In linear regression, what does the slope represent?

• A. The correlation coefficient.
• B. The intercept of the regression line.
• C. The average change in the dependent variable for each unit change in the independent variable.
• D. The standard deviation of residuals.

Answer: (C)

The slope captures the rate at which the dependent variable changes as the independent variable increases. In the simple regression form y = β0 + β1 x, the slope β1 is the amount by which y is expected to change for each one-unit increase in x, with units of y per unit of x. The sign shows direction—positive means higher x tends to raise y, negative means higher x tends to lower y—and the magnitude reflects how strong that change is in the context of the given units. This slope is estimated to minimize the squared discrepancies between observed and predicted y values.

This differs from the correlation coefficient, which is a unitless measure of the strength and direction of a linear relationship and not the actual rate of change. It also differs from the intercept, which is the predicted y value when x equals zero, and from the standard deviation of residuals, which describes how spread out the prediction errors are rather than the rate of change itself.