In linear regression, what do the slope and R-squared represent?

• A. Slope indicates change in outcome per unit predictor; R-squared is the proportion of variance explained
• B. Slope is the intercept; R-squared is the correlation coefficient
• C. Slope is the p-value; R-squared is the standard error
• D. Slope measures variance of the outcome; R-squared measures model complexity

Answer: (A)

In linear regression, the slope expresses how much the outcome changes for each one-unit increase in the predictor. It tells you the rate of change: a positive slope means the outcome tends to rise as the predictor increases, while a negative slope means it tends to fall.

R-squared shows how well the model explains the variation in the outcome. It is the proportion of the total variance in the outcome that the model accounts for (ranging from 0 to 1). In simple linear regression, R-squared equals the squared correlation between the predictor and the outcome, so a higher value means the predictor does a better job of explaining the outcome’s variability.

For example, if the predictor is hours studied and the slope is 2, each additional hour is associated with a 2-point increase in the predicted outcome. If R-squared is 0.64, about 64% of the variability in the outcome is explained by hours studied, with the remaining 36% due to other factors or randomness.

The intercept is a separate parameter representing the predicted outcome when the predictor is zero, and the p-value or standard error relate to the statistical precision of the slope estimate. R-squared is not a measure of correlation alone, nor is the slope the intercept or a direct measure of model complexity.