In the simple regression model Y = b0 + b1 X, what does b1 represent?

In the simple regression model Y = b0 + b1 X, what does b1 represent?

• A. The intercept of the regression line.
• B. The predicted value of Y when X = 0.
• C. The slope, i.e., the change in Y for a one-unit change in X.
• D. The correlation coefficient.

Answer: (C)

In simple linear regression, the parameter b1 is the slope of the regression line. It tells you how much Y is expected to change for each one-unit change in X. Put differently, if X increases by one unit, Y changes by b1 units on average (positive means Y goes up, negative means Y goes down). This interpretation depends on the units of X and Y, since b1 has those units attached. This is distinct from the intercept b0, which is the predicted value of Y when X is zero, and from the correlation coefficient, which measures the strength and direction of the linear relationship but is not the slope of the line.

In simple linear regression, the parameter b1 is the slope of the regression line. It tells you how much Y is expected to change for each one-unit change in X. Put differently, if X increases by one unit, Y changes by b1 units on average (positive means Y goes up, negative means Y goes down). This interpretation depends on the units of X and Y, since b1 has those units attached. This is distinct from the intercept b0, which is the predicted value of Y when X is zero, and from the correlation coefficient, which measures the strength and direction of the linear relationship but is not the slope of the line.