Refer to the SENIC data set in Appendix C. I and Project 1.45.
a. For each of the three fitted regression models, obtain the residuals and prepare a residual plot against X and a normal probability plot. Summarize your conclusions. Is linear regression model (2.1) more apt in one case than in the others?
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b. Obtain the fitted regression function for the relation between length of stay and infection risk after deleting cases 47 (X47 = 6.5, Y47 = 19.56) and 112 (Xm = 5.9, Y112 = 17.94). From this fitted regression function obtain separate 95 percent prediction intervals for new Y observations at X = 6.5 and X = 5.9, respectively. Do observations Y47 and Y112 fall outside these prediction intervals? Discuss the significance of this.
Appendix C. I
The primary objective of the Study on the Efficacy of Nosocomial Infection Control (SENIC Project) was to determine whether infection surveillance and control programs have reduced the rates of nosocomial (hospital-acquired) infection in United States hospitals. This data set consists of a random sample of 113 hospitals selected from the original 338 hospitals
surveyed. Each line of the data set has an identification number and provides information on 11 other variables for a single hospital. The data presented here are for the 1975-76 study period. The 12 variables are:
Refer to the SENIC data set in Appendix C.l. The average length of stay in a hospital (Y) is anticipated to be related to infection risk, available facilities and services, and routine chest X-ray ratio. Assume that first-order regression model (1.1) is appropriate for each of the three predictor variables.
a. Regress average length of stay on each of the three predictor variables. State the estimated regression functions.
b. Plot the three estimated regression functions and data on separate graphs. Does a linear relation appear to provide a good fit for each of the three predictor variables?
c. Calculate MSE for each of the three predictor variables. Which predictor variat!le leads to the smallest variability around the fitted regression line?