Question: Predicting the MPG. The following data were originally collected from Consumer Reports for a survey on fuel efficiency for 1978 and 1979 model automobiles. Measurements on 33 cars are available. The gas mileage in miles per gallon (MPG) was measured by Consumers’ Union on a test track. Other values, as reported by automobile manufacturer, are

• Drive Ratio
• Horsepower —— measured in in Watts
• Cylinder — Number of Cylinders

Refer to the output shown Figure 4. (a) State the fitted regression model.

(a) State the fitted regression model.

(b) Predict the gas mileage (in miles per gallon) for a car that has a drive ratio of 2.80, 135 horse- power and 5 cylinders.

(c) How reliable would this prediction be for a car with the same specifications manufactured 10 years ago? Provide some reasoning for your answer, i.e. explain why or Why not the prediction would be valid.

(d) It is 1979, and your grandparents want to buy a car with the specifications for x1, x2, and x3 as given in part (b). Should they expect the MPG for their new car to be exactly equal to the predicted value you calculated? Explain your answer.

(e) What, if anything, could be done with the data already collected to provide better information for your grandparents? Be specific, but do not carry out any calculations.

(f) How much variability in the MPG ratings can be explained by the fitted regression model?

(g) Assume that the assumptions, necessary for any regression inference, are met. Using a = 0.01 test the overall utility of the model. Make sure to include all relevant steps, i.e. state the null and alternative hypothesis, provide the value of the test statistic, the corresponding p-value, a decision and a conclusion within the context of the problem.

(h) The data analyst at Consumer Reports has been asked to establish evidence for a linear relationship between the horsepower of a car and the MPG. Provide a complete statistical argument for him that he can present to Consumer Reports.

(i) Report the value of the RMSE?

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