5 For a data set consisting of 32 different cars consider th

5. For a data set consisting of 32 different cars, consider the linear regression of their quarter-mile time qsec (seconds) on three variables: hp (gross horsepower), disp (displacement, cu. in.), and wt (weight, lb/1000).

(a) With gross horsepower in the model, is there evidence that the terms for displacement and weight are needed? State H0 and Ha for a test that answers this question. [3 pts]

(b) For the least squares fit of the model with hp, disp, and wt as predictors, the residual sum of squares (RSS) is 31.6. For the model with only hp, the RSS is 49.3. Compute an F-statistic appropriate for testing the hypotheses of the previous part. [5 pts]

Solution

a) With gross horsepower in the model, is there evidence that the terms for displacement and weight are needed? State H0 and Ha for a test that answers this question. [3 pts]

Ho: the terms for displacement and weight are needed

Ha: the terms for displacement and weight are not needed

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(b) For the least squares fit of the model with hp, disp, and wt as predictors, the residual sum of squares (RSS) is 31.6. For the model with only hp, the RSS is 49.3. Compute an F-statistic appropriate for testing the hypotheses of the previous part. [5 pts]

F test = MSR/MSE

=(SSR/(df))/ (SSE/(df))

=(49.3/2)/(31.6/(32-3))

=22.62184