Adjusted R-squared differs from R-squared in that adjusted R-squared:

Correct Answer

C) Penalizes the model for variables that do not help

Why this is correct: Adjusted R-squared penalizes the model for variables that do not help. The governing concept is that R-squared always increases when a new variable is added, even if it's irrelevant, which can lead to overfitting. Adjusted R-squared corrects this by incorporating a penalty for adding variables that do not improve the model's explanatory power, providing a more accurate measure of goodness-of-fit for multiple regression. Why the other choices are wrong: 'Measures the sample's average error' is wrong because that describes a metric like the standard error of the estimate, not R-squared. 'Always exceeds the unadjusted figure' is wrong because adjusted R-squared is typically lower than or equal to R-squared; it only increases if a new variable adds sufficient explanatory power. 'Applies only to single-variable regression models' is wrong because adjusted R-squared is specifically designed for and most useful in models with multiple independent variables. Exam tip: Remember, if adding a variable doesn't help, adjusted R-squared goes down, while plain R-squared never does. This is the key distinction.