For this assignment use the data set senic.xlsx. This data set consists of a random sample of 113 hospitals. The objective is to study the infection risk and what factors influence it. The variables from the data set are: Variable Name Identification number Length of stay Age Infection risk Routing culturing ratio Routine chest X-ray ratio Number of beds Medical school affiliation Average daily census Number of nurses Available facilities and services Description 1-113 Average length of stay in hospital (in days) Average age of patients (in years) Average estimated probability of acquiring infection in hospital (in percent) Ratio of number of cultures performed to number of patients without signs or symptoms of pneumonia, times 100 Ratio of number of X-rays performed to number of patients without signs or symptoms of pneumonia, times 100 Average number of beds in hospital 0 = Yes, 1 = No Average number of patients in hospital per day Average number of full-time licensed practical nurses Percent of 35 potential facilities and services that are provided by the hospital The goal is to fit the best multiple regression model to the response (infection risk). Do an analysis using the first 108 observations. Use the stepwise regression method to see which model is the best. Repeat using subset regression. Do they agree? Are there any outliers in the data? Look for x-outliers, y-outliers, and high-influence points. Come up with one model that you think best describes the data and can be used for future predictions. Show the residual plot for this one. Does the model seem appropriate? Use this model to predict (using prediction interval) y for the last 5 observations of the data and see if the model is doing well. id stay 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 age 7.13 8.82 8.34 8.95 11.2 9.76 9.68 11.18 8.67 8.84 11.07 8.3 12.78 7.58 9 11.08 8.28 11.62 9.06 9.35 7.53 10.24 9.78 9.84 9.2 8.28 9.31 8.19 11.65 9.89 11.03 9.84 11.77 13.59 9.74 10.33 9.97 7.84 10.47 8.16 8.48 10.72 11.2 10.12 8.37 10.16 19.56 risk 55.7 58.2 56.9 53.7 56.5 50.9 57.8 45.7 48.2 56.3 53.2 57.2 56.8 56.7 56.3 50.2 48.1 53.9 52.8 53.8 42 49 52.3 62.2 52.2 49.5 47.2 52.1 54.5 50.5 49.9 53 54.1 54 54.4 55.8 58.2 49.1 53.2 60.9 51.1 53.8 45 51.7 50.7 54.2 59.9 culturing xray beds 4.1 9 39.6 1.6 3.8 51.7 2.7 8.1 74 5.6 18.9 122.8 5.7 34.5 88.9 5.1 21.9 97 4.6 16.7 79 5.4 60.5 85.8 4.3 24.4 90.8 6.3 29.6 82.6 4.9 28.5 122 4.3 6.8 83.8 7.7 46 116.9 3.7 20.8 88 4.2 14.6 76.4 5.5 18.6 63.6 4.5 26 101.8 6.4 25.5 99.2 4.2 6.9 75.9 4.1 15.9 80.9 4.2 23.1 98.9 4.8 36.3 112.6 5 17.6 95.9 4.8 12 82.3 4 17.5 71.1 3.9 12 113.1 4.5 30.2 101.3 3.2 10.8 59.2 4.4 18.6 96.1 4.9 17.7 103.6 5 19.7 102.1 5.2 17.7 72.6 5.3 17.3 56 6.1 24.2 111.7 6.3 11.4 76.1 5 21.2 104.3 2.8 16.5 76.5 4.6 7.1 87.9 4.1 5.7 69.1 1.3 1.9 58 3.7 12.1 92.8 4.7 23.2 94.1 3 7 78.9 5.6 14.9 79.1 5.5 15.1 84.8 4.6 8.4 51.5 6.5 17.2 113.7 school 279 80 107 147 180 150 186 640 182 85 768 167 322 97 72 387 108 133 134 833 95 195 270 600 298 546 170 176 248 167 318 210 196 312 221 266 90 60 196 73 166 113 130 362 115 831 306 census nurses 1 207 241 1 51 52 1 82 54 1 53 148 1 134 151 1 147 106 1 151 129 0 399 360 1 130 118 1 59 66 0 591 656 1 105 59 0 252 349 1 59 79 1 61 38 1 326 405 1 84 73 1 113 101 1 103 125 1 547 519 1 47 49 1 163 170 0 240 198 1 468 497 0 244 236 0 413 436 1 124 173 1 156 88 1 217 189 1 113 106 1 270 335 1 200 239 1 164 165 1 258 169 1 170 172 1 181 149 1 69 42 1 50 45 1 168 153 1 49 21 1 145 118 1 90 107 1 95 56 0 313 264 1 96 88 0 581 629 1 273 172 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 10.9 7.67 8.88 11.48 9.23 11.41 12.07 8.63 11.15 7.14 7.65 10.73 11.46 10.42 11.18 7.93 9.66 7.78 9.42 10.02 8.58 9.61 8.03 7.39 7.08 9.53 10.05 8.45 6.7 8.9 10.23 8.88 10.3 10.79 7.94 7.63 8.77 8.09 9.05 7.91 10.39 9.36 11.41 8.86 8.93 8.92 8.15 9.77 57.2 51.7 51.5 57.6 51.6 61.1 43.7 54 56.5 59 47.1 50.6 56.9 58 51 64.1 52.1 45.5 50.6 49.5 55 52.4 54.2 51 52 51.5 52 38.8 48.6 49.7 53.2 55.8 59.6 44.2 49.5 52.1 54.5 56.9 51.2 52.8 54.6 54.1 50.4 51.3 56 53.9 54.9 50.2 5.5 1.8 4.2 5.6 4.3 7.6 7.8 3.1 3.9 3.7 4.3 3.9 4.5 3.4 5.7 5.4 4.4 5 4.3 4.4 3.7 4.5 3.5 4.2 2 5.2 4.5 3.4 4.5 2.9 4.9 4.4 5.1 2.9 3.5 5.5 4.7 1.7 4.1 2.9 4.3 4.8 5.8 2.9 2 1.3 5.3 5.3 10.6 2.5 10.1 20.3 11.6 16.6 52.4 8.4 7.7 2.6 16.4 19.3 15.6 8 18.8 7.5 9.9 20.9 24.8 8.3 7.4 6.9 24.3 14.6 12.3 15 36.7 12.9 13 12.7 9.9 14.1 27.8 2.6 6.2 11.6 5.2 7.6 20.5 11.9 14 18.3 23.8 9.5 6.2 2.2 12.3 15.7 71.9 40.4 86.9 82 42.6 97.9 105.3 56.2 73.9 75.8 65.7 101 97.7 59 55.9 98.1 98.3 71.6 62.8 93 95.9 87.2 87.3 88.4 56.4 65.7 87.5 85 80.8 86.9 77.9 76.8 88.9 56.6 92.3 61.1 47 56.9 79.8 79.5 88.3 90.6 73 87.5 72.5 79.5 79.8 89.7 593 106 305 252 620 535 157 76 281 70 318 445 191 119 595 68 83 489 508 265 304 487 97 72 87 298 184 235 76 52 752 237 175 461 195 197 143 92 195 477 353 165 424 100 95 56 99 154 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 446 93 238 207 413 330 115 39 217 37 265 374 153 67 546 42 66 391 421 191 248 404 65 38 52 241 144 143 51 37 595 165 113 320 139 109 85 61 127 349 223 127 359 65 59 40 55 123 211 35 197 251 420 273 76 44 199 35 314 345 132 64 392 49 95 329 528 202 218 220 55 67 57 193 151 124 79 35 446 182 73 196 116 110 87 61 112 188 200 158 335 53 56 14 71 148 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 8.54 8.66 12.01 7.95 10.15 9.76 9.89 7.14 13.95 9.44 10.8 7.14 8.02 11.8 9.5 7.7 17.94 9.41 56.1 52.8 52.8 51.8 51.9 53.2 45.2 57.6 65.9 52.5 63.9 51.7 55 53.8 49.3 56.9 56.2 59.5 2.5 3.8 4.8 2.3 6.2 2.6 4.3 2.7 6.6 4.5 2.9 1.4 2.1 5.7 5.8 4.4 5.9 3.1 27 6.8 10.8 4.6 16.4 6.9 11.8 13.1 15.6 10.9 1.6 4.1 3.8 9.1 42 12.2 26.4 20.6 82.5 69.5 96.9 54.9 59.2 80.1 108.7 92.6 133.5 58.5 57.4 45.7 46.5 116.9 70.9 67.9 91.8 91.7 98 246 298 163 568 64 190 92 356 297 130 115 91 571 98 129 835 29 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 57 178 237 128 452 47 141 40 308 230 69 90 44 441 68 85 791 20 75 177 115 93 371 55 112 50 182 263 62 19 32 469 46 136 407 22 facilities 60 40 20 40 40 40 40 60 40 40 80 40 57.1 37.1 17.1 57.1 37.1 37.1 37.1 77.1 17.1 37.1 57.1 57.1 57.1 57.1 37.1 37.1 37.1 37.1 57.1 54.3 34.3 54.3 54.3 54.3 34.3 34.3 54.3 14.3 34.3 34.3 34.3 54.3 34.3 74.3 51.4 51.4 11.4 51.4 51.4 71.4 51.4 31.4 31.4 51.4 31.4 51.4 51.4 31.4 31.4 68.6 28.6 28.6 48.6 48.6 48.6 48.6 48.6 28.6 28.6 28.6 48.6 68.6 48.6 28.6 28.6 68.6 48.6 45.7 65.7 45.7 45.7 25.7 45.7 45.7 65.7 65.7 45.7 45.7 25.7 25.7 5.7 25.7 25.7 45.7 45.7 45.7 42.9 62.9 22.9 42.9 22.9 62.9 42.9 22.9 22.9 22.9 62.9 22.9 62.9 62.9 22.9