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 x3 average length of patients’ stay (in days). Figure gives the Excel output of a regression analysis of the data using the model
y = β0 + β1x1 + β2x2 + β3x3 = ε
Note that the variables x1, x2, and x3 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 b1, b2, and b3. Interpret b1, b2, and b3. Note that the negative value of b3 (413.7578) might say that, when XRay and BedDays stay constant, an increase in LengthStay implies less patient turnover and thus fewer start-up hours needed for the initial care of new patients.
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?