5 When creating models for data an important way of deciding

5. When creating models for data, an important way of deciding which variables to use for predictions is the principle of parsimony. The principle of parsimony essentially suggests we should use the simplest possible model (as few predictors as possible) while maintain precision of predictions. With regard to parsimony, we may simply try to only use variables that are significant in our model. The output for one such model is given here.

Model 4

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 58.52 2.457 23.818 < 2e-16 ***

Sedan 8.026e-01 3.263e-01 2.459 0.0144 *

HP -1.423e-01 1.151e-02 -12.367 < 2e-16 ***

Weight -8.535e-03 1.011e-03 -8.441 6.64e-16 ***

I(HP^2) 6.271e-05 2.677e-05 2.342 0.0197 *

HP:Weight 2.381e-05 3.808e-06 6.253 1.08e-09 ***

a.State and interpret the Sedan dummy variable coefficient.

b.Calculate a 95% confidence interval for the Sedan coefficient. Note that t_.025,381=1.966

c.(c) For ALL four of the models for which output has been provided, give the point prediction for the city gas mileage of a vehicle that is a sedan, has a 2 liter engine with 4 cylinders and 112 horsepower, weighs 2500 pounds, is 175 inches long and 67 inches wide. Compare these predictions.

d.(d) For the four predictions in (c), even though they are all for the same car, there is some variability in the predictions. Why are there differences? Which prediction do you trust the most? Why? (If you can’t think of one to trust: Which one do you distrust the most and why?)

Solution