Your Textbook Presented You with the Following Regression Output

Question

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The Answer is (a)The new regression line would be

(a)The new regression line would be = 6.989 - 0.0228 × STR.Hence the decimal point would simply move two digits to the left.The interpretation remains the same,since an increase in the student-teacher ratio by 2,say,increases the new testscore by 0.0456 points on the new testscore scale,which is 4.56 in the original testscores. (b)The regression R2 should not change,since,if it did,an objective measure of fit would depend on whim (the units of measurement).The SER will change (from 18.6 to 0.186).This is to be expected,since the TSS obviously changes,and with the regression R2 unchanged,the SSR (and hence SER)have to adjust accordingly. (c)Since statistical inference will depend on the ratio of the estimator and its standard error,the standard error must change in proportion to the estimator.If this was not true,then statistical inference again would depend on the whim of the investigator.

= 6.989 - 0.0228 × STR.Hence the decimal point would simply move two digits to the left.The interpretation remains the same,since an increase in the student-teacher ratio by 2,say,increases the new testscore by 0.0456 points on the new testscore scale,which is 4.56 in the original testscores.
(b)The regression R2 should not change,since,if it did,an objective measure of fit would depend on whim (the units of measurement).The SER will change (from 18.6 to 0.186).This is to be expected,since the TSS obviously changes,and with the regression R2 unchanged,the SSR (and hence SER)have to adjust accordingly.
(c)Since statistical inference will depend on the ratio of the estimator and its standard error,the standard error must change in proportion to the estimator.If this was not true,then statistical inference again would depend on the whim of the investigator.

Your Textbook Presented You with the Following Regression Output

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