Question

5. The file Cardata.xlsx provides the following information for 392 different car models: Cylinders Displacement Horsepower Weight Acceleration Miles per gallon (MPG) Determine an equation that can predict MPG. Why do you think all the independent variables are not significant? D E F. G H 7 K M cyl disp wt 9 HP 304 307 360 193 200 215 accel mpg 4732 18.5 4376 15 4615 14 10 10 00 00 00 00 00 00 400 150 4997 14 11 11 350 180 11 3664 4633 11 11 8 11 429 318 350 400 8 208 210 160 167 180 180 198 13.5 13.5 12.5 8 8 4382 4456 4906 4955 4499 4952 4951 11.5 383 350 429 12 12 12 12 12 12.5 00 00 00 11.5 455 225 11 12

Answer 1

The OLS regression model with "mpg" as the dependent variable and "Cyl", "disp", "HP", "wet" and "accel" as independent variables, as estimated in excel is as follows:

The OLS regression model is:

Predicted mpg = 17.7508442797323 + 0*Cyl + -0.00981628183179254*disp -0.0134126049103457*HP + 0.00145546843271424*wt -0.547042008901501*accel

It shall be noted that the explanatory variables such as "Cyl", "disp", "HP", and "wt" are not statistically significant at 5% level of significance.

"Cyl" takes a constant value throughout, so it is not considered an explanatory variable for predicting "mpg"

The "disp", "HP" and "wt" are not statistically significant because there is a problem of multi-collinearity

This is indicated by correlation analysis presented below:

	disp	HP	wt	accel
disp	1	0.104896539	0.545701912	-0.701369701
HP	0.104896539	1	-0.01817517	-0.08724795
wt	0.545701912	-0.018175166	1	0.046634023
accel	-0.701369701	-0.08724795	0.046634023	1

Thus, "disp" and "accel" are highly correlated and hence, there is a problem of multi-collinearity.

Thus, R-squared is high but most of the explanatory variables are statistically insignificant.