In MATHSTATSOU/Intro2MLR: Introduction to MLR

knitr::opts_chunk$set(echo = TRUE)

Introduction

Multi-collinearity can be found in the following regression.

FTC2 data

library(Intro2MLR)
data(ftc2)

Model 1

names(ftc2)
fit1 <- lm(CO ~ TAR + NICOTINE + WEIGHT, data = ftc2)
summary(fit1)
car::vif(fit1)
cor(ftc2[,1:3])

New model

We should remove the X with most variance inflation. Note that NICOTINE is highly correlated with TAR. So we should remove NICOTINE or TAR -- we will choose to remove NICOTINE since it has the largest VIF. We will use the car package to calculate the VIF

$$VIF_i = \frac{1}{1-R^2_i}$$

fit2 <- lm(CO ~ TAR + WEIGHT, data = ftc2)
summary(fit2)
car::vif(fit2)

Remove WEIGHT

Weight is shows very little evidence that it will impact predictions (see P value and T stats).

We will remove WEIGHT

fit3 <- lm(CO ~ TAR , data = ftc2)
summary(fit3)
anova(fit3,fit2)

Notice that the test produced by the anova function produces evidence against:

$$H_0: \beta_2 = 0$$ where $\beta_2$ is the coefficient of WEIGHT. You need to see that this is a situation where k-g=1 and hence the F test corresponds to a two tailed T test, where $F=T^2$.

sm1<-summary(fit1)
sm2<-summary(fit2)
sm3<-summary(fit3)

sm2$coefficients[3,]

In this case $f_{calc} = t_{calc}^2 = r sm2$coefficients[3,3]^2$ and the two pvalues are identical.

$R^2_a$

We will now trace the adjusted R squared.

sm1$adj.r.squared
sm2$adj.r.squared
sm3$adj.r.squared

The last model has the largest adjusted R squared.

MATHSTATSOU/Intro2MLR documentation built on Dec. 11, 2020, 9:01 p.m.