In linear regression, what does R^2 represent?

• A. Minimize the sum of absolute residuals.
• B. Keep the residuals as large as possible.
• C. Proportion of variance explained by the model.
• D. The slope of the regression line.

Answer: (C)

R^2 shows how much of the variation in the outcome your regression model can explain. It’s the proportion of total variance in Y that the model accounts for, computed as 1 minus the residual sum of squares divided by the total sum of squares. This means values near 1 indicate a model that captures most of the data’s variability, while values near 0 indicate little explained variability.

That’s why the correct description is the proportion of variance explained by the model. The other statements describe different ideas: minimizing the sum of absolute residuals is a different fitting criterion, keeping residuals large is the opposite of a good fit, and the slope describes the rate of change, not how well the model fits.