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If we add another explanatory variable and re-run the regression, we should expect a) the R-square...

If we add another explanatory variable and re-run the regression, we should expect

a) the R-square to increase while the effect on the adjusted R-square is unknown.

b) both the R-square and the adjusted R-square to increase.

c) the adjusted R-square to increase while the effect on the R-square is unknown.

d) the adjusted R-square to stay the same and the R-square to decrease.

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Answer #1

Option (a) is right answer. When more variables are added, r-squared values typically increase. Adding more independent variables or predictors to a regression model tends to increase the R-squared value, which tempts makers of the model to add even more. The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance.

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