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Are more selective colleges more expensive? This is a question asked by students enrolled in a statistics course at a liberal arts college. To answer this question, the students collected information on a random sample of 41 liberal arts colleges across the nation. They considered the regression model given below. it\" = .80 + ,31 PRIVATE + .32 ADM,RA1'E Variable Description COST Average cost of attendance PRIVATE Is the school private? (0 = no, 1 = yes) ADATDDA Below is the output the students obtained from their favorite statistical software package. Estimate Std. Error tvalue 33670. 89 5486. 87 6.137 PRIVATE 22713.66 3566.25 6.369 ADM_RATE -186.60 68.73 -2.715 R2 = 0.6009 Adj.R2 = 0.5799 s = 3864 Reference: Ref 117 If all assumptions necessary for inference are valid and we wished to determine the overall utility of the model, what hypotheses should we test? A- Ho: B1 = .32 = 0 versus 1-1.: at least one i at 0 b.13- H',:B2 = Oversus 1-1.:32 9k 0 (TIC-Ho: 31 = 0 versus 1-1.: .31 > 0 A D-H9: B1 = B2 = 0 versus 1-1.: at least one i > 0 Figure 2: Plot of Predicted Y' v. Residuals o O 15 O 05 Residuals O O O ooo oo -15 130,000 120,000 130,DO0 140,DO0 150,000 160,000 170,000 180,000 190,000 200,000 Predicted Number of weekly riders Reference: Ref. 1 What might the above plot be useful for? OA. Rejecting the null hypothesis OB. Detecting heterosexuality OC. Testing the null hypothesis D. Detecting multicollinearity