B C D E 1 x1 x2 x3 x4 Y 18 2 2463 566.52 15.57 44.02 472.92 1339.75 3 9.5 2048 3940 696.82 1033.15 4. 20.42 12.8 5 18.74 6505 620.25 568.33 1497.6 36.7 1603.62 49.2 5723 35.7 6 7 8 1611.37 1613.27 11520 24 44.92 55.48 1365.83 1687 5779 9 59.28 5969 1639.92 10 8461 2872.33 94.39 128.02 20106 3655.08 11 12 96 13313 2912 43.3 1854.17 46.7 2160.55 78.7 2305.58 180.5 3503.93 60.9 3571.89 103.7 3741.4 126.8 4026.52 157.7 10343.81 169.4 11732.17 331.4 15414.94 2 10771 3921 131.42 127.21 N" 15543 3865.67 252.9 15 16 17 409.2 36194 7684.1 34703 12446.33 39204 14098.4 463.7 510.22 18 86533 15524 371.6 18854.45 Question 1: US Navy Hospital collected data on the following variables Y = monthly labout hours X monthly X-ray exposure X, = monthly occupied bed days X3 = eligible population in the area (in 1000) X4 = average length of patients' stay (in days) Data are in the given EXCEL file under tab q1". The chief biostatistician in the hospital decided to analyze this data ser using the model Y = Bo + B, X,1 + B, X;2+ B3X3 + B4X4 +ti for i=1,...,n with the assumption that the errors are iid normal with mean 0 and variance o?. a. Let W = (Y. X1, X2, X3, Xa)'. 1. Find the correlation matrix of W. 2. Based on the correlation matrix, do you expect to encounter multicollinearity problem? Why? b. Besides your answer in part (a), use two other measures to justify if multicollinearity exists. C. Based on residual plots, check if all the assumptions are satisfied. B C D E 1 x1 x2 x3 x4 Y 18 2 2463 566.52 15.57 44.02 472.92 1339.75 3 9.5 2048 3940 696.82 1033.15 4. 20.42 12.8 5 18.74 6505 620.25 568.33 1497.6 36.7 1603.62 49.2 5723 35.7 6 7 8 1611.37 1613.27 11520 24 44.92 55.48 1365.83 1687 5779 9 59.28 5969 1639.92 10 8461 2872.33 94.39 128.02 20106 3655.08 11 12 96 13313 2912 43.3 1854.17 46.7 2160.55 78.7 2305.58 180.5 3503.93 60.9 3571.89 103.7 3741.4 126.8 4026.52 157.7 10343.81 169.4 11732.17 331.4 15414.94 2 10771 3921 131.42 127.21 N" 15543 3865.67 252.9 15 16 17 409.2 36194 7684.1 34703 12446.33 39204 14098.4 463.7 510.22 18 86533 15524 371.6 18854.45 Question 1: US Navy Hospital collected data on the following variables Y = monthly labout hours X monthly X-ray exposure X, = monthly occupied bed days X3 = eligible population in the area (in 1000) X4 = average length of patients' stay (in days) Data are in the given EXCEL file under tab q1". The chief biostatistician in the hospital decided to analyze this data ser using the model Y = Bo + B, X,1 + B, X;2+ B3X3 + B4X4 +ti for i=1,...,n with the assumption that the errors are iid normal with mean 0 and variance o?. a. Let W = (Y. X1, X2, X3, Xa)'. 1. Find the correlation matrix of W. 2. Based on the correlation matrix, do you expect to encounter multicollinearity problem? Why? b. Besides your answer in part (a), use two other measures to justify if multicollinearity exists. C. Based on residual plots, check if all the assumptions are satisfied