Because the coefficient of determination R2, always increases when a new independent variable is added to a model, it is tempting to include many variables in the model in order to force R2 to be near 1. However, doing so reduces the number of degrees of freedom available for estimating (:2 which adversely affects our ability to make reliable inferences. Suppose you want to use 20 psychological and sociological factors to predict a student's standardized test score. You fit the model y = [30 +l31x1 + + [320x20 + s where y = test score and x1. x2..... x20 are the psychological and sociological factors. Only 22 years of data (n = 22) are used to fit the model. and you obtain R2 = 097. Test to see whether this impressive-looking R2 is large enough for you to infer that the model is usefulthat is, that at least one term in the model is important in predicting test scores, Use or = 0.025. What are the correct hypotheses for this test? l'_:lA. H0:[31=2=...= k=O,Ha:All[#0 .H0:B1=2=...= k=O,H0:1#z#...Bk0 . H0:B1=[32=...= k=0.Ha:Exactlyone [3i#0 [3D, H0:[31=132= .= k=0,Ha:Atleastone[5i0 The test statistic is F = (Round to two decimal alaces as needed.) The p-value is . (Round to three decimal places as needed.) Because the coefficient of determination R2, always increases when a new independent variable is added to a model, it is tempting to include many variables in the model in order to force R2 to be near 1. However, doing so reduces the number of degrees of freedom available for estimating 62 which adversely affects our ability to make reliable inferences. Suppose you want to use 20 psychological and sociological factors to predict a student's standardized test score. You fit the model y = [30 + 61x1 + + [320x20 + s where y = test score and x1, x2...., x20 are the psychological and sociological factors. Only 22 years of data (n = 22) are used to fit the model. and you obtain R2 = 097. Test to see whether this impressive-looking R2 is large enough for you to infer that the model is usefulthat is, that at least one term in the model is important in predicting test scores. Use or =0.025. The test statistic is F = (Round to two decimal alaces as needed.) The p-value is . (Round to three decimal p aces as needed.) Draw a conclusion, Choose the correct answer below. C? A. Since the observed value of the test statistic does not fall in the rejection region, H0 is not rejected. There is insufficient evidence to indicate the model is adequate at this (x. Since the obsen/ed value of the test statistic falls in the rejection region. H0 is rejected. There is sufficient evidence to indicate the model is adequate at this (x. C" C. Since the observed value of the test statistic does not fall in the rejection region, H0 is not rejected. There is sufficient evidence to indicate the model is adequate at this (x. D. Since the obsen/ed value of the test statistic falls in the rejection region, H0 is rejected. There is insufficient evidence to indicate the model is adequate at this (x