In a simple linear regression with one predictor, which statement best describes the slope coefficient?

In a simple linear regression with one predictor, which statement best describes the slope coefficient?

• A. The strength of association between predictor and response.
• B. The p-value for the slope.
• C. The average change in the response variable for a one-unit increase in the predictor, holding other factors constant if present.
• D. The overall average value of the response variable.

Answer: (C)

The slope coefficient represents how much, on average, the response changes for each one-unit increase in the predictor, holding other factors constant if there are additional predictors. It’s the rate of change of y with respect to x, with units of y per unit of x, and it can be positive or negative depending on the direction of the relationship. For example, in predicting exam score from study hours, a slope of 5 means each extra hour of study is associated with about 5 more points on average, assuming the model is appropriate. This value is not a measure of how strong the association is (that would be captured by correlation or R-squared), nor is it the p-value for testing whether the slope is zero. It also isn’t the overall average of the response variable—that would be the mean of y, or, at x = 0, the intercept.

The slope coefficient represents how much, on average, the response changes for each one-unit increase in the predictor, holding other factors constant if there are additional predictors. It’s the rate of change of y with respect to x, with units of y per unit of x, and it can be positive or negative depending on the direction of the relationship. For example, in predicting exam score from study hours, a slope of 5 means each extra hour of study is associated with about 5 more points on average, assuming the model is appropriate.

This value is not a measure of how strong the association is (that would be captured by correlation or R-squared), nor is it the p-value for testing whether the slope is zero. It also isn’t the overall average of the response variable—that would be the mean of y, or, at x = 0, the intercept.