Refer to Patient satisfaction Problem 6.15. Assume that regression model (6.5) for three predictor variables with independent normal error terms is appropriate.

a. Test whether there is a regression relation; use  = 10. State the alternatives, decision rule, and conclusion. What does your test imply about ß_l ß₂, and ß₃? What is the P-value of the test?

b. Obtain joint interval estimates of ß_I. ß₂' and ß₃, using a 90 percent family confidence coefficient. Interpret your results.

c. Calculate the coefficient of multiple determination. What does it indicate here?

Problem 6.15

Patient satisfaction. A hospital administrator wished to study the l-elation between patient satisfaction (Y) and patient's age (X _I, in years), severity of illness (X₂, an index), and anxiety level (X₃ an index). The administrator randomly selected 46 patients and collected the data presented below, where larger values of Y, X₂ , and X₃ are, respectively, associated with more satisfaction, increased severity of illness, and more anxiety.

a. Prepare a stem-and-leaf plot for each of the predictor variables. Are any noteworthy features revealed by these plots?

b. Obtain the scatter plot matrix and the correlation matrix. Interpret these and state your principal findings.

c. Fit regression model (6.5) for three predictor variables to the data and state the estimated regression function. How is b₂ interpreted here?

d. Obtain the residuals and prepare a box plot of the residuals. Do there appear to be any outliers?

e. Plot the residuals against , each of the predictor variables, and each two-factor interaction term on separate graphs. Also prepare a normal probability plot. Interpret your plots and summarize your findings.

f. Can you conduct a formal test for lack of fit here?

g. Conduct the Breusch-Pagan test for constancy of the error variance, assuming log σ_i² =

 State the alternatives, decision rule, and conclusion.