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Questions also attached in file labeled: Unit 7 Homework: 1. The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and trucks. A portion of the data for 311 compact, midsized, and large cars is contained in the file fueldata.xlsx which you can download from the class D2L shell. The dataset contains the following variables:
Class identifies the size of the car; Compact, Midsize, or Large
Displacement = engine displacement in liters
FuelType shows whether the car uses premium (P) or regular (R) fuel
HwyMPG = fuel efficiency rating for highway driving in miles per gallon
a. Develop an estimated regression equation to predict the fuel efficiency for highway driving given the engine’s displacement. Plot the residuals from this regression to see if you see any pattern. Conduct a hypothesis test to determine whether the coefficient on Displacement is statistically significantly different from 0 using the 0.05 level of significance. How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?
b. Create a scatter chart with HwyMPG on the y-axis and displacement on the x-axis for which the points representing compact, midsize, and large automobiles are shown in different shapes and/or colors. What does this chart suggest about the relationship between the class of automobile (compact, midsize, and large) and HwyMPG?
c. Add dummy variables ClassMidsize and ClassLarge to the simple linear regression model in part a. The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of ClassMidsize and the value of ClassLarge are both 0. Estimate the new regression equation. What happened to the adjusted R2 when these variables were added to the regression? What does this tell you?
d. Use significance level of 0.05 to determine whether the dummy variables added to the model in part c are significant.
e. Finally add the dummy variable FuelPremium, (which is 1 if the car uses premium fuel and 0 if the car uses regular fuel) to the regression. What happened to the adjusted R2 when these variables were added to the regression? What does this tell you?
f. For the estimated regression equation developed in part e, test for the significance of the overall regression relationship (using the F-statistic) and for each of the independent variables the 0.05 level of significance for each test.
Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).
2. Return to the ‘cars.xlsx’ dataset that was used in the Unit 6 Homework. Recall that this dataset includes data on the 0-60 time (TIME), top speed (SPEED), curb weight (WEIGHT), and horsepower (HP) of 30 automobiles.
There are good reasons based in physics to believe that the relationship between horsepower and 0-60 time is non-linear. Look again at the scatter plot of HP (x-axis) and 0-60 time (y-axis) from the Unit 6 Homework. To test the goodness of fit of one possible non-linear relationship estimate the following quadratic regression: TIMEi =ß0 + ß1HPi + ß2HPi2 + e Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).
Compare the results from this regression to those from the Unit 6 Homework. Which do you prefer and why?
3. Use the “BEER” data set to answer the following question. (Also on the course D2L site). The data set includes 30 observations on beer consumption and related data. The variables included are as follows:
q = quantity of beer purchased (in liters)
pB = price of beer (in dollars)
pL = price of other liquor (in dollars)
pR = price of remaining (non-alcoholic) goods & services (in dollars)
m = income (in dollars)
a. What sign do you expect for each coefficient and why?
b. Estimate a regression to explain the quantity of beer purchased as a function of the price, price of liquor, price of remaining goods, and income. Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).
c. Interpret the parameters.
d. Are any of the regressors individually significant in explaining the quantity of beer purchased? If so, at what level?
e. Suppose that beer industry representatives hypothesize that the marginal propensity to buy beer out of an additional dollar of income is $0.01. Conduct a hypothesis test to determine if there is any validity to their conjecture. Usea = 1%.
f. Conduct a hypothesis test to determine if the regressors are jointly significant in explaining the quantity of beer purchased. Be sure to state the null and alternative hypotheses formally.