1. Statistics 350 Review

2. Today Today: Review

3. Simple Linear Regression Simple linear regression model: Y i =  for i=1,2,…,n Distribution of errors

4. Simple Linear Regression In practice, do not know the values of the  ’s nor  2 Use data to estimate model parameters giving estimated regression equation Want to get the “line of best fit”…what does this mean?

5. Apartment Example

6. Least Squares Estimation via least squares: Q= Know how to derive For simple linear regression and multiple linear regression Related simplified models are fair game

7. Properties Know properties of estimators and also residuals Example: sum of residuals is Show estimates of regression parameters are unbiased How do you use the estimated regression line (function)?

8. Maximum likelihood Know how to derive MLE for regression parameters and variance

9. Inference Interested in making inference about regression parameters are the function Example: Inference about  i : Prediction intervals: Confidence intervals:

10. Inference Interested in making inference about regression parameters are the function Example: Inference about  i : Simultaneous Inference:

11. Inference Prediction intervals: Confidence intervals:

12. ANOVA Know/understand ANOVA approach ANOVA decomposition: Hypotheses

13. Residual Diagnostics Motivation Plots Remedial Measures…when to transform X or Y

14. Diagnostics Could also do a Lack of Fit Test

15. Multiple regression Derivations, inference R 2 and adjusted R 2 Extra sums of squares: Multi-collinearity Model Building: Criteria and all sub-sets Automatic methods

16. Final Steps Model Validation: Partial Regression Plots:

17. Exam