The first step is to look at the relationship of the respons

The first step is to look at the relationship of the response variable with the predictor variables and the relationships between the predictor variables. Examine the scatterplot matrix given below. This shows scatterplots for each possible pair of variables.

Provide answers to the following questions:

a. Does there appear to be a linear relationship between the response variable and each predictor variable? If not, which variables seem to have a non-linear relationship with the response variable?

b. Is there any evidence of multicollinearity among the predictor variables? If so, which variable groups might there be an issue with? Justify why we might expect multicollinearity for these variables. Note that the bottom left side of the scatter plot matrix contains the value for the linear correlation coefficient for each respective variable pair.

0.0 0.4 0.8 2 3 45 6 100 300 500 140 180 220 CMPG r= 0.35 Sedan r=-0.52 | |Truc r=-0.33 TruckSUV r=-0.71 r=-0.28 r= 0.31 Engine r=-0.67 r-0.20 0.21 r= 0.91 r=-0.67 -0.26 r= 0.12 r= 0.78 r= 0.79 HP r--0.74 r=-0.38 r= 0.52 r= 0.81 r= 0.73 r= 0.63 Weight r=-0.47 r= 0.09 r= 0.081 r= 0.62 r= 0.55 r= 0.38 r= 0.65 Length r=-0.59 r=-0.32 r= 0.33 r= 0.73 r= 0.62 r= 0.50 r= 0.81 r= 0.75 Width 10 30 50 0.0 0.4 0.8 4 68 12 2000 5000 65 75

Solution

The first step is to look at the relationship of the response variable with the predictor variables and the relationships between the predictor variables. Examine the scatterplot matrix given below. This shows scatterplots for each possible pair of variables.

Sedan TruckSUV : There is no correlation between predictor and response variable

Engine, hp, weight and and length there is positive correlation between predictor and response variable.

And Cyl : There is no correlation between predictor and response variable.

It is the strong relationship amongst the predictor variables that is called multicollinearity and causes problems when fitting multiple regression models.