Recall that Table 14.6 (page 590) presents data concerning the need for labor in 16 U.S. Navy hospitals. This table gives values of the dependent variable Hours (monthly labor hours) and of the independent variables Xray (monthly X-ray exposures), BedDays (monthly occupied bed days-a hospital has one occupied bed day if one bed is occupied for an entire day), and Length (average length of patients' stay, in days). The data in Table 14.6 are part of a larger data set analyzed by the Navy. The complete data set consists of two additional independent variables- Load (average daily patient load) and Pop (eligible population in the area, in thousands)-values of which are given on the page margin. Figure 15.18 gives Excel and MINITAB outputs of multicollinearity analysis and model building for the complete hospital labor needs data set.
a. Find the three largest simple correlation coefficients between the independent variables in Figure 15.18(a). Also, find the three largest variance inflation factors in Figure 15.18(b).
b. Based on your answers to part a, which independent variables are most strongly involved in multicollinearity?
c. Do any least squares point estimates have a sign (positive or negative) that is different from what we would intuitively expect-another indication of multicollinearity?
d. The p-value associated with F(model) for the model in Figure 15.18(b) is less than .0001. In general, if the p-value associated with F(model) is much smaller than any of the p-values associated with the independent variables, this is another indication of multicollinearity. Is this true in this situation?
e. Figure 15.18(c) indicates that the two best hospital labor needs models are the model using Xray. BedDays. Pop. and Length, which we will call Model I. and the model using Xray, BedDays, and Length, which we will call Model 2. Which model gives the smallest value of s and the largest value of 2? Which model gives the smallest value of C? Consider a question¬able hospital for which Xray = 56,194, BedDays = 14,077.88, Pop = 329.7, and Length = 6.89. The 95 percent prediction intervals given by Models 1 and 2 for labor hours corresponding to this combination of values of the independent variables are, respectively, [14,888.43, 16,861.30) and [14,906.24, 16,886.261. Which model gives the shortest prediction interval?