Regression analysis was employed to investigate the determinants of survival size of nonprofit hospitals

(Applied Economics,Vol. 18,1986). For a given sample of hospitals, survival size, y, is defined as the largest size hospital (in terms of number of beds) exhibiting growth in market share over a specific time interval.

Suppose 10 states are randomly sclccted and the survival size for all nonprofit hospitals in each state is determined for two time periods five years apart, yielding two observations per state. The 20 survival sizes are listed in the table on page 589, along with the following data for each state, for the second year in each time interval:

xl = Percentage of beds that are for-profit hospitals x2 = Ratio of the number of persons enrolled in health maintenance organizations (HMOs) to the number of persons covered by hospital insurance x3 = State population (in thousands)

I I x4 = Percent of state that is urban The article hypothesized that the following model characterizes the relationship between survival size and the four variables just listed:

a. The model was fit to the data in the table using SAS, with the results given in the printout below. Report the least squares prediction equation.

b. Find the regression standard deviation s and interpret its value in the context of the problem.

c. Use an F-test to investigate the usefulness of the hypothesized model. Report the observed significance level, and use a = .025 to reach your conclusion.

d. Prior to collccting the data it was hypothesized that increases in the number of for-profit hospital beds would decrease the survival size of nonprofit hospitals. Do the data support this hypothesis? Test using a = .05.