A researcher is interested in developing a model that describes the gas mileage, measured in miles per gallon (mpg), of automobiles. Based on input from an engineer, she decides that the explanatory variables might be engine size (liters), curb weight (pounds), and horsepower. From a random sample of 13 automobiles, she obtains the following data:

(a) Find the least-squares regression equation
yÌ… = b0 + b1x1 + b2x2 + b3x3, where x1 is engine size, x2 is
curb weight, x3 is horsepower, and y is the response variable, miles per gallon.
(b) Use a partial F-test to determine whether engine size and curb weight do not significantly help to predict the response variable, miles per gallon.
(c) Use forward selection, backward elimination, or stepwise regression to identify the best model in predicting asking price.
(d) Draw residual plots, a boxplot of residuals, and a normal probability plot of residuals to assess the adequacy of the model found in part (c).
(e) Interpret the regression coefficients for the least-squares regression equation found in part (c).
(f) Construct 95% confidence and prediction intervals for the gas mileage of an automobile that weighs 3100 pounds, has a 2.5-liter engine, and 200 horsepower. Interpret the results.

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Engine Size Curb Weight Horsepower Miles per Gallon 2.4 3289 177 24 3263 2.4 158 25 2.5 3230 170 24 3.5 3580 272 22 2.8 3175 255 18 3643 3.5 263 22 3.5 3497 306 3.0 3340 230 21 3.6 3861 263 19 2.4 3287 173 24 3629 3.3 234 21 2.5 3270 170 22 3.5 3292 270 22