REGRESSION What is Regression? What is the Regression Equation? What is the Least-Squares Solution? How is Regression Based on Correlation? What are the.

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Presentation transcript:

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 are the Assumptions for Using Regression?

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

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

Regression Line X Y low high o o o o o o o o o o o o o o o o o o o o o o o o o o o

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

How is Regression Based on Correlation? Replace x and y with z X and z Y : z Y = bz X + a and the y-intercept becomes 0: z Y = bz X and the slope becomes r: z Y = rz X

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

Heteroscedasticity X Y low high o o o o o o o o o o o o o o o o o o o o o o o o o o o

Homoscedasticity X Y low high o o o o o o o o o o o o o o o o o o o o o o o o o o o

Homoscedasticity X Y low high o o o o o o o o o o o o o o o o o o o o o o o o o o o

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