Which statistic measures dispersion of residuals around the regression line in simple linear regression?

• A. Standard deviation of X
• B. Mean of Y
• C. Standard deviation of the residuals
• D. R^2

Answer: (C)

The key idea is measuring how far the actual data fall from the fitted regression line. In simple linear regression, residuals are the differences between observed Y values and their predicted ŷ values on the line. The spread of those residuals tells you how tightly the line captures the data, and this spread is quantified by the standard deviation of the residuals (the standard error of the estimate). A smaller standard deviation means the points cluster more closely around the line, indicating a better fit; a larger one means more scatter around the line.

The other statistics don’t describe this dispersion around the line: the standard deviation of X is about how spread out the predictor values are, the mean of Y is just the central tendency of the outcomes, and R^2 indicates the proportion of the variance in Y explained by X but not the typical deviation of observed points from the line. Hence, the standard deviation of the residuals best measures dispersion around the regression line.