What adjustment is made to the R-squared value in multiple regression analysis?

In multiple regression analysis, the adjustment made to the R-squared value is designed to account for the number of predictors in the model. This adjustment helps prevent the misleading interpretation of R-squared, which tends to increase as more variables are added to the model, regardless of their actual contribution to explaining the variability in the dependent variable.

The adjusted R-squared provides a more accurate reflection of the model's explanatory power by penalizing the addition of non-significant predictors. Specifically, it adjusts the R-squared value by considering not only the proportion of variance explained by the model but also the number of predictors used. This means that if adding a new variable does not improve the model significantly beyond what is already being explained by the existing predictors, the adjusted R-squared may actually decrease. This makes the adjusted R-squared a more reliable metric for comparing models with a different number of predictors, ensuring that the complexity of the model is taken into account when evaluating its goodness of fit.