Question

The data provided give the gasoline mileage​ (in miles per​ gallon) based on the horsepower of a​ car's engine and the weight of the car​ (in pounds). Using the data​ provided, determine the VIF for each independent variable in the model. Is there reason to suspect the existence of​ collinearity?

Determine the VIF for each independent variable in the model.

MPG	Horsepower	Weight
15.8	185	4,758
19.7	106	3,534
20.3	141	3,220
18.8	172	4,466
17.3	166	4,293
27.5	75	3,186
44.8	60	2,110
27.3	79	2,487
28.2	83	2,610
21.2	134	3,868

Round to three decimal places as​ needed.

Answer 1

use lm function in R fit a linear regression of MPG on Horsepower and weight

Then install library package and use vif function to get the multicollinearity.

Rcode:

MPG <- c(15.8,19.7,20.3,18.8,17.3,27.5,44.8,27.3,28.2,21.2)
Horsepower <- c(185,106,141,172,166,75,60,79,83,134)
weight <- c(4758,3538,3220,4466,4293,3186,2110,2487,2610,3868)
MPG
Horsepower
weight
linmod <- lm(MPG~Horsepower+weight)
coefficients(linmod)
library(car)
car::vif(linmod)

From output:

VIF for each independent variable in the model.

VIF1=7.307

VIF2=7.307

since VIF>5

Yes,there is a problem with multicollinearity.