1. Regression Maarten Buis 12-12-2005

2. Outline Recap Estimation Goodness of Fit Goodness of Fit versus Effect Size transformation of variables and effect size

3. Recap With regression we looked at the effect of one variable on another an effect is a comparison of groups Effect of for instance age consists of a comparison of too many groups so, look at an average effect implies a straight line average effect is slope

5. mean and regression Mean summarizes observations with one number that minimizes the sum of squared deviations from that number Regression summarizes observations with one line that minimizes the sum of squared deviations from that line.

8. Ordinary Least Squares (OLS) So we want to minimize: by choosing optimal values of b 0 and b 1

9. What you need to know How to find the slope and intercept in: –a graph –a regression equation –SPSS output How to interpret the slope and intercept

10. COMPUTE age10 = age/10. COMPUTE incmid1000 = incmid/1000. COMPUTE age55 = age-55.

11. How well does the regression fit? We started with variation in the dependent variable We fitted a regression, which has less variation around the regression line The decrease in variation (Proportion of variance explained) is a measure of fit. R 2

13. Standard Error of the Estimate Unfortunate choice, should have been standard deviation of the estimate Measures the (unexplained) variation around the regression line.