1 (25 points) Environment Canada’s Fuel Economy Guide provides fuel efficiency data for 2020 model year cars and trucks. The Fuel Efficiency data for 500 cars is attached. The column labeled Manufacturer shows the name of the company that manufactured the car; the column labeled Displacement shows the engine’s displacement in liters; the column labeled Fuel shows the required or recommended type of fuel (regular or premium gasoline); the column labeled Drive identifies the type of drive (F for front wheel, R for rear wheel, and A for all wheel); and the column labeled Hwy MPG shows the fuel efficiency rating for highway driving in terms of miles per gallon. Analyzing Environment Canada’s Fuel Economy Guide data, write a briefing report that will help the trade department decide on import quota restrictions that may take either fixed in terms of value or quantity of the cars which can be imported over the coming decades.
In your report, include: Estimated regression equation that you would recommend to predict the fuel efficiency for highway driving given the engine’s displacement, the dummy variable FuelPremium, and the dummy variables FrontWheel and RearWheel; an interpretation of the estimated regression coefficients for this equation and test for overall significance and individual significance at α = 0.05 and discussion of your findings and conclusions.
2. (25 points) Fortune magazine publishes an annual list of the 100 best companies to work for. The data is provided in the file named FortuneBest and it shows a portion of the data for a random sample of 30 of the companies that made the top 100 list for 2020. The column labeled Rank shows the rank of the company in the Fortune 100 list; the column labeled Size indicates whether the company is a small, midsize, or large company; the column labeled Salaried ($1000s) shows the average annual salary for salaried employees rounded to the nearest $1000; and the column labeled Hourly ($1000s) shows the average annual salary for hourly employees rounded to the nearest $1000. Fortune defines large companies as having more than 10,000 employees, midsize companies as having between 2500 and 10,000 employees, and small companies as
having fewer than 2500 employees.
a. Use methods of descriptive statistics to summarize the FortuneBest data and comment on your findings.
b. Based upon the results of your analysis, what estimated regression equation would you recommend to predict the average annual salary for salaried employees given the average annual salary for hourly employees and the size of the company. Provide an interpretation of the estimated regression coefficients for this equation.
c. Determine the significance of the independent variables.. Discuss the need for other independent variables that could be added to the model. What additional variable/s might be helpful?
3. (25 points) When trying to decide what car to buy, real value is not necessarily determined by how much you spend on the initial purchase. Instead, cars that are reliable and don’t cost much to own often represent the best values. But no matter how reliable or inexpensive a car may cost to own, it must also perform well.
To measure value, Consumer Reports developed a statistic referred to as a value score. The value score is based upon five-year owner costs, overall road-test scores, and predicted reliability ratings. Five-year owner costs are based upon the expenses incurred in the first five years of ownership, including depreciation, fuel, maintenance and repairs, and so on. Using a national average of 12,000 miles per year, an average cost per mile driven is used as the measure of five-year owner costs. Road-test scores are the results of more than 50 tests and evaluations and are based on a 100-point scale, with higher scores indicating better performance, comfort, convenience, and fuel economy. The highest road-test score obtained in the tests conducted by Consumer Reports was a 99 for a Lexus LS 460L. Predicted-reliability ratings (1 = Poor, 2 = Fair, 3 = Good, 4 = Very Good, and 5 = Excellent) are based upon data from Consumer Reports’ Annual Auto Survey.
A car with a value score of 1.0 is considered to be an ‘‘average-value” car. A car with a value score of 2.0 is considered to be twice as good a value as a car with a value score of 1.0; a car with a value score of 0.5 is considered half as good as average; and so on. The data for three sizes of cars (13 small sedans, 20 family sedans, and 21 upscale sedans), including the price ($) of each car tested, are contained in the file named CarValues. You may use dummy variables to incorporate the effect of size of car[categorical variable with three values]. Your report should include:
a. an estimated regression with Family-Sedan and Upscale-Sedan as the independent variables, and treating Cost/Mile as the dependent variable. Discuss your findings.
b. Estimated regression equation using Cost/Mile, Road-Test Score, Predicted Reliability, Family-Sedan, and Upscale-Sedan as the independent variables, and treating Value Score as the dependent variable.
c. Delete any independent variables that are not significant from the estimated regression equation developed using α = 0.05 level of significance. After deleting any independent variables that are not significant, develop a new estimated regression equation.
d. Suppose someone claims that ‘‘smaller cars provide better values than larger cars.” For the data in this case, the Small Sedans represent the smallest type of car and the Upscale Sedans represent the largest type of car. Does your analysis support this claim?
e. Develop an estimated regression equation that could be used to predict the value score given the value of the Road-Test Score and the Predicted Reliability. What conclusions can you derive from your analysis?
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