1. Regression

2. Population Covariance and Correlation

3. Sample Correlation

4. .98 -.04 -.79

5. Linear Model DATA REGRESSION LINE

6. (Still) Linear Model DATA REGRESSION CURVE

7. Parameter Estimation Minimize SSE over possible parameter values

8. Fitting a linear model in R

9. Intercept parameter is significant at.0623 level

10. Fitting a linear model in R Slope parameter is significant at.001 level, so reject

11. Fitting a linear model in R Residual Standard Error:

12. Fitting a linear model in R R-squared is the correlation squared, also % of variation explained by the linear regression

13. Create a Best Fit Scatter Plot

14. Add X and Y Labels

15. Inspect Residuals

16. Multiple Regression Example: we could try to predict change in diameter using both change in height as well as starting height and Fertilizer

17. Multiple Regression All variables are significant at.05 level The Error went down and R-squared went up (this is good) Can even handle categorical variables