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LINEAR REGRESSION: What it Is and How it Works

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

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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

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

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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

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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)

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Regression Lines

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

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Residuals

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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

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

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