In a linear regression of a dependent variable on an independent variable, what does the slope indicate?

• A. The rate of change in the dependent variable per unit increase in the independent variable.
• B. The strength and direction of the linear relationship.
• C. The intercept of the regression line on the y-axis.
• D. The sum of squared residuals.

Answer: (A)

The slope tells you how fast the dependent variable changes as the independent variable changes. In a simple regression line, it is the amount by which Y is predicted to change when X increases by one unit. If the slope is positive, Y tends to rise as X increases; if it’s negative, Y tends to fall. The exact value reflects the units used for X and Y, so it describes the rate of change per unit of X rather than an overall strength of the relationship. The intercept tells where the line crosses the Y axis, and measures like correlation or R-squared gauge how well the line fits the data, not the slope itself. The sum of squared residuals is a separate measure of fit, not the rate of change.