Load the dataset Admissions.csv into R and answer the following questions. Please submit your R file with the appropriate code and discussions (as comments in R code). 1. Randomly split the sample into 80% training and 20% testing. Then train a linear regression to predict Chance_Admit using all possible predictors based on the training sample. Obtain AIC and BIC. Also, compute MSPE based on the testing sample. 2. Continuing from question 1, conduct a forward variable selection using AIC as the criterion. Which variables are selected? Obtain AIC and BIC. Compute MSPE based on the testing sample. 3. Continuing from question 1, conduct a backward variable selection using BIC as the criterion. Which variables are selected? Does it end up Serial_NumGRE_ScoreTOEFL_ScoreUniversity_RatingSOP LOR CGPA Research Chance_of_Admit 1 337 118 4 4.5 4.5 9.65 1 0.92 2 324 107 4 4 4.5 8.87 1 0.76 3 316 104 3 3 3.5 8 1 0.72 4 322 110 3 3.5 2.5 8.67 1 0.8 5 314 103 2 2 3 8.21 0 0.65 6 330 115 5 4.5 3 9.34 1 0.9 7 321 109 3 3 4 8.2 1 0.75 8 308 101 2 3 4 7.9 0 0.68 9 302 102 1 2 1.5 8 0 0.5 10 323 108 3 3.5 3 8.6 0 0.45 11 325 106 3 3.5 4 8.4 1 0.52 12 327 111 4 4 4.5 9 1 0.84 13 328 112 4 4 4.5 9.1 1 0.78 14 307 109 3 4 3 8 1 0.62 15 311 104 3 3.5 2 8.2 1 0.61 16 314 105 3 3.5 2.5 8.3 0 0.54 17 317 107 3 4 3 8.7 0 0.66 18 319 106 3 4 3 8 1 0.65 19 318 110 3 4 3 8.8 0 0.63 20 303 102 3 3.5 3 8.5 0 0.62 21 312 107 3 3 2 7.9 1 0.64 22 325 114 4 3 2 8.4 0 0.7 23 328 116 5 5 5 9.5 1 0.94 24 334 119 5 5 4.5 9.7 1 0.95 25 336 119 5 4 3.5 9.8 1 0.97 26 340 120 5 4.5 4.5 9.6 1 0.94 27 322 109 5 4.5 3.5 8.8 0 0.76 28 298 98 2 1.5 2.5 7.5 1 0.44 29 295 93 1 2 2 7.2 0 0.46 30 310 99 2 1.5 2 7.3 0 0.54 31 300 97 2 3 3 8.1 1 0.65 32 327 103 3 4 4 8.3 1 0.74 33 338 118 4 3 4.5 9.4 1 0.91 34 340 114 5 4 4 9.6 1 0.9 35 331 112 5 4 5 9.8 1 0.94 36 320 110 5 5 5 9.2 1 0.88 37 299 106 2 4 4 8.4 0 0.64 38 300 105 1 1 2 7.8 0 0.58 39 304 105 1 3 1.5 7.5 0 0.52 40 307 108 2 4 3.5 7.7 0 0.48 41 308 110 3 3.5 3 8 1 0.46 42 316 105 2 2.5 2.5 8.2 1 0.49 43 313 107 2 2.5 2 8.5 1 0.53 44 332 117 4 4.5 4 9.1 0 0.87 45 326 113 5 4.5 4 9.4 1 0.91 46 322 110 5 5 4 9.1 1 0.88 47 329 114 5 4 5 9.3 1 0.86 48 339 119 5 4.5 4 9.7 0 0.89 49 321 110 3 3.5 5 8.85 1 0.82 50 327 111 4 3 4 8.4 1 0.78 51 313 98 3 2.5 4.5 8.3 1 0.76 52 312 100 2 1.5 3.5 7.9 1 0.56 53 334 116 4 4 3 8 1 0.78 54 324 112 4 4 2.5 8.1 1 0.72 55 322 110 3 3 3.5 8 0 0.7 56 320 103 3 3 3 7.7 0 0.64 57 316 102 3 2 3 7.4 0 0.64 58 298 99 2 4 2 7.6 0 0.46 59 300 99 1 3 2 6.8 1 0.36 60 311 104 2 2 2 8.3 0 0.42 61 309 100 2 3 3 8.1 0 0.48 62 307 101 3 4 3 8.2 0 0.47 63 304 105 2 3 3 8.2 1 0.54 64 315 107 2 4 3 8.5 1 0.56 65 325 111 3 3 3.5 8.7 0 0.52 66 325 112 4 3.5 3.5 8.92 0 0.55 67 327 114 3 3 3 9.02 0 0.61 68 316 107 2 3.5 3.5 8.64 1 0.57 69 318 109 3 3.5 4 9.22 1 0.68 70 328 115 4 4.5 4 9.16 1 0.78 71 332 118 5 5 5 9.64 1 0.94 72 336 112 5 5 5 9.76 1 0.96 73 321 111 5 5 5 9.45 1 0.93 74 314 108 4 4.5 4 9.04 1 0.84 75 314 106 3 3 5 8.9 0 0.74 76 329 114 2 2 4 8.56 1 0.72 77 327 112 3 3 3 8.72 1 0.74 78 301 99 2 3 2 8.22 0 0.64 79 296 95 2 3 2 7.54 1 0.44 80 294 93 1 1.5 2 7.36 0 0.46 81 312 105 3 2 3 8.02 1 0.5 82 340 120 4 5 5 9.5 1 0.96 83 320 110 5 5 4.5 9.22 1 0.92 84 322 115 5 4 4.5 9.36 1 0.92 85 340 115 5 4.5 4.5 9.45 1 0.94 86 319 103 4 4.5 3.5 8.66 0 0.76 87 315 106 3 4.5 3.5 8.42 0 0.72 88 317 107 2 3.5 3 8.28 0 0.66 89 314 108 3 4.5 3.5 8.14 0 0.64 90 316 109 4 4.5 3.5 8.76 1 0.74 91 318 106 2 4 4 7.92 1 0.64 92 299 97 3 5 3.5 7.66 0 0.38 93 298 98 2 4 3 8.03 0 0.34 94 301 97 2 3 3 7.88 1 0.44 95 303 99 3 2 2.5 7.66 0 0.36 96 304 100 4 1.5 2.5 7.84 0 0.42 97 306 100 2 3 3 8 0 0.48 98 331 120 3 4 4 8.96 1 0.86 99 332 119 4 5 4.5 9.24 1 0.9 100 323 113 3 4 4 8.88 1 0.79 101 322 107 3 3.5 3.5 8.46 1 0.71 102 312 105 2 2.5 3 8.12 0 0.64 103 314 106 2 4 3.5 8.25 0 0.62 104 317 104 2 4.5 4 8.47 0 0.57 105 326 112 3 3.5 3 9.05 1 0.74 106 316 110 3 4 4.5 8.78 1 0.69 107 329 111 4 4.5 4.5 9.18 1 0.87 108 338 117 4 3.5 4.5 9.46 1 0.91 109 331 116 5 5 5 9.38 1 0.93 110 304 103 5 5 4 8.64 0 0.68 111 305 108 5 3 3 8.48 0 0.61 112 321 109 4 4 4 8.68 1 0.69 113 301 107 3 3.5 3.5 8.34 1 0.62 114 320 110 2 4 3.5 8.56 0 0.72 115 311 105 3 3.5 3 8.45 1 0.59 116 310 106 4 4.5 4.5 9.04 1 0.66 117 299 102 3 4 3.5 8.62 0 0.56 118 290 104 4 2 2.5 7.46 0 0.45 119 296 99 2 3 3.5 7.28 0 0.47 120 327 104 5 3 3.5 8.84 1 0.71 121 335 117 5 5 5 9.56 1 0.94 122 334 119 5 4.5 4.5 9.48 1 0.94 123 310 106 4 1.5 2.5 8.36 0 0.57 124 308 108 3 3.5 3.5 8.22 0 0.61 125 301 106 4 2.5 3 8.47 0 0.57 126 300 100 3 2 3 8.66 1 0.64 127 323 113 3 4 3 9.32 1 0.85 128 319 112 3 2.5 2 8.71 1 0.78 129 326 112 3 3.5 3 9.1 1 0.84 130 333 118 5 5 5 9.35 1 0.92 131 339 114 5 4 4.5 9.76 1 0.96 132 303 105 5 5 4.5 8.65 0 0.77 133 309 105 5 3.5 3.5 8.56 0 0.71 134 323 112 5 4 4.5 8.78 0 0.79 135 333 113 5 4 4 9.28 1 0.89 136 314 109 4 3.5 4 8.77 1 0.82 137 312 103 3 5 4 8.45 0 0.76 138 316 100 2 1.5 3 8.16 1 0.71 139 326 116 2 4.5 3 9.08 1 0.8 140 318 109 1 3.5 3.5 9.12 0 0.78 141 329 110 2 4 3 9.15 1 0.84 142 332 118 2 4.5 3.5 9.36 1 0.9 143 331 115 5 4 3.5 9.44 1 0.92 144 340 120 4 4.5 4 9.92 1 0.97 145 325 112 2 3 3.5 8.96 1 0.8 146 320 113 2 2 2.5 8.64 1 0.81 147 315 105 3 2 2.5 8.48 0 0.75 148 326 114 3 3 3 9.11 1 0.83 149 339 116 4 4 3.5 9.8 1 0.96 150 311 106 2 3.5 3 8.26 1 0.79 151 334 114 4 4 4 9.43 1 0.93 152 332 116 5 5 5 9.28 1 0.94 153 321 112 5 5 5 9.06 1 0.86 154 324 105 3 3 4 8.75 0 0.79 155 326 108 3 3 3.5 8.89 0 0.8 156 312 109 3 3 3 8.69 0 0.77 157 315 105 3 2 2.5 8.34 0 0.7 158 309 104 2 2 2.5 8.26 0 0.65 159 306 106 2 2 2.5 8.14 0 0.61 160 297 100 1 1.5 2 7.9 0 0.52 161 315 103 1 1.5 2 7.86 0 0.57 162 298 99 1 1.5 3 7.46 0 0.53 163 318 109 3 3 3 8.5 0 0.67 164 317 105 3 3.5 3 8.56 0 0.68 165 329 111 4 4.5 4 9.01 1 0.81 166 322 110 5 4.5 4 8.97 0 0.78 167 302 102 3 3.5 5 8.33 0 0.65 168 313 102 3 2 3 8.27 0 0.64 169 293 97 2 2 4 7.8 1 0.64 170 311 99 2 2.5 3 7.98 0 0.65 171 312 101 2 2.5 3.5 8.04 1 0.68 172 334 117 5 4 4.5 9.07 1 0.89 173 322 110 4 4 5 9.13 1 0.86 174 323 113 4 4 4.5 9.23 1 0.89 175 321 111 4 4 4 8.97 1 0.87 176 320 111 4 4.5 3.5 8.87 1 0.85 177 329 119 4 4.5 4.5 9.16 1 0.9 178 319 110 3 3.5 3.5 9.04 0 0.82 179 309 108 3 2.5 3 8.12 0 0.72 180 307 102 3 3 3 8.27 0 0.73 181 300 104 3 3.5 3 8.16 0 0.71 182 305 107 2 2.5 2.5 8.42 0 0.71 183 299 100 2 3 3.5 7.88 0 0.68 184 314 110 3 4 4 8.8 0 0.75 185 316 106 2 2.5 4 8.32 0 0.72 186 327 113 4 4.5 4.5 9.11 1 0.89 187 317 107 3 3.5 3 8.68 1 0.84 188 335 118 5 4.5 3.5 9.44 1 0.93 189 331 115 5 4.5 3.5 9.36 1 0.93 190 324 112 5 5 5 9.08 1 0.88 191 324 111 5 4.5 4 9.16 1 0.9 192 323 110 5 4 5 8.98 1 0.87 193 322 114 5 4.5 4 8.94 1 0.86 194 336 118 5 4.5 5 9.53 1 0.94 195 316 109 3 3.5 3 8.76 0 0.77 196 307 107 2 3 3.5 8.52 1 0.78 197 306 105 2 3 2.5 8.26 0 0.73 198 310 106 2 3.5 2.5 8.33 0 0.73 199 311 104 3 4.5 4.5 8.43 0 0.7 200 313 107 3 4 4.5 8.69 0 0.72 201 317 103 3 2.5 3 8.54 1 0.73 202 315 110 2 3.5 3 8.46 1 0.72 203 340 120 5 4.5 4.5 9.91 1 0.97 204 334 120 5 4 5 9.87 1 0.97 205 298 105 3 3.5 4 8.54 0 0.69 206 295 99 2 2.5 3 7.65 0 0.57 207 315 99 2 3.5 3 7.89 0 0.63 208 310 102 3 3.5 4 8.02 1 0.66 209 305 106 2 3 3 8.16 0 0.64 210 301 104 3 3.5 4 8.12 1 0.68 211 325 108 4 4.5 4 9.06 1 0.79 212 328 110 4 5 4 9.14 1 0.82 213 338 120 4 5 5 9.66 1 0.95 214 333 119 5 5 4.5 9.78 1 0.96 215 331 117 4 4.5 5 9.42 1 0.94 216 330 116 5 5 4.5 9.36 1 0.93 217 322 112 4 4.5 4.5 9.26 1 0.91 218 321 109 4 4 4 9.13 1 0.85 219 324 110 4 3 3.5 8.97 1 0.84 220 312 104 3 3.5 3.5 8.42 0 0.74 221 313 103 3 4 4 8.75 0 0.76 222 316 110 3 3.5 4 8.56 0 0.75 223 324 113 4 4.5 4 8.79 0 0.76 224 308 109 2 3 4 8.45 0 0.71 225 305 105 2 3 2 8.23 0 0.67 226 296 99 2 2.5 2.5 8.03 0 0.61 227 306 110 2 3.5 4 8.45 0 0.63 228 312 110 2 3.5 3 8.53 0 0.64 229 318 112 3 4 3.5 8.67 0 0.71 230 324 111 4 3 3 9.01 1 0.82 231 313 104 3 4 4.5 8.65 0 0.73 232 319 106 3 3.5 2.5 8.33 1 0.74 233 312 107 2 2.5 3.5 8.27 0 0.69 234 304 100 2 2.5 3.5 8.07 0 0.64 235 330 113 5 5 4 9.31 1 0.91 236 326 111 5 4.5 4 9.23 1 0.88 237 325 112 4 4 4.5 9.17 1 0.85 238 329 114 5 4.5 5 9.19 1 0.86 239 310 104 3 2 3.5 8.37 0 0.7 240 299 100 1 1.5 2 7.89 0 0.59 241 296 101 1 2.5 3 7.68 0 0.6 242 317 103 2 2.5 2 8.15 0 0.65 243 324 115 3 3.5 3 8.76 1 0.7 244 325 114 3 3.5 3 9.04 1 0.76 245 314 107 2 2.5 4 8.56 0 0.63 246 328 110 4 4 2.5 9.02 1 0.81 247 316 105 3 3 3.5 8.73 0 0.72 248 311 104 2 2.5 3.5 8.48 0 0.71 249 324 110 3 3.5 4 8.87 1 0.8 250 321 111 3 3.5 4 8.83 1 0.77 251 320 104 3 3 2.5 8.57 1 0.74 252 316 99 2 2.5 3 9 0 0.7 253 318 100 2 2.5 3.5 8.54 1 0.71 254 335 115 4 4.5 4.5 9.68 1 0.93 255 321 114 4 4 5 9.12 0 0.85 256 307 110 4 4 4.5 8.37 0 0.79 257 309 99 3 4 4 8.56 0 0.76 258 324 100 3 4 5 8.64 1 0.78 259 326 102 4 5 5 8.76 1 0.77 260 331 119 4 5 4.5 9.34 1 0.9 261 327 108 5 5 3.5 9.13 1 0.87 262 312 104 3 3.5 4 8.09 0 0.71 263 308 103 2 2.5 4 8.36 1 0.7 264 324 111 3 2.5 1.5 8.79 1 0.7 265 325 110 2 3 2.5 8.76 1 0.75 266 313 102 3 2.5 2.5 8.68 0 0.71 267 312 105 2 2 2.5 8.45 0 0.72 268 314 107 3 3 3.5 8.17 1 0.73 269 327 113 4 4.5 5 9.14 0 0.83 270 308 108 4 4.5 5 8.34 0 0.77 271 306 105 2 2.5 3 8.22 1 0.72 272 299 96 2 1.5 2 7.86 0 0.54 273 294 95 1 1.5 1.5 7.64 0 0.49 274 312 99 1 1 1.5 8.01 1 0.52 275 315 100 1 2 2.5 7.95 0 0.58 276 322 110 3 3.5 3 8.96 1 0.78 277 329 113 5 5 4.5 9.45 1 0.89 278 320 101 2 2.5 3 8.62 0 0.7 279 308 103 2 3 3.5 8.49 0 0.66 280 304 102 2 3 4 8.73 0 0.67 281 311 102 3 4.5 4 8.64 1 0.68 282 317 110 3 4 4.5 9.11 1 0.8 283 312 106 3 4 3.5 8.79 1 0.81 284 321 111 3 2.5 3 8.9 1 0.8 285 340 112 4 5 4.5 9.66 1 0.94 286 331 116 5 4 4 9.26 1 0.93 287 336 118 5 4.5 4 9.19 1 0.92 288 324 114 5 5 4.5 9.08 1 0.89 289 314 104 4 5 5 9.02 0 0.82 290 313 109 3 4 3.5 9 0 0.79 291 307 105 2 2.5 3 7.65 0 0.58 292 300 102 2 1.5 2 7.87 0 0.56 293 302 99 2 1 2 7.97 0 0.56 294 312 98 1 3.5 3 8.18 1 0.64 295 316 101 2 2.5 2 8.32 1 0.61 296 317 100 2 3 2.5 8.57 0 0.68 297 310 107 3 3.5 3.5 8.67 0 0.76 298 320 120 3 4 4.5 9.11 0 0.86 299 330 114 3 4.5 4.5 9.24 1 0.9 300 305 112 3 3 3.5 8.65 0 0.71 301 309 106 2 2.5 2.5 8 0 0.62 302 319 108 2 2.5 3 8.76 0 0.66 303 322 105 2 3 3 8.45 1 0.65 304 323 107 3 3.5 3.5 8.55 1 0.73 305 313 106 2 2.5 2 8.43 0 0.62 306 321 109 3 3.5 3.5 8.8 1 0.74 307 323 110 3 4 3.5 9.1 1 0.79 308 325 112 4 4 4 9 1 0.8 309 312 108 3 3.5 3 8.53 0 0.69 310 308 110 4 3.5 3 8.6 0 0.7 311 320 104 3 3 3.5 8.74 1 0.76 312 328 108 4 4.5 4 9.18 1 0.84 313 311 107 4 4.5 4.5 9 1 0.78 314 301 100 3 3.5 3 8.04 0 0.67 315 305 105 2 3 4 8.13 0 0.66 316 308 104 2 2.5 3 8.07 0 0.65 317 298 101 2 1.5 2 7.86 0 0.54 318 300 99 1 1 2.5 8.01 0 0.58 319 324 111 3 2.5 2 8.8 1 0.79 320 327 113 4 3.5 3 8.69 1 0.8 321 317 106 3 4 3.5 8.5 1 0.75 322 323 104 3 4 4 8.44 1 0.73 323 314 107 2 2.5 4 8.27 0 0.72 324 305 102 2 2 2.5 8.18 0 0.62 325 315 104 3 3 2.5 8.33 0 0.67 326 326 116 3 3.5 4 9.14 1 0.81 327 299 100 3 2 2 8.02 0 0.63 328 295 101 2 2.5 2 7.86 0 0.69 329 324 112 4 4 3.5 8.77 1 0.8 330 297 96 2 2.5 1.5 7.89 0 0.43 331 327 113 3 3.5 3 8.66 1 0.8 332 311 105 2 3 2 8.12 1 0.73 333 308 106 3 3.5 2.5 8.21 1 0.75 334 319 108 3 3 3.5 8.54 1 0.71 335 312 107 4 4.5 4 8.65 1 0.73 336 325 111 4 4 4.5 9.11 1 0.83 337 319 110 3 3 2.5 8.79 0 0.72 338 332 118 5 5 5 9.47 1 0.94 339 323 108 5 4 4 8.74 1 0.81 340 324 107 5 3.5 4 8.66 1 0.81 341 312 107 3 3 3 8.46 1 0.75 342 326 110 3 3.5 3.5 8.76 1 0.79 343 308 106 3 3 3 8.24 0 0.58 344 305 103 2 2.5 3.5 8.13 0 0.59 345 295 96 2 1.5 2 7.34 0 0.47 346 316 98 1 1.5 2 7.43 0 0.49 347 304 97 2 1.5 2 7.64 0 0.47 348 299 94 1 1 1 7.34 0 0.42 349 302 99 1 2 2 7.25 0 0.57 350 313 101 3 2.5 3 8.04 0 0.62 351 318 107 3 3 3.5 8.27 1 0.74 352 325 110 4 3.5 4 8.67 1 0.73 353 303 100 2 3 3.5 8.06 1 0.64 354 300 102 3 3.5 2.5 8.17 0 0.63 355 297 98 2 2.5 3 7.67 0 0.59 356 317 106 2 2 3.5 8.12 0 0.73 357 327 109 3 3.5 4 8.77 1 0.79 358 301 104 2 3.5 3.5 7.89 1 0.68 359 314 105 2 2.5 2 7.64 0 0.7 360 321 107 2 2 1.5 8.44 0 0.81 361 322 110 3 4 5 8.64 1 0.85 362 334 116 4 4 3.5 9.54 1 0.93 363 338 115 5 4.5 5 9.23 1 0.91 364 306 103 2 2.5 3 8.36 0 0.69 365 313 102 3 3.5 4 8.9 1 0.77 366 330 114 4 4.5 3 9.17 1 0.86 367 320 104 3 3.5 4.5 8.34 1 0.74 368 311 98 1 1 2.5 7.46 0 0.57 369 298 92 1 2 2 7.88 0 0.51 370 301 98 1 2 3 8.03 1 0.67 371 310 103 2 2.5 2.5 8.24 0 0.72 372 324 110 3 3.5 3 9.22 1 0.89 373 336 119 4 4.5 4 9.62 1 0.95 374 321 109 3 3 3 8.54 1 0.79 375 315 105 2 2 2.5 7.65 0 0.39 376 304 101 2 2 2.5 7.66 0 0.38 377 297 96 2 2.5 2 7.43 0 0.34 378 290 100 1 1.5 2 7.56 0 0.47 379 303 98 1 2 2.5 7.65 0 0.56 380 311 99 1 2.5 3 8.43 1 0.71 381 322 104 3 3.5 4 8.84 1 0.78 382 319 105 3 3 3.5 8.67 1 0.73 383 324 110 4 4.5 4 9.15 1 0.82 384 300 100 3 3 3.5 8.26 0 0.62 385 340 113 4 5 5 9.74 1 0.96 386 335 117 5 5 5 9.82 1 0.96 387 302 101 2 2.5 3.5 7.96 0 0.46 388 307 105 2 2 3.5 8.1 0 0.53 389 296 97 2 1.5 2 7.8 0 0.49 390 320 108 3 3.5 4 8.44 1 0.76 391 314 102 2 2 2.5 8.24 0 0.64 392 318 106 3 2 3 8.65 0 0.71 393 326 112 4 4 3.5 9.12 1 0.84 394 317 104 2 3 3 8.76 0 0.77 395 329 111 4 4.5 4 9.23 1 0.89 396 324 110 3 3.5 3.5 9.04 1 0.82 397 325 107 3 3 3.5 9.11 1 0.84 398 330 116 4 5 4.5 9.45 1 0.91 399 312 103 3 3.5 4 8.78 0 0.67 400 333 117 4 5 4 9.66 1 0.95