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 (properties of residuals and fitted values)

Use the fitted model regressing lpsa on lcavol, lweight, age, lbph, and svi for the prostate data.

(a) What is the sum of the residuals

Solution

(b) Compute the correlation between the residuals and the fitted values.

Solution

(c)Based on your answers in (a) and (b), what pattern would you expect to observe if you constructed a scatter

plot of the residuals (y-axis) versus the fitted values (x-axis)?

Solution

(d)Compute the correlation between the residuals and the lweight regressor.

Solution

(e)Based on your answers in (a) and (d), what pattern would you expect to observe if you constructed a scatter

plot of the residuals (y-axis) versus a regressor (x-axis)?