Load the prostate data set from the faraway package. The data are from a study of 97 men with

prostate cancer who were due to receive a radical prostatectomy. More details can be found by running

?faraway::prostate in the R Console. The variables in the data set include:

lcavol: log(cancer volume)

lweight: log(prostate weight)

age: subject age (years)

lbph: log(benign prostatic hyperplasia amount)

svi: seminal vesicle invasion

lcp: log(capsular penetration)

gleason: Gleason score

pgg45: percentage Gleason scores 4 or 5

lpsa: log(prostate specific antigen)

Unfortunately, units are not provided.

data(prostate, package = "faraway")

We will consider the relationship between the response lpsa and several of the other variables in the data set.

Problem 1 (Basic model fitting)

(a)Fit a linear model regressing lpsa on lcavol, lweight, age, lbph, and svi. Summarize the fitted model

using the summary function.

Solution

(b)Write the equation for the fitted model.

Problem 2 (R2 computation)

We will quantify how well the model fits the available data.

(a) Obtain the RSS from the model fit.

Solution

(b) Compute the TSS from the model fit.

Solution

(c)Manually compute the formula using the formula 1 RSS/TSS.

Solution

(d)What statistic in the output of summary does your answer in (c) correspond to?

Solution

(e)Compute the squared correlation between the response and the fitted values. How does this compare to the

answers in (c) and (d)?

solution