Golden Years Easy Retirement Homes owns several adult care facilities throughout the southeast United States. A budget analyst for Golden Years has collected the data found in the file Dat9-10.xlsx that accompanies this book describing for each facility: the number of beds (X₁), the annual number of medical in-patient days (X₂), the total annual patient days (X₃), and whether or not the facility is in a rural location (X₄). The analyst would like to build a multiple regression model to estimate the annual nursing salaries (Y) that should be expected for each facility.

 

a. Prepare scatter plots showing the relationship between the nursing salaries and each of the independent variables. What sort of relationship does each plot suggest?

b. If the budget analyst wanted to build a regression model using only one independent variable to predict the nursing salaries, what variable should be used?

c. If the budget analyst wanted to build a regression model using only two independent variables to predict the nursing salaries, what variables should be used?

d. If the budget analyst wanted to build a regression model using three independent variables to predict the nursing salaries, what variables should be used?

e. What set of independent variables results in the highest value for the adjusted R² statistic?

f. Suppose the personnel director chooses to use the regression function with all independent variables X₁, X₂, and X₃. What is the estimated regression function?

g. In your spreadsheet, calculate an estimated annual nursing salary for each facility using the regression function identified in part f. Based on this analysis, which facilities, if any, should the budget analyst be concerned about? Explain your answer.