Question

In order to avoid the possibility of R2 creating a false impression, virtually all software packages include adjusted R2. Unlike R2, adjusted R2 explicitly accounts for what?

A. The number of samples taken
B. Multicollinearity
C. The sample size n
D. The number of predictor variables k

Answer 1

Adjusted R2 accounts for the number of predictor variables in a model, refining the R2 value by penalizing for unnecessary variables and providing a more accurate assessment in multiple regression models.

Step-by-step explanation:

The adjusted R2 explicitly accounts for the number of predictor variables k in a regression model in addition to the sample size. Unlike R2, which measures the proportion of variation explained by all of the independent variables included in a model, adjusted R2 adjusts the statistic based on the number of independent variables, providing a more accurate measure in the case of multiple regression models.

The coefficient of determination, R2, is the square of the correlation coefficient, r, and indicates the percentage of the variance in the dependent variable that is predictable from the independent variable(s).

However, R2 can sometimes give a misleadingly high value when numerous predictor variables are included in the model, even if some of them do not contribute to the explanatory power of the model. This is where adjusted R2 becomes valuable, as it penalizes the addition of predictors that do not improve the model