The coefficients are not significant at all because the p value is higher than alpha for all independent variables.#ASSUMPTIONS
# Testing homoskedasticity: Breusch-Pagan test
lmtest::bptest(regression)##
## studentized Breusch-Pagan test
##
## data: regression
## BP = 0.69309, df = 2, p-value = 0.7071# Outliers
car::outlierTest(regression) # If Bonferroni p-value < 5%, then that observation is an outlier## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferroni p
## 17 -1.241559 0.21588 NA# Non-independence of errors
car::durbinWatsonTest(regression)## lag Autocorrelation D-W Statistic p-value
## 1 0.01856574 1.952929 0.75
## Alternative hypothesis: rho != 0# Global validation
gv1 <- gvlma::gvlma(regression)
gv1##
## Call:
## lm(formula = youtube2 ~ facebook + newspaper, data = m1)
##
## Coefficients:
## (Intercept) facebook newspaper
## 0.4233608 0.0018651 0.0006701
##
##
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance = 0.05
##
## Call:
## gvlma::gvlma(x = regression)
##
## Value p-value Decision
## Global Stat 3.332e+01 1.027e-06 Assumptions NOT satisfied!
## Skewness 3.266e-05 9.954e-01 Assumptions acceptable.
## Kurtosis 3.236e+01 1.279e-08 Assumptions NOT satisfied!
## Link Function 9.550e-01 3.285e-01 Assumptions acceptable.
## Heteroscedasticity 1.135e-03 9.731e-01 Assumptions acceptable.- Run grouped regressions of sales on facebook and newspaper by using the youtube dummy variable as the grouping variable. Interpret the results. Test the regression assumptions
glimpse(marketing)## Rows: 200
## Columns: 4
## $ youtube <dbl> 276.12, 53.40, 20.64, 181.80, 216.96, 10.44, 69.00, 144.24, …
## $ facebook <dbl> 45.36, 47.16, 55.08, 49.56, 12.96, 58.68, 39.36, 23.52, 2.52…
## $ newspaper <dbl> 83.04, 54.12, 83.16, 70.20, 70.08, 90.00, 28.20, 13.92, 1.20…
## $ sales <dbl> 26.52, 12.48, 11.16, 22.20, 15.48, 8.64, 14.16, 15.84, 5.76,…ggplot(m1, aes(x= youtube, y =sales, col= facebook))
plot(m1$youtube2, m1$facebook)
ggplot(m1,aes(x= youtube2, y= facebook)) + geom_point()
#group 1: youtube2=1
#group 2: youtube2=0
splitdata <- split(m1, m1$youtube2)
above <- splitdata$`1`
below <- splitdata$`0`
above## youtube facebook newspaper sales youtube2
## 1 276.12 45.36 83.04 26.52 1
## 4 181.80 49.56 70.20 22.20 1
## 5 216.96 12.96 70.08 15.48 1
## 10 239.76 3.12 25.44 12.72 1
## 12 257.64 28.80 4.80 20.88 1
## 15 244.92 39.48 55.20 22.80 1
## 16 234.48 57.24 63.48 26.88 1
## 18 337.68 47.52 66.96 29.28 1
## 21 262.08 33.24 64.08 21.60 1
## 22 284.88 6.12 28.20 15.00 1
## 24 273.96 20.28 31.44 18.60 1
## 26 315.48 4.20 23.40 14.40 1
## 28 288.12 20.04 27.48 19.08 1
## 29 298.56 32.52 27.48 22.68 1
## 31 351.48 33.96 51.84 25.68 1
## 34 318.72 24.00 0.36 20.88 1
## 36 348.84 4.92 10.20 15.36 1
## 37 320.28 52.56 6.00 30.48 1
## 40 273.60 45.24 38.40 25.80 1
## 41 243.00 26.76 37.92 19.92 1
## 42 212.40 40.08 46.44 20.52 1
## 43 352.32 33.24 2.16 24.84 1
## 44 248.28 10.08 31.68 15.48 1
## 46 210.12 27.00 37.80 17.88 1
## 48 287.88 49.80 22.20 27.84 1
## 49 272.64 18.96 59.88 17.76 1
## 51 239.76 3.72 41.52 13.68 1
## 53 259.68 50.04 47.52 27.12 1
## 54 219.12 55.44 70.44 25.44 1
## 55 315.24 34.56 19.08 24.24 1
## 56 238.68 59.28 72.00 28.44 1
## 59 252.96 59.52 45.24 28.56 1
## 60 252.84 35.40 11.16 22.08 1
## 62 313.56 51.24 65.64 29.04 1
## 63 287.16 18.60 32.76 18.84 1
## 69 284.88 33.00 13.20 22.68 1
## 70 260.16 52.68 32.64 26.76 1
## 71 238.92 36.72 46.44 21.96 1
## 75 256.08 29.52 15.72 20.40 1
## 82 287.76 4.92 44.28 14.76 1
## 85 256.20 51.60 40.56 26.04 1
## 86 231.84 22.08 78.84 18.24 1
## 93 261.24 40.20 70.80 23.28 1
## 94 301.08 43.80 86.76 26.64 1
## 96 195.96 37.92 63.48 20.28 1
## 97 237.12 4.20 7.08 14.04 1
## 98 221.88 25.20 26.40 18.60 1
## 99 347.64 50.76 61.44 30.48 1
## 101 266.88 5.16 59.76 14.04 1
## 102 355.68 43.56 121.08 28.56 1
## 103 336.24 12.12 25.68 17.76 1
## 104 225.48 20.64 21.48 17.64 1
## 105 285.84 41.16 6.36 24.84 1
## 110 306.48 32.28 6.60 23.76 1
## 111 270.96 9.84 67.80 16.08 1
## 112 290.04 45.60 27.84 26.16 1
## 113 210.84 18.48 2.88 16.92 1
## 114 251.52 24.72 12.84 19.08 1
## 123 268.80 2.88 18.72 13.92 1
## 125 275.40 38.76 89.04 23.64 1
## 129 264.36 58.80 3.84 29.64 1
## 132 318.24 3.48 51.60 15.24 1
## 134 263.76 40.20 54.12 23.52 1
## 138 328.44 34.68 71.64 24.96 1
## 140 221.88 52.68 2.04 24.84 1
## 142 232.44 42.48 90.72 23.04 1
## 143 264.60 39.84 45.48 24.12 1
## 147 288.12 8.76 10.44 15.84 1
## 148 291.84 58.80 53.16 30.48 1
## 151 336.84 16.68 44.40 19.32 1
## 153 237.12 27.96 17.04 19.92 1
## 154 205.56 47.64 45.24 22.80 1
## 155 225.36 25.32 11.40 18.72 1
## 158 179.76 1.56 29.16 12.12 1
## 161 207.00 21.72 36.84 17.28 1
## 163 226.08 21.72 30.72 17.88 1
## 164 196.20 44.16 8.88 21.60 1
## 166 281.40 4.08 101.76 14.28 1
## 168 248.16 6.24 23.28 14.64 1
## 169 258.48 28.32 69.12 20.52 1
## 170 341.16 12.72 7.68 18.00 1
## 172 197.40 25.08 56.88 17.40 1
## 174 202.08 8.52 15.36 14.04 1
## 175 266.88 4.08 15.72 13.80 1
## 176 332.28 58.68 50.16 32.40 1
## 177 298.08 36.24 24.36 24.24 1
## 178 204.24 9.36 42.24 14.04 1
## 179 332.04 2.76 28.44 14.16 1
## 180 198.72 12.00 21.12 15.12 1
## 181 187.92 3.12 9.96 12.60 1
## 182 262.20 6.48 32.88 14.64 1
## 184 345.12 51.60 86.16 31.44 1
## 185 304.56 25.56 36.00 21.12 1
## 186 246.00 54.12 23.52 27.12 1
## 188 229.32 34.44 21.84 20.76 1
## 189 343.20 16.68 4.44 19.08 1
## 194 200.16 50.40 4.32 23.52 1
## 198 212.40 11.16 7.68 15.36 1
## 199 340.32 50.40 79.44 30.60 1
## 200 278.52 10.32 10.44 16.08 1below## youtube facebook newspaper sales youtube2
## 2 53.40 47.16 54.12 12.48 0
## 3 20.64 55.08 83.16 11.16 0
## 6 10.44 58.68 90.00 8.64 0
## 7 69.00 39.36 28.20 14.16 0
## 8 144.24 23.52 13.92 15.84 0
## 9 10.32 2.52 1.20 5.76 0
## 11 79.32 6.96 29.04 10.32 0
## 13 28.56 42.12 79.08 11.04 0
## 14 117.00 9.12 8.64 11.64 0
## 17 81.36 43.92 136.80 15.00 0
## 19 83.04 24.60 21.96 13.56 0
## 20 176.76 28.68 22.92 17.52 0
## 23 15.84 19.08 59.52 6.72 0
## 25 74.76 15.12 21.96 11.64 0
## 27 171.48 35.16 15.12 18.00 0
## 30 84.72 19.20 48.96 12.60 0
## 32 135.48 20.88 46.32 14.28 0
## 33 116.64 1.80 36.00 11.52 0
## 35 114.84 1.68 8.88 11.40 0
## 38 89.64 59.28 54.84 17.64 0
## 39 51.72 32.04 42.12 12.12 0
## 45 30.12 30.84 51.96 10.20 0
## 47 107.64 11.88 42.84 12.72 0
## 50 80.28 14.04 44.16 11.64 0
## 52 120.48 11.52 4.32 12.84 0
## 57 8.76 33.72 49.68 6.60 0
## 58 163.44 23.04 19.92 15.84 0
## 61 64.20 2.40 25.68 9.72 0
## 64 123.24 35.52 10.08 16.80 0
## 65 157.32 51.36 34.68 21.60 0
## 66 82.80 11.16 1.08 11.16 0
## 67 37.80 29.52 2.64 11.40 0
## 68 167.16 17.40 12.24 16.08 0
## 72 131.76 17.16 38.04 14.88 0
## 73 32.16 39.60 23.16 10.56 0
## 74 155.28 6.84 37.56 13.20 0
## 76 20.28 52.44 107.28 10.44 0
## 77 33.00 1.92 24.84 8.28 0
## 78 144.60 34.20 17.04 17.04 0
## 79 6.48 35.88 11.28 6.36 0
## 80 139.20 9.24 27.72 13.20 0
## 81 91.68 32.04 26.76 14.16 0
## 83 90.36 24.36 39.00 13.56 0
## 84 82.08 53.40 42.72 16.32 0
## 87 91.56 33.00 19.20 14.40 0
## 88 132.84 48.72 75.84 19.20 0
## 89 105.96 30.60 88.08 15.48 0
## 90 131.76 57.36 61.68 20.04 0
## 91 161.16 5.88 11.16 13.44 0
## 92 34.32 1.80 39.60 8.76 0
## 95 128.88 16.80 13.08 13.80 0
## 100 162.24 50.04 55.08 20.64 0
## 106 165.48 55.68 70.80 23.04 0
## 107 30.00 13.20 35.64 8.64 0
## 108 108.48 0.36 27.84 10.44 0
## 109 15.72 0.48 30.72 6.36 0
## 115 93.84 56.16 41.40 17.52 0
## 116 90.12 42.00 63.24 15.12 0
## 117 167.04 17.16 30.72 14.64 0
## 118 91.68 0.96 17.76 11.28 0
## 119 150.84 44.28 95.04 19.08 0
## 120 23.28 19.20 26.76 7.92 0
## 121 169.56 32.16 55.44 18.60 0
## 122 22.56 26.04 60.48 8.40 0
## 124 147.72 41.52 14.88 18.24 0
## 126 104.64 14.16 31.08 12.72 0
## 127 9.36 46.68 60.72 7.92 0
## 128 96.24 0.00 11.04 10.56 0
## 130 71.52 14.40 51.72 11.64 0
## 131 0.84 47.52 10.44 1.92 0
## 133 10.08 32.64 2.52 6.84 0
## 135 44.28 46.32 78.72 12.96 0
## 136 57.96 56.40 10.20 13.92 0
## 137 30.72 46.80 11.16 11.40 0
## 139 51.60 31.08 24.60 11.52 0
## 141 88.08 20.40 15.48 13.08 0
## 144 125.52 6.84 41.28 12.48 0
## 145 115.44 17.76 46.68 13.68 0
## 146 168.36 2.28 10.80 12.36 0
## 149 45.60 48.36 14.28 13.08 0
## 150 53.64 30.96 24.72 12.12 0
## 152 145.20 10.08 58.44 13.92 0
## 156 4.92 13.92 6.84 3.84 0
## 157 112.68 52.20 60.60 18.36 0
## 159 14.04 44.28 54.24 8.76 0
## 160 158.04 22.08 41.52 15.48 0
## 162 102.84 42.96 59.16 15.96 0
## 165 140.64 17.64 6.48 14.28 0
## 167 21.48 45.12 25.92 9.60 0
## 171 60.00 13.92 22.08 10.08 0
## 173 23.52 24.12 20.40 9.12 0
## 183 67.44 6.84 35.64 10.44 0
## 187 167.40 2.52 31.92 12.36 0
## 190 22.44 14.52 28.08 8.04 0
## 191 47.40 49.32 6.96 12.96 0
## 192 90.60 12.96 7.20 11.88 0
## 193 20.64 4.92 37.92 7.08 0
## 195 179.64 42.72 7.20 20.76 0
## 196 45.84 4.44 16.56 9.12 0
## 197 113.04 5.88 9.72 11.64 0modelo_above<- lm(sales~facebook+newspaper,data = above)
modelo_below<- lm(sales~facebook+newspaper,data = below)
summary(modelo_above)$coef## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.588688336 0.377873105 33.314592 6.657034e-55
## facebook 0.277368569 0.010158798 27.303286 2.526274e-47
## newspaper 0.007560243 0.006804784 1.111019 2.693066e-01summary(modelo_below)$coef## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.179455291 0.71929513 14.1519870 2.518154e-25
## facebook 0.086432381 0.02270908 3.8060722 2.472636e-04
## newspaper 0.004953095 0.01572088 0.3150648 7.533892e-01#For both groups 1 & 2 the null hypothesis for the coefficient of facebook is rejected
# so facebook coefficient is significant because their P Values are smaller than 5%.
#For both groups 1 & 2 the null hypothesis for the coefficient of newspaper is not rejected
# so facebook coefficient is not significant because their P Values are higher than 5%.#ASSUMPTIONS
# Testing homoskedasticity: Breusch-Pagan test
lmtest::bptest(modelo_above)##
## studentized Breusch-Pagan test
##
## data: modelo_above
## BP = 22.168, df = 2, p-value = 1.536e-05lmtest::bptest(modelo_below)##
## studentized Breusch-Pagan test
##
## data: modelo_below
## BP = 14.371, df = 2, p-value = 0.0007576# Outliers
car::outlierTest(modelo_above) # If Bonferroni p-value < 5%, then that observation is an outlier## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferroni p
## 4 -2.840367 0.005502 0.5502car::outlierTest(modelo_below)## rstudent unadjusted p-value Bonferroni p
## 131 -3.727644 0.00032672 0.032672# Non-independence of errors
car::durbinWatsonTest(modelo_above)## lag Autocorrelation D-W Statistic p-value
## 1 -0.00548723 2.008134 0.974
## Alternative hypothesis: rho != 0car::durbinWatsonTest(modelo_below)## lag Autocorrelation D-W Statistic p-value
## 1 -0.07286263 2.141837 0.492
## Alternative hypothesis: rho != 0# Global validation
gv1 <- gvlma::gvlma(modelo_above)
gv1##
## Call:
## lm(formula = sales ~ facebook + newspaper, data = above)
##
## Coefficients:
## (Intercept) facebook newspaper
## 12.58869 0.27737 0.00756
##
##
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance = 0.05
##
## Call:
## gvlma::gvlma(x = modelo_above)
##
## Value p-value Decision
## Global Stat 0.237117 0.9935 Assumptions acceptable.
## Skewness 0.008739 0.9255 Assumptions acceptable.
## Kurtosis 0.009113 0.9239 Assumptions acceptable.
## Link Function 0.180676 0.6708 Assumptions acceptable.
## Heteroscedasticity 0.038590 0.8443 Assumptions acceptable.gv2 <- gvlma::gvlma(modelo_below)
gv2##
## Call:
## lm(formula = sales ~ facebook + newspaper, data = below)
##
## Coefficients:
## (Intercept) facebook newspaper
## 10.179455 0.086432 0.004953
##
##
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance = 0.05
##
## Call:
## gvlma::gvlma(x = modelo_below)
##
## Value p-value Decision
## Global Stat 6.12328 0.19013 Assumptions acceptable.
## Skewness 4.96138 0.02592 Assumptions NOT satisfied!
## Kurtosis 0.86584 0.35211 Assumptions acceptable.
## Link Function 0.03436 0.85295 Assumptions acceptable.
## Heteroscedasticity 0.26171 0.60895 Assumptions acceptable.