Using Prostate Cancer Study data set, fit a logistic regression model with capsule penetration (CAPSULE) as the response variable with explanatory variables age

(AGE), prostatic specific antigen (PSA), and tumor volume (VOL). For the resulting fitted model,

(a) determine whether or not there are collinearity problems.

(b) test the goodness-of-fit of this model.

(c) compute a 95% confidence interval for the odds ratio for a one unit increase in the variable VOL when Age and PSA are held fixed.

(d) determine the deviance for this model.

(e) are there any explanatory variables that should be dropped from the model?