STAT 2 - LAB 2

Question 1

fit a linear model with 2 coefficients

Answer 1

lm.multiple <- lm(formula = medv ~ rm+chas,
data=Boston)
summary(lm.multiple)

Question 2

fit a model with 2 coefficients and their interaction

Answer 2

lm.multiple.add <- lm(formula = medv ~ rm*chas, data=Boston)
summary(lm.multiple.add)

Question 3

test ß3 = 0 using anova

Answer 3

anova(lm.multiple,lm.multiple.add)
1. model with 2 coefficient
2. model with interaction terms

Question 4

create a fitted vs residuals plot

Answer 4

plot(fitted(lm.simple),resid(lm.simple),xlab = “Fitted values”,ylab=”Residuals”)
abline(h=0,col=”orange”)

Question 5

Fit a polynomial of order 2 to predict medv through rm

Answer 5

lm.poly <- lm(formula = medv ~ rm+ I(rm^2), data=Boston)

Question 6

Fit a polynomial of order 4 to predict medv through rm

Answer 6

lm.fit.nonlinear4 <- lm(formula = medv ~ poly(rm,4,raw=T), data=Boston)

Question 7

Create four diagnostic plots of the model in EQ. 4 using the function plot.

Answer 7

plot(lm.poly)

Question 8

Are there any points of large leverage?

Answer 8

sum(hatvalues(lm.poly) > 2*mean(hatvalues(lm.poly)))

Question 9

Are there any point with a large residual?

Answer 9

sum(abs(rstandard(lm.poly))>2)

Question 10

Are there any influential points

Answer 10

cooks.lm.poly <- cooks.distance(lm.poly)
sum(cooks.lm.poly>4/length(cooks.lm.poly))

Question 11

Fit the model in EQ. 4 on the Boston data if we remove the influential points.

Answer 11

no.cooks <- cooks.lm.poly <=4/length(cooks.lm.poly)
lm.no.cooks <- lm(formula = medv ~ rm + I(rm^2), data=Boston, subset = no.cooks)

Question 12

after you remove influential points, check the fitted vs residuals

Answer 12

plot(fitted(lm.no.cooks),residuals(lm.no.cooks), xlab=”Fitted values”, ylab=”Residuals)
abline(h=0,col=”orange”)

Question 13

Fit the multiple linear regression model with medv as the response variable, and all other variables as predictors except rad.

Answer 13

lm.fit.multiple(formula= medv ~ . -rad, data=Boston)

Question 14

Calculate variance inflation factor (VIF) score for the predictor variables. Your comments?

Answer 14

library(car)
car::vif(lm.fit.multiple)
the ones above 3 are quite high