What is the formula for Adjusted R-squared (Ra^2)?

The formula for Adjusted R-squared (Ra^2) is correctly represented as Ra^2 = 1 - [(n-1)/(n-k-1)] * (1 - R^2). This formula adjusts the traditional R-squared value to account for the number of predictors in a regression model, providing a more accurate measure of goodness-of-fit.

The traditional R-squared value can be misleading when comparing models with different numbers of independent variables, as it always increases or stays the same when more variables are added, regardless of their actual effectiveness in explaining the variance in the dependent variable. The Adjusted R-squared modifies the R-squared by incorporating the number of predictors (k) and the sample size (n).

By penalizing the addition of variables that do not improve the model, the Adjusted R-squared provides a more realistic assessment of model quality. If a new variable does not contribute significantly to explaining the variance, the value of (1 - R^2) becomes significant, leading to a decrease in the Adjusted R-squared, thus indicating that the model might be overfitted.

This nuanced calculation allows analysts and data scientists to better evaluate the performance of their regression models, especially in contexts where variable selection