Multicollinearity, VIF, and nested F-tests

require(mosaic)
require(car)

Researchers observed the following data on 20 individuals with high blood pressure:

• blood pressure (BP, in mm Hg)
• age (Age, in years)
• weight (Weight, in kg)
• body surface area (BSA, in m^2)
• duration of hypertension (Dur, in years)
• basal pulse (Pulse, in beats per minute)
• stress index (Stress)

Our goal is to build a model for blood pressure as a function of (some subset) of the other variables. In this case all of our variables are quantitative, so we can get a quick look at their relationships using the a pairs plot.

BP <- read.csv("http://www.math.smith.edu/~bbaumer/mth247/labs/bloodpress.csv")
pairs(BP)

# Better than the standard pairs plot is the generalized pairs plot. 
#install.packages("gpairs")
#gpairs(BP)

• What do you see in these scatterplots? Which of the variables are most highly correlated with BP?

Hint: use cor to calculate the correlation coefficient matrix.

A First Model

Weight seems to be highly correlated with BP, so as a first step, we should understand how well a simple linear model for blood pressure as a function of weight works. Keep in mind that it accords with our intuition that there would be a strong link between a person’s weight and their blood pressure.

xyplot(BP ~ Weight, data=BP, pch=19, alpha=0.5, cex=1.5, type=c("p", "r"))