A modified version of R-squared considers the number of predictors in a regression model. While R-squared increases as more predictors are added, even if those predictors do not meaningfully improve the model, this metric penalizes the inclusion of unnecessary variables. Its value provides an estimate of the proportion of variance in the dependent variable that is explained by the independent variables, adjusted for the number of independent variables in the model. For example, if a model with numerous predictors shows a small increase in R-squared compared to a simpler model, this metric may decrease, indicating that the added complexity does not justify the marginal improvement in explanatory power.
This adjusted measure addresses a key limitation of R-squared, which can be artificially inflated by including irrelevant predictors. By accounting for model complexity, it provides a more realistic assessment of the model’s ability to generalize to new data. Historically, this adjustment became essential as statistical modeling techniques advanced, allowing for the inclusion of a greater number of potentially confounding variables. It assists in selecting the most parsimonious model that effectively explains the variance in the dependent variable without overfitting the data.
