The MINITAB output given in Figure 10.15 resulted from fitting a logistic regression model to the binary response variable prostatic capsule tumor penetration

(CAPSULE) and the explanatory variables age (AGE) and prostatic specific antigen

(PSA) on the Prostate Cancer Study data set. Use the information in Figure 10.15 to answer the following questions.

(a) Test the goodness-of-fit of this model.

(b) Are there any collinearity problems suggested by the VIF values?

(c) Does the age of a male appear to influence the probability of prostatic capsule tumor penetration? Explain.

(d) Compute a 95% confidence interval for the odds ratio associated with a one unit increase in the explanatory variable PSA when the value of AGE is held constant.

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Coefficients Term Coef SE Coef Z-Value P-Value VIF Constant 0.42 1.13 0.37 0.708 AGE 0.0105 0.0170 0.62 0.538 1.00 PSA -0.05032 0.00927 -5.43 0.000 1.00 Goodness-of-Fit Tests Test DF Chi-Square P-Value Hosmer Lemeshow 8 5.05 0.752