#3.1
For the prostate data, fit a model with lpsa as the response and the other variables 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-values for age in the regression summary?
(b) Compure and display a 95% joint confidence region for the parameters associated 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) Suppose a new patient with the following values arrives:
|
lcavol |
lweight |
age |
lbph |
svi |
lcp |
gleason |
pgg45 |
|
1.44692 |
3.62301 |
65.00000 |
0.30010 |
0.00000 |
-0.79851 |
7.00000 |
15.00000 |
Predict the lpsa for this patient along with an appropriate 95% CI.
(d) Repeat the last question for a patient with the same values except that he or she is age 20.
Explain why the CI is wider.
(e) 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, 3] gets you the t-statistic you need if the model is called g.)