1. The problem is to understand the meaning and correct usage of $\bar{R}^2$ (R-bar squared) in statistics, particularly in regression analysis. 2. $\bar{R}^2$, or adjusted R-squared, is a modified version of the coefficient of determination $R^2$ that adjusts for the number of predictors in a model. 3. The formula for adjusted R-squared is: $$\bar{R}^2 = 1 - \left(1 - R^2\right) \frac{n - 1}{n - p - 1}$$ where: - $n$ is the number of observations, - $p$ is the number of predictors (independent variables), - $R^2$ is the coefficient of determination. 4. Important rules: - $R^2$ always increases or stays the same when more predictors are added, even if they are irrelevant. - Adjusted $R^2$ penalizes adding unnecessary predictors, so it can decrease if the new predictor does not improve the model sufficiently. 5. To calculate $\bar{R}^2$, first compute $R^2$ from your regression model. 6. Then plug $R^2$, $n$, and $p$ into the formula above. 7. This gives a more accurate measure of model fit, especially when comparing models with different numbers of predictors. 8. If $\bar{R}^2$ is "unfortunately wrong," it usually means the formula was misapplied or the values of $n$, $p$, or $R^2$ were incorrect. 9. Always double-check the inputs and use the formula carefully to get the correct adjusted R-squared value.