2. LINEAR REGRESSION: What it Is and How it Works

3. Overview What is Bivariate Linear Regression? The Regression Equation How It’s Based on r

4. What is Bivariate Linear Regression? Predict future scores on Y based on measured scores on X Predictions are based on a correlation from a sample where both X and Y were measured

5. Why is it Bivariate? Two variables: X and Y X - independent variable/predictor variable Y - dependent/outcome/criterion variable

6. Why is it Linear? Based on the linear relationship (correlation) between X and Y The relationship can be described by the equation for a straight line

7. The Regression Equation y = b 0 + b 1 x i + e i y = predicted score on criterion variable b 0 = intercept x i = measured score on predictor variable b 1 = slope e i = residual (error score)

8. Regression Lines

9. Least-Squares Solution Minimize squared error in prediction. Error (residual) = difference between predicted y and actual y

10. Residuals

11. How It’s Based on r Replace x and y with z X and z Y : z Y = b o + b 1 z X and the y-intercept becomes 0: z Y = b 1 z X and the slope becomes r: z Y = rz X

12. Take-Home Point Linear regression is a way of using information about a correlation to make predictions