Table 14.6 presents data concerning the need for labor in 16 U.S. Navy hospitals. Here, y = monthly labor hours required; x1 = monthly X-ray exposures; x2 = monthly occupied bed days (a hospital has one occupied bed day if one bed is occupied for an entire day); and b3 = average length of patients' stay (in days). Figure 14.8 gives the Excel output of a regression analysis of the data using the model
y = β0+ β1x1 + β2x2 + β3b3 + ε
The variables x1 x2 and b3 are denoted as XRay. BedDays. and LengthStay on the output.
a. Find (on the output) and report the values of b1, b2, and b3, the least squares point estimates of β1, β2. and β3 Interpret b1, b2, and b3.
b. Consider a questionable hospital for which XRay = 56,194. BedDays = 14,077.88, and LengthStay = 6.89. A point prediction of the labor hours corresponding to this combination of values of the independent variables is given on the Excel add-in output. Report this point prediction and show (within rounding) how it has been calculated.
c. If the actual number of labor hours used by the questionable hospital was y = 17,207.31. how does this y value compare with the point prediction?