Which statement about R-squared is true?

Which statement about R-squared is true?

• A. It measures the probability that the predictor is causing the outcome.
• B. It always increases when adding predictors regardless of fit.
• C. It measures the proportion of variance in the response explained by the model.
• D. It is unaffected by the scale of the response variable.

Answer: (C)

R-squared represents the fraction of the variation in the outcome that the model explains. It’s defined as 1 minus the residual variation (the part the model fails to explain) divided by the total variation in the outcome, so it directly quantifies how much of the outcome’s variability is captured by the predictors. It doesn’t measure causation or the probability of any causal effect; a high R-squared doesn’t imply that the predictor causes the outcome. Regarding the other statements: adding a predictor in ordinary least squares cannot decrease the model’s explanatory power, but it can leave it unchanged if the new predictor brings no new information. So it does not always increase. The idea that R-squared is unaffected by the scale of the outcome is a more technical point about how scaling the response affects the sums of squares; while that scaling property holds, the most direct and widely used interpretation of R-squared is its role as the proportion of variance explained by the model. Hence the statement that it measures the proportion of variance in the response explained by the model is the best answer.

R-squared represents the fraction of the variation in the outcome that the model explains. It’s defined as 1 minus the residual variation (the part the model fails to explain) divided by the total variation in the outcome, so it directly quantifies how much of the outcome’s variability is captured by the predictors.

It doesn’t measure causation or the probability of any causal effect; a high R-squared doesn’t imply that the predictor causes the outcome.

Regarding the other statements: adding a predictor in ordinary least squares cannot decrease the model’s explanatory power, but it can leave it unchanged if the new predictor brings no new information. So it does not always increase. The idea that R-squared is unaffected by the scale of the outcome is a more technical point about how scaling the response affects the sums of squares; while that scaling property holds, the most direct and widely used interpretation of R-squared is its role as the proportion of variance explained by the model. Hence the statement that it measures the proportion of variance in the response explained by the model is the best answer.