Qn. 8.40. Refer to the SENIC data set in Appendix C.1. Infection risk (Y ) is to be regressed against length of stay (X1), age (X2), routine chest X-ray ratio (X3), and medical school affiliation (X4).

a. Fit a first-order regression model. Let X4 = 1 if the hospital has medical school affiliation and 0 if not.

b. Estimate the effect of medical school affiliation on infection risk using a 98 percent confidence interval. Interpret your interval estimate.

c. It has been suggested that the effect of medical school affiliation on infection risk may interact with the effects of age and routine chest X-ray ratio. Add appropriate interaction terms to the regression model, fit the revised regression model, and test whether the interaction term is helpful: use = .10. State the alternatives, decision rules, and conclusions.

The following variables are available.

id: id of hospitals

X1: Length of stay: Average length of stay of all patients in the hospital (measured in days)

X2: Age :Average age of patients (in years)

X3: Infection Risk: Average estimated probability of acquiring infection in hospital (in percent)

X4: Routine Culturing Ratio: Ratio of number of cultures performed to number of patients without signs or symptoms of hospital-acquired infection, times 100

X5: Routine Chest X-ray Ratio: Ratio of number of X-rays performed to number of patients without signs or symptoms of pneumonia, times 100

X6: Number of Beds: Average number of beds in hospital during study period

X7: Medical School Affiliation:1=Yes, 2=No

X8: Region: Geographic Region, where 1=NE, 2=NC, 3=S, 4=W

X9: Average Daily Census: Average number of patients in hospital per day during study period

X10: Number of Nurses: Average number of full-time equivalent registered and licensed practical nurses

X11: Available Facilities and Services: Percent of 35 potential facilities and services that are provided by the hospital

The list below is the dataset for this project.

id length age risk culture xray beds school region census nurses facility 1 7.13 55.7 4.1 9.0 39.6 279 2 4 207 241 60.0 2 8.82 58.2 1.6 3.8 51.7 80 2 2 51 52 40.0 3 8.34 56.9 2.7 8.1 74.0 107 2 3 82 54 20.0 4 8.95 53.7 5.6 18.9 122.8 147 2 4 53 148 40.0 5 11.20 56.5 5.7 34.5 88.9 180 2 1 134 151 40.0 6 9.76 50.9 5.1 21.9 97.0 150 2 2 147 106 40.0 7 9.68 57.8 4.6 16.7 79.0 186 2 3 151 129 40.0 8 11.18 45.7 5.4 60.5 85.8 640 1 2 399 360 60.0 9 8.67 48.2 4.3 24.4 90.8 182 2 3 130 118 40.0 10 8.84 56.3 6.3 29.6 82.6 85 2 1 59 66 40.0 11 11.07 53.2 4.9 28.5 122.0 768 1 1 591 656 80.0 12 8.30 57.2 4.3 6.8 83.8 167 2 3 105 59 40.0 13 12.78 56.8 7.7 46.0 116.9 322 1 1 252 349 57.1 14 7.58 56.7 3.7 20.8 88.0 97 2 2 59 79 37.1 15 9.00 56.3 4.2 14.6 76.4 72 2 3 61 38 17.1 16 11.08 50.2 5.5 18.6 63.6 387 2 3 326 405 57.1 17 8.28 48.1 4.5 26.0 101.8 108 2 4 84 73 37.1 18 11.62 53.9 6.4 25.5 99.2 133 2 1 113 101 37.1 19 9.06 52.8 4.2 6.9 75.9 134 2 2 103 125 37.1 20 9.35 53.8 4.1 15.9 80.9 833 2 3 547 519 77.1 21 7.53 42.0 4.2 23.1 98.9 95 2 4 47 49 17.1 22 10.24 49.0 4.8 36.3 112.6 195 2 2 163 170 37.1 23 9.78 52.3 5.0 17.6 95.9 270 1 1 240 198 57.1 24 9.84 62.2 4.8 12.0 82.3 600 2 3 468 497 57.1 25 9.20 52.2 4.0 17.5 71.1 298 1 4 244 236 57.1 26 8.28 49.5 3.9 12.0 113.1 546 1 2 413 436 57.1 27 9.31 47.2 4.5 30.2 101.3 170 2 1 124 173 37.1 28 8.19 52.1 3.2 10.8 59.2 176 2 1 156 88 37.1 29 11.65 54.5 4.4 18.6 96.1 248 2 1 217 189 37.1 30 9.89 50.5 4.9 17.7 103.6 167 2 2 113 106 37.1 31 11.03 49.9 5.0 19.7 102.1 318 2 1 270 335 57.1 32 9.84 53.0 5.2 17.7 72.6 210 2 2 200 239 54.3 33 11.77 54.1 5.3 17.3 56.0 196 2 1 164 165 34.3 34 13.59 54.0 6.1 24.2 111.7 312 2 1 258 169 54.3 35 9.74 54.4 6.3 11.4 76.1 221 2 2 170 172 54.3 36 10.33 55.8 5.0 21.2 104.3 266 2 1 181 149 54.3 37 9.97 58.2 2.8 16.5 76.5 90 2 2 69 42 34.3 38 7.84 49.1 4.6 7.1 87.9 60 2 3 50 45 34.3 39 10.47 53.2 4.1 5.7 69.1 196 2 2 168 153 54.3 40 8.16 60.9 1.3 1.9 58.0 73 2 3 49 21 14.3 41 8.48 51.1 3.7 12.1 92.8 166 2 3 145 118 34.3 42 10.72 53.8 4.7 23.2 94.1 113 2 3 90 107 34.3 43 11.20 45.0 3.0 7.0 78.9 130 2 3 95 56 34.3 44 10.12 51.7 5.6 14.9 79.1 362 1 3 313 264 54.3 45 8.37 50.7 5.5 15.1 84.8 115 2 2 96 88 34.3 46 10.16 54.2 4.6 8.4 51.5 831 1 4 581 629 74.3 47 19.56 59.9 6.5 17.2 113.7 306 2 1 273 172 51.4 48 10.90 57.2 5.5 10.6 71.9 593 2 2 446 211 51.4 49 7.67 51.7 1.8 2.5 40.4 106 2 3 93 35 11.4 50 8.88 51.5 4.2 10.1 86.9 305 2 3 238 197 51.4 51 11.48 57.6 5.6 20.3 82.0 252 2 1 207 251 51.4 52 9.23 51.6 4.3 11.6 42.6 620 2 2 413 420 71.4 53 11.41 61.1 7.6 16.6 97.9 535 2 3 330 273 51.4 54 12.07 43.7 7.8 52.4 105.3 157 2 2 115 76 31.4 55 8.63 54.0 3.1 8.4 56.2 76 2 1 39 44 31.4 56 11.15 56.5 3.9 7.7 73.9 281 2 1 217 199 51.4 57 7.14 59.0 3.7 2.6 75.8 70 2 4 37 35 31.4 58 7.65 47.1 4.3 16.4 65.7 318 2 4 265 314 51.4 59 10.73 50.6 3.9 19.3 101.0 445 1 2 374 345 51.4 60 11.46 56.9 4.5 15.6 97.7 191 2 3 153 132 31.4 61 10.42 58.0 3.4 8.0 59.0 119 2 1 67 64 31.4 62 11.18 51.0 5.7 18.8 55.9 595 1 2 546 392 68.6 63 7.93 64.1 5.4 7.5 98.1 68 2 4 42 49 28.6 64 9.66 52.1 4.4 9.9 98.3 83 2 2 66 95 28.6 65 7.78 45.5 5.0 20.9 71.6 489 2 3 391 329 48.6 66 9.42 50.6 4.3 24.8 62.8 508 2 1 421 528 48.6 67 10.02 49.5 4.4 8.3 93.0 265 2 2 191 202 48.6 68 8.58 55.0 3.7 7.4 95.9 304 2 3 248 218 48.6 69 9.61 52.4 4.5 6.9 87.2 487 2 3 404 220 48.6 70 8.03 54.2 3.5 24.3 87.3 97 2 1 65 55 28.6 71 7.39 51.0 4.2 14.6 88.4 72 2 2 38 67 28.6 72 7.08 52.0 2.0 12.3 56.4 87 2 3 52 57 28.6 73 9.53 51.5 5.2 15.0 65.7 298 2 3 241 193 48.6 74 10.05 52.0 4.5 36.7 87.5 184 1 1 144 151 68.6 75 8.45 38.8 3.4 12.9 85.0 235 2 2 143 124 48.6 76 6.70 48.6 4.5 13.0 80.8 76 2 4 51 79 28.6 77 8.90 49.7 2.9 12.7 86.9 52 2 1 37 35 28.6 78 10.23 53.2 4.9 9.9 77.9 752 1 2 595 446 68.6 79 8.88 55.8 4.4 14.1 76.8 237 2 2 165 182 48.6 80 10.30 59.6 5.1 27.8 88.9 175 2 2 113 73 45.7 81 10.79 44.2 2.9 2.6 56.6 461 1 2 320 196 65.7 82 7.94 49.5 3.5 6.2 92.3 195 2 2 139 116 45.7 83 7.63 52.1 5.5 11.6 61.1 197 2 4 109 110 45.7 84 8.77 54.5 4.7 5.2 47.0 143 2 4 85 87 25.7 85 8.09 56.9 1.7 7.6 56.9 92 2 3 61 61 45.7 86 9.05 51.2 4.1 20.5 79.8 195 2 3 127 112 45.7 87 7.91 52.8 2.9 11.9 79.5 477 2 3 349 188 65.7 88 10.39 54.6 4.3 14.0 88.3 353 2 2 223 200 65.7 89 9.36 54.1 4.8 18.3 90.6 165 2 1 127 158 45.7 90 11.41 50.4 5.8 23.8 73.0 424 1 3 359 335 45.7 91 8.86 51.3 2.9 9.5 87.5 100 2 3 65 53 25.7 92 8.93 56.0 2.0 6.2 72.5 95 2 3 59 56 25.7 93 8.92 53.9 1.3 2.2 79.5 56 2 2 40 14 5.7 94 8.15 54.9 5.3 12.3 79.8 99 2 4 55 71 25.7 95 9.77 50.2 5.3 15.7 89.7 154 2 2 123 148 25.7 96 8.54 56.1 2.5 27.0 82.5 98 2 1 57 75 45.7 97 8.66 52.8 3.8 6.8 69.5 246 2 3 178 177 45.7 98 12.01 52.8 4.8 10.8 96.9 298 2 1 237 115 45.7 99 7.95 51.8 2.3 4.6 54.9 163 2 3 128 93 42.9 100 10.15 51.9 6.2 16.4 59.2 568 1 3 452 371 62.9 101 9.76 53.2 2.6 6.9 80.1 64 2 4 47 55 22.9 102 9.89 45.2 4.3 11.8 108.7 190 2 1 141 112 42.9 103 7.14 57.6 2.7 13.1 92.6 92 2 4 40 50 22.9 104 13.95 65.9 6.6 15.6 133.5 356 2 1 308 182 62.9 105 9.44 52.5 4.5 10.9 58.5 297 2 3 230 263 42.9 106 10.80 63.9 2.9 1.6 57.4 130 2 3 69 62 22.9 107 7.14 51.7 1.4 4.1 45.7 115 2 3 90 19 22.9 108 8.02 55.0 2.1 3.8 46.5 91 2 2 44 32 22.9 109 11.80 53.8 5.7 9.1 116.9 571 1 2 441 469 62.9 110 9.50 49.3 5.8 42.0 70.9 98 2 3 68 46 22.9 111 7.70 56.9 4.4 12.2 67.9 129 2 4 85 136 62.9 112 17.94 56.2 5.9 26.4 91.8 835 1 1 791 407 62.9 113 9.41 59.5 3.1 20.6 91.7 29 2 3 20 22 22.9