For the prostate data, fit a model with lpsa as the response and the other vari- ables as…

For the prostate data, fit a model with lpsa as the response and the other vari- ables as predictors: (a) Compute 90 and 95% CIs for the parameter associated with age. Using just these intervals, what could we have deduced about the p-value for age in the regression summary? (b) Compute and display a 95% joint confidence region for the parameters asso- ciated with age and lbph. Plot the origin on this display. The location of the origin on the display tells us the outcome of a certain hypothesis test. State that test and its outcome. (C) In the text, we made a permutation test corresponding to the F-test for the significance of all the predictors. Execute the permutation test corresponding to the t-test for age in this model. (Hint: summary (g) $coef[4,31 gets you the 1-statistic you need if the model is called g.) (d) Remove all the predictors that are not significant at the 5% level. Test this model against the original model. Which model is preferred?

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