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.

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First, run the following code in the R Console. The update function takes an existing fitted model and

updates it. The notation . ~ . + var means keep the existing response and regressors but add var to the

model.

# fit model with an intercept

lmod1 <- lm(lpsa ~ 1, data = prostate)

summary(lmod1)$r.squared

# fit model with an intercept and lcavol

lmod2 <- update(lmod1, . ~ . + lcavol, data = prostate)

summary(lmod2)$r.squared

# fit model with an intercept, lcavol, and lweight

lmod3 <- update(lmod2, . ~ . + lweight, data = prostate)

summary(lmod3)$r.squared

# fit model with an intercept, lcavol, lweight, and age

lmod4 <- update(lmod3, . ~ . + age, data = prostate)

summary(lmod4)$r.squared

lmod5 <- update(lmod4, . ~ . + lbph, data = prostate)

summary(lmod5)$r.squared

lmod6 <- update(lmod5, . ~ . + svi, data = prostate)

summary(lmod6)$r.squared

lmod7 <- update(lmod6, . ~ . + lcp, data = prostate)

summary(lmod7)$r.squared

lmod8 <- update(lmod7, . ~ . + gleason, data = prostate)

summary(lmod8)$r.squared

lmod9 <- update(lmod7, . ~ . + rnorm(97), data = prostate)

summary(lmod9)$r.squared

(a)

Complete a table with the results from the code above with the following format. Replace x with the R2

value from the fitted model.