In a study designed to develop an equation for predicting survival time of patients undergoing a liver surgery, 54 patients were randomly selected for analysis. Prior to the surgery, information was taken on each patient, and then the survival time in days was observed. The data are shown in Appendix D, Table D.1. One of the potential predictors is a liver function test score (LV) which the surgeons felt should be a good indicator of survival time (TIME).

a. Fit the simple linear model TIME+8,LIV+e. Display the parameter estimates, their standard errors, -statistics and P-values as in Table 2.10.

b. Complete the analysis of variance as shown in Table 2.5 including the computation of R. Note the relation between the F-statistic from this table and the r-statistic associated with 8.

e. Determine the vectors of residuals r and predicted values. Plot against and against Compute the sample correlations corrir, fl and corrir, y), and relate to these plots. Compare corrir, sl and

d. Note the location of case 13 in the plot of residuals against predicted values. Would you label case 13 as an outlier or an extreme point? Compute the standardized and Studentized residuals and Cook's distance for this case, and compare with suggested critical values. Would you consider deletion of case 13? Determine the q~g plot to check for normality. Compare this plot with Figure 2.9 to see if there is evidence of non-normal residuals. Determine the 95% confidence interval and the 95% prediction interval for LIV-3.95. Comment on the interpretation of these intervals in general and in particular for case 13.