Download the data on Gas Mileage. This is a sample of 81 passenger cars with information about gas consumption and other technical details.
a. Estimate the following model, MPG_{i} _{ }= b_{0} + b_{1} * WT_{i} + b_{2} * SP_{i} + b_{3} * HP_{i} + e_{i}
Where: MPG = Miles driven per gallon of gasoline by the i-th car, in miles.
WT = Vehicle weight of the i-th car, in hundreds of lbs.
SP = Top speed of the i-th car, in miles per hour.
HP = Engine horsepower of the i-th car.
and write down your results in full reporting mode.
b. Since you are using cross-sectional data, you want to check for the existence of Heteroskedasticity. You do not have any specific correction factor in mind. So, you decide to run a White-test. Describe the procedure and write down your results in full reporting mode.
c. Run a chi-square test to check for Heteroskedasticity in your data and report your conclusions.
d. Assuming that you have rejected the null hypothesis of Homoskedasticity, you suspect that HP may be the variable that is causing Heteroskedasticity. Run a Park test to check your suspicions, write down your results and report your conclusions.
e. Plot a scatter graph of the residuals from your equation in (a) above against the HP variable to visually verify the existence of heteroskedasticity.
f. Assuming that you have confirmed your suspicions, proceed with the necessary transformation of your data to run a Weighted Least Squares regression, and write down your results.
g. Explain the differences between the two models that you have estimated in (a) and (f) in terms of formulation, and signs and sizes of estimated coefficients. Which of the two models (a) or (f) do you prefer?