In the regression equation y = b x + a, what does the parameter b represent?

In the regression equation y = b x + a, what does the parameter b represent?

• A. Intercept
• B. Slope
• C. Error variance
• D. Correlation

Answer: (B)

The slope of the regression line. In the equation y = b x + a, b tells you how much predicted y changes for each one-unit increase in x. A positive b means higher x is associated with higher y, while a negative b means higher x is associated with lower y. The larger the absolute value of b, the stronger the predicted change in y per unit of x. This coefficient is distinct from the intercept a, which is the predicted value of y when x is zero; it is also distinct from the error variance, which concerns how spread out the actual data are around the line, and from the correlation, which is a separate measure of the strength and direction of the linear relationship. In population terms, b is the slope (often called beta1), and what you estimate from data is its sample slope.

The slope of the regression line. In the equation y = b x + a, b tells you how much predicted y changes for each one-unit increase in x. A positive b means higher x is associated with higher y, while a negative b means higher x is associated with lower y. The larger the absolute value of b, the stronger the predicted change in y per unit of x. This coefficient is distinct from the intercept a, which is the predicted value of y when x is zero; it is also distinct from the error variance, which concerns how spread out the actual data are around the line, and from the correlation, which is a separate measure of the strength and direction of the linear relationship. In population terms, b is the slope (often called beta1), and what you estimate from data is its sample slope.