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

The model is fitted using R:

lmod <- lm(lpsa ~ lcavol+lweight+age+lbph+svi, prostate)

summary(lmod)

(b)Write the equation for the fitted model.

Fitted model is:

lpsa=0.9510+0.56561*lcavol+0.42369*lweight-0.01489*age+0.11184*lbph+0.72095*svi

Problem2(R²interpretation)(a)

Construct a scatter plot of the response (the y-axis) versus the fitted values (the x-axis). Add the line y= x,i.e.,thelinewithintercept0andslope1.

Solution

(b)

Usingtheplotin(a),doesthecoefficientofdetermination,R²seemtobeanappropriatemeasureofmodelfitforthisdata?

Solution

(c)

Interpretthecomputedcoefficientofdeterminationinthecontextoftheproblem.

Solution

Problem3(Orthogonality)(a)

Whichregressorvariablesinthemodelareorthogonaltotheintercept?Justifyyouranswer.

Solution

(b)

Whichregressorsinthemodelareorthogonaltoeachother?Justifyyouranswer.

Solution