Load the prostate data set from the faraway package[data(prostate, package = "faraway")]. 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)

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

using the summary function.

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

i.e., the line with intercept 0 and slope 1.

3> Using the plot in (2), does the coefficient of determination, R² seem to be an appropriate measure of model

fit for this data?

4> Interpret the computed coefficient of determination in the context of the problem.

5> Which regressor variables in the model are orthogonal to the intercept? Justify your answer.

6> Which regressors in the model are orthogonal to each other? Justify your answer.

Just do it