Question

Write R code:

Here are the first six observations from the prostate data set found in the faraway library. Use help(prostate) to describe the dataset and the variables in the data sets.

obs	lcavol	lweight	age	lbph	svi	lcp	gleason	pgg45	lpsa
1	-0.579819	2.7695	50	-1.38629	0	-1.38629	6	0	-0.43078
2	-0.994252	3.3196	58	-1.38629	0	-1.38629	6	0	-0.16252
3	-0.510826	2.6912	74	-1.38629	0	-1.38629	7	20	-0.16252
4	-1.203973	3.2828	58	-1.38629	0	-1.38629	6	0	-0.16252
5	0.7514161	3.4324	62	-1.38629	0	-1.38629	6	0	0.37156
6	-1.049822	3.2288	50	-1.38629	0	-1.38629	6	0	0.76547

Perform a simple linear regression with lpsa as the response and lcavol as the predictor. Show the ANOVA table and provide a histogram of the residuals.

Hint: If your linear model name is “lmod” then

      > residuals(lmod)   #prints out the residuals

Answer 1

R code

install.packages("faraway")

library(faraway)

data("prostate")

head(prostate)

model = lm(lpsa~lcavol,data=prostate)

summary(model)

hist(residuals(model),main="Histogram of Residuals")

anova(model)

Output

> library(faraway)

Warning message:

package ‘faraway’ was built under R version 3.6.2

> library(faraway)

> data("prostate")

> head(prostate)

      lcavol lweight age      lbph svi      lcp gleason pgg45     lpsa

1 -0.5798185 2.7695 50 -1.386294   0 -1.38629       6     0 -0.43078

2 -0.9942523 3.3196 58 -1.386294   0 -1.38629       6     0 -0.16252

3 -0.5108256 2.6912 74 -1.386294   0 -1.38629       7    20 -0.16252

4 -1.2039728 3.2828 58 -1.386294   0 -1.38629       6     0 -0.16252

5 0.7514161 3.4324 62 -1.386294   0 -1.38629       6     0 0.37156

6 -1.0498221 3.2288 50 -1.386294   0 -1.38629       6     0 0.76547

> model = lm(lpsa~lcavol,data=prostate)

> summary(model)

Call:

lm(formula = lpsa ~ lcavol, data = prostate)

Residuals:

     Min       1Q   Median       3Q      Max

-1.67625 -0.41648 0.09859 0.50709 1.89673

Coefficients:

            Estimate Std. Error t value Pr(>|t|)   

(Intercept) 1.50730    0.12194   12.36   <2e-16 ***

lcavol       0.71932    0.06819   10.55   <2e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7875 on 95 degrees of freedom

Multiple R-squared: 0.5394, Adjusted R-squared: 0.5346

F-statistic: 111.3 on 1 and 95 DF, p-value: < 2.2e-16

> head(residuals(model))

          1           2           3           4           5           6

-1.52100281 -0.95463223 -1.30237079 -0.80377605 -1.67624667 0.01333025

> hist(residuals(model))

> hist(residuals(model),main="Histogram of Residuals")

> anova(model)

Analysis of Variance Table

Response: lpsa

          Df Sum Sq Mean Sq F value    Pr(>F)   

lcavol     1 69.003 69.003 111.27 < 2.2e-16 ***

Residuals 95 58.915   0.620                     

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1