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An Analyst Has Identified 3 Independent Variables (X1, X2, X3)

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An analyst has identified 3 independent variables (X1, X2, X3) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R2 value for the X3 model the same as the R2 value for the X1 and X3 model, but the Adjusted R2 values differ? An analyst has identified 3 independent variables (X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>)  which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R<sup>2</sup> value for the X<sub>3</sub> model the same as the R<sup>2</sup> value for the X<sub>1</sub> and X<sub>3</sub> model, but the Adjusted R<sup>2</sup> values differ?   A)  The standard error for X<sub>1</sub> is greater than the standard error for X<sub>3</sub>. B)  X<sub>1</sub> does not reduce ESS enough to compensate for its addition to the model. C)  X<sub>1</sub> does not reduce TSS enough to compensate for its addition to the model. D)  X<sub>1</sub> and X<sub>3</sub> represent similar factors so multicollinearity exists.


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