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REGRESSION

REGRESSION. What is Regression? What is the Regression Equation? What is the Least-Squares Solution? How is Regression Based on Correlation? What are the Assumptions for Using Regression?. What is Regression?. Predict future scores on Y based on measured scores on X

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REGRESSION

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  1. REGRESSION • What is Regression? • What is the Regression Equation? • What is the Least-Squares Solution? • How is Regression Based on Correlation? • What are the Assumptions for Using Regression?

  2. What is 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

  3. What is the Regression Equation? Equation is linear: y = bx + a y = predicted score on y x = measured score on x b = slope a = y-intercept

  4. high o o o o o o o o o o o o o o o Y o o o o o o o o o o o o low high X Regression Line

  5. What is the Least-Squares Solution? • Draw the regression line to minimize squared error in prediction. • Error in prediction = difference between predicted y and actual y • Positive and negative errors are both important

  6. How is Regression Based on Correlation? Replace x and y with zX and zY: zY = bzX + a and the y-intercept becomes 0: zY = bzX and the slope becomes r: zY = rzX

  7. What are the Assumptions for Using Regression? • Predict for the same population from which you sampled • Normal distributions for both variables • Linear relationship between variables • homoscedasticity - y scores are spread out the same degree for every x score

  8. Heteroscedasticity o high o o o o o o o o o o o o Y o o o o o o o o o o o o o o low high X

  9. high o o o o o o o o o o o o o o o Y o o o o o o o o o o o o low high X Homoscedasticity

  10. Homoscedasticity o high o o o o o o o o o o o o o Y o o o o o o o o o o o o o low high X

  11. What is the Standard Error of the Estimate? • Average distance of y scores from predicted y scores • Index of how far off predictions are expected to be • Larger r means smaller standard error

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