In simple linear regression, how do you interpret the slope coefficient beta1?

In simple linear regression, how do you interpret the slope coefficient beta1?

• A. It represents the intercept of the regression line.
• B. It represents the change in Y for a one-unit change in X.
• C. It is the predicted value of Y when X = 0.
• D. It measures the strength of the linear relationship.

Answer: (B)

The slope tells you the rate at which the predicted value of Y changes as X changes. In the regression equation, increasing X by one unit changes the predicted Y by beta1 units on average. The sign shows direction (positive means Y increases with X, negative means Y decreases). The larger the magnitude, the bigger the change per unit of X. It’s about how fast Y responds to X, not about how strong the overall linear relationship is—that strength is captured by measures like R-squared. The intercept, not the slope, gives the predicted Y when X is zero. So the slope best describes the per-unit change in Y with respect to X.

The slope tells you the rate at which the predicted value of Y changes as X changes. In the regression equation, increasing X by one unit changes the predicted Y by beta1 units on average. The sign shows direction (positive means Y increases with X, negative means Y decreases). The larger the magnitude, the bigger the change per unit of X. It’s about how fast Y responds to X, not about how strong the overall linear relationship is—that strength is captured by measures like R-squared. The intercept, not the slope, gives the predicted Y when X is zero. So the slope best describes the per-unit change in Y with respect to X.