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LINEAR REGRESSION: What it Is and How it Works
Overview What is Bivariate Linear Regression? The Regression Equation How It’s Based on r
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
Why is it Bivariate? Two variables: X and Y X - independent variable/predictor variable Y - dependent/outcome/criterion variable
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
The Regression Equation y = b 1 x i + b 0 + 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)
Least-Squares Solution Minimize squared error in prediction. Error (residual) = difference between predicted y and actual y
How It’s Based on r Replace x and y with z X and z Y : z Y = b 1 z X + b o and the y-intercept becomes 0: z Y = b 1 z X and the slope becomes r: z Y = rz X
Take-Home Point Linear regression is a way of using information about a correlation to make predictions
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LINEAR REGRESSION: What it Is and How it Works Overview What is Bivariate Linear Regression? The Regression Equation How It’s Based on r.
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LINEAR REGRESSION: What it Is and How it Works. Overview What is Bivariate Linear Regression? The Regression Equation How It’s Based on r Assumptions.
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