Question

a.State (here) in words the specific meaning of the numerical value of the regression coefficient on engine horsepower, weight and transmission type in terms of what it measures for this problem. Does this coefficient make sense, according to what you would expect for it?

Regression Equation

Transmission(X3)          
0(A)   MPG (Y)   =   55.39 - 0.1437 Horsepower (X1) - 0.00460 Weight (X2)
            
1(M)   MPG (Y)   =   51.77 - 0.1437 Horsepower (X1) - 0.00460 Weight (X2)

Coefficients

Term   Coef   SE Coef   T-Value   P-Value   VIF
Constant   55.39   2.48   22.35   0.000     
Horsepower (X1)   -0.1437   0.0401   -3.59   0.001   3.19
Weight (X2)   -0.00460   0.00162   -2.84   0.007   3.26
Transmission(X3)                 
1(M)   -3.62   1.28   -2.82   0.007   1.08

Answer 1

For a unit Increase in Horsepower the mileage decreases by 0.14(as it is given negative) provided all other factors are kept fixed.

For a unit Increase in weight the Mileage decreases by 0.004 provided other factors are kept fixed.

For a change in transmission type there is a change of mileage of 3.62 units.

Yes the coefficient makes sense because we expect as Horsepower Increases there is more consumption of fuel and hence decreases the mileage. Also when the weight Increases the Vehichle has to make more efforts to move so the mileage decreases.

So all the coefficients make sense and they are significant as well since their p value is very low.