please explain the reasons Best Subsets Regression: Earnings (S) versus DrDist,

Question

please explain the reasons

Best Subsets Regression: Earnings (S) versus DrDist, DrAccu,.. Response is Earnings () S S o acu n r n d a c m e DAal B i cGvi a R- Sq R-Sq Mallows Vars R-5q (ad)(pred) 5.0 2 15.4 14.1 11.1 14.1 13.6 13.1 12.2 Cp 1 8.17.4 19.0 997373 3 19.9 17.9 4 21.3 18.6 5 22.419.2 6 22.6 18.6 9.9 960722 X 5.1 939054 5.0 934761 5.2 931759 7.0 934739 X X X X X X 6. Based on this output, the predictor with the highest correlation in absohute vaue with Earnings is absolute vaue of its correlation with Earnings is (Remember to briefly explain your ansner) The best simple regression predictor has the highest r in absolute value. 7. By the criterion of Best Subsets Regression, the best model for this dataset uses which predictors? (Remember to briefly plainyour answer.)

Explanation / Answer

6. Based on this output, the predictor with the highest correlation in absolute value with Earnings is Var 6. The absolute valure of its correlation with Earnings is 0.4754.

for simple linear regression (when there is one indpendent variable) the R-sq is the square of the correlation (r) between dependent (y) variable and independent(x) variable.

(7) By the criterion of Best Subsets Regression, the best model for this dataset uses predictor 6.

higher the R-sq better is the model, predictor 6 has the highest R-sq

following information has been generated from the given information

vars % R-Sq R-Sq r 1 8.1 0.081 0.2846 2 15.4 0.154 0.3924 3 19.9 0.199 0.4461 4 21.3 0.213 0.4615 5 22.4 0.224 0.4733 6 22.6 0.226 0.4754

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