Q5. The attached “hospital” data presents data concerning the need for labor in
ID: 3150563 • Letter: Q
Question
Q5. The attached “hospital” data presents data concerning the need for labor in 17 U.S. Navy hospitals. The Navy evaluates the performance of its hospitals in terms of how many labor hours are used relative to how many labor hours are needed. The Navy selected 17 hospitals that were efficiently run to construct a regression model to evaluate hospital efficiency. The complete data consists of 6 variables. The dependent variable is hours measured as monthly labor hours required. The independent variables are: 1) Xray measured as monthly X-ray exposures, 2) BedDays measured as monthly occupied bed days (a hospital has one bed day if one bed is occupied for an entire day), 3) Length measured as the average length of patient stay, 4) load measured as average daily patient load, 5) Pop measured as the eligible population in the area. Please answer the following questions regarding the potential presence of multicollinearity:
Find the 3 largest simple correlation coefficients between the independent variables. Also, find the three largest variance inflation factors.
Based on your answers to part (a), which independent variables are most strongly correlated with one another?
Do any least squares point estimates have a sign that is different from what we would expect? Note: This is another indication of multicollinearity?
The p-value associated with F(model) for the regression of the dependent variable on all independent variables is less than .0001. In general, if the p-value associated with F(model) is much smaller than all of the p-values of the independent variables, this is another indication of multicollinearity. Is this true in this case?
xray beddays length load pop hours 2463 472.92 4.45 15.57 18 566.52 2048 1339.75 6.92 44.02 9.5 696.82 3940 620.25 4.28 20.42 12.8 1033.15 6505 568.33 3.9 18.74 36.7 1603.62 5723 1497.6 5.5 49.2 35.7 1611.37 11520 1365.83 4.6 44.92 24 1613.27 5779 1687 5.62 55.48 43.3 1854.17 5969 1639.92 5.15 59.28 46.7 2160.55 8461 2872.33 6.18 94.39 78.7 2305.58 20106 3655.08 6.15 128.02 180.5 3503.93 13313 2912 5.88 96 60.9 3571.89 10771 3921 4.88 131.42 103.7 3741.4 15543 3865.67 5.5 127.21 126.8 4026.52 36194 7684.1 7 252.9 157.7 10343.81 34703 12446.33 10.78 409.2 169.4 11732.17 39204 14098.4 7.05 463.7 331.4 15414.94 86533 15524 6.35 510.22 371.6 18854.45Explanation / Answer
The correlation matrix ix
The three largest correlation is between beddays & load (0.9999), load & pop (0.9357) and beddays & pop (0.9332).
Beddays & load have a correlation coefficient of 0.9999 and hence are most strongly correlated.
The sign of the least square estimate for xray, beddays and length are positive where as there correlation with hours is positive. Hence they would have a sign that is different from what we would expect.
The indiation of multicollinearity is true in this case.
xray beddays length load pop xray 1 0.9071 0.4466 0.9074 0.9105 beddays 0.9071 1 0.6711 0.9999 0.9332 length 0.4466 0.6711 1 0.6712 0.4629 load 0.9074 0.9999 0.6712 1 0.9357 pop 0.9105 0.9332 0.4629 0.9357 1Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.