12.72 Case Study: Consider the data set for Exercise 12.12, page 472 (hospital data), repeated here.

Site x1 x2 x3 x4 x5 y 123456789 10 11 12 13 14 15 16 17 15.57 44.02 20.42 18.74 49.20 44.92 55.48 59.28 94.39 128.02 96.00 131.42 127.21 252.90 409.20 463.70 510.22 2463 2048 3940 6505 5723 11,520 5779 5969 8461 20,106 13,313 10,771 15,543 36,194 34,703 39,204 86,533 472.92 1339.75 620.25 568.33 1497.60 1365.83 1687.00 1639.92 2872.33 3655.08 2912.00 3921.00 3865.67 7684.10 12,446.33 14,098.40 15,524.00 18.0 9.5 12.8 36.7 35.7 24.0 43.3 46.7 78.7 180.5 60.9 103.7 126.8 157.7 169.4 331.4 371.6 4.45 6.92 4.28 3.90 5.50 4.60 5.62 5.l5 6.18 6.15 5.88 4.88 5.50 7.00 10.75 7.05 6.35 566.52 696.82 1033.15 1003.62 1611.37 1613.27 1854.17 2160.55 2305.58 3503.93 3571.59 3741.40 4026.52 10,343.81 11,732.17 15,414.94 18,854.45

(a) The SAS PROC REG outputs provided in Figures 12.9 and 12.10 supply a considerable amount of information.
Goals are to do outlier detection and eventually determine which model terms are to be used in the final model.

(b) Often the role of a single regressor variable is not apparent when it is studied in the presence of several other variables. This is due to multicollinearity.
With this in mind, comment on the importance of x2 and x3 in the full model as opposed to their importance in a model in which they are the only variables.

(c) Comment on what other analyses should be run.

(d) Run appropriate analyses and write your conclusions concerning the final model.

F Value 237.79 Pr F |t| Intercept Intercept 1 1962.94816 1071.36170 1.83 0.0941 x1 x2 x3 x4 Average Daily Patient Load Monthly X-Ray Exposure Monthly Occupied Bed Days Eligible Population in the Area/100 1 -15.85167 97.65299 -0.16 0.8740 1 0.05593 0.02126 2.63 0.0234 1 1.58962 3.09208 0.51 0.6174 1 -4.21867 7.17656 -0.59 0.5685 x5 Average Length of Patients Stay in Days 1 -394.31412 209.63954 -1.88 0.0867