1. Stat 512 – Lecture 19 Wrap-Up

2. Announcements Review sheet online  Office hours  Review session next week?  Updated final exam signup on web Review problems online Last PP (17) due Thursday  Questions on material  Example exam questions Independence Defining parameters Hypothetical inference Comparison vs. association

3. Today Wrap up multiple regression Handout Presentations? Course evaluation(s)?

4. Last Time – Multiple Regression Can add any number of explanatory variables to the model Predicted Y =   x    x   …  Never hurts R 2 = coefficient of multiple determination  Use R 2 (adj) to compare models  Interpretation of coefficients is change in predicted response after conditioning on other variables in the model (if all other variables fixed…)  Overall F test looks at “model” significance (H 0 : all population slopes = 0)  Individual t tests look at individual variables, conditional on other variables being in the model

5. Last Time – Multiple Regression Can look at multiple scatterplots to display all the relationships  Need to be cautious of highly related explanatory variables (“multicollinearity”) Will check technical conditions again by examining same residual plots

6. Example 3: Housing Prices (cont.) housingTranformed.mtw Incorporating a qualitative variable into the model

7. Interpreting coefficients The regression equation is log(price) = 2.81 + 0.872 log(sqft) - 0.120 N/S “If N/S increases by one…” A house in So CA, on average, costs.120 less (on log(price) scale) than a house in No CA.

8. In fact Are ways to incorporate non-binary qualitative variables… So can use regression to carry out ANOVA… Can use regression to carry out two-sample t tests… Can use (logistic) regression with qualitative response variables… ALL is regression!

9. HW Questions? Treating temperature as the response SAS output has two-sided p-values Double check which parts I’ve asked for (and sometimes extra stuff)

10. PP 17

11. Lecture 19 You will be randomly assigned a study/research question Identify and carry out the appropriate analysis Be ready to share your analysis with the rest of the class

12. For next time Presentations! Finish handout? Review review handout online, bring questions PP 17