1. More Topics in Regression

3. Simulation Imagine that you find yourself out of college and in a job. Take a look at the sheet. See what your monthly income is Decide how to allocate money, and record values in each category. You must have shelter, food, transportation, and clothing. You may have multiples of these things. You cannot spend any more than you have You have to allocate all of your money to something, whether it is consumer goods or charity or savings or whatever.

4. Heteroskedasticity We will plot savings against income What I expect to see is more variance at high values If your income is low, all of your income goes to providing necessities If it is high, can go to fun or savings

5. Heteroskedasticity

6. An example of Heteroskedasticity Regression model assumes that errors are of equal average magnitude at all values of IV. Problem- sometimes in the real world, this does not happen Difference of variance at low and high values. That is, fit is tighter at one end than at the other

10. Heteroskedasticity Causes There may be an underlying interactive relationship missing There may be different measurement error at different values Causes estimates of b’s to be less precise. Can lead to real results looking insignificant.

11. Modeling Interactive Relationships in Regression Income=b 1 (sex)+b 2 (education)+c Income=b 1 (sex)+b 2 (education)+b 3 (sex x education)+c In both cases, b 1 gives us the difference for being a man or woman, b 2 gives the impact of education. What does b 3 tell us? b 3 is the interaction, tells us if there is a differential impact of education among the genders For sex, let 0=m, 1=f, education in years, income in dollars

12. Education incomeincome

13. incomeincome Men Women

14. Education incomeincome Men Women

15. Education incomeincome Women Men

16. Using Interaction Terms Easiest when one is a dummy variable (0-1) other is either continuous or a dummy Multiply the two together Include all lesser terms (that is, in a two way, have x 1,x 2, and x 1 *x 2. In a three way, include x 1,x 2,x 3, x 1 *x 2, x 1,x 3, x 2,x 3, and x 1 *x 2 *x 3 For interpretation, you can add the slope of the interaction term to the slope of the appropriate variable, use to create two sets of predicted values

17. An Example- Internet and Personality Research question- does internet have differential impact on political knowledge for people depending on their motivation to seek information. Look at Need for Cognition and Need to Evaluate Set up regression with political knowledge as DV. NE, NC, media use, and interactions as IVs

18. Looking at Results Model 2- No interactions, but includes important traits including media use. Model 3- includes interactions between NC and all media types. NC is significant and positive. Negative interaction with cable. Model 4- interactions with NE. NE is significant and positive, Negative interaction with cable and internet

19. NE KnowledgeKnowledge No internet internet

20. Challenges to Interaction Terms Interpretation –Dummy*continuous is tricky –Continuous*continuous is trickier –Three ways are especially challenging Example- Miller and Krosnick 2000 Trust*knowledge*condition Results- all three required for effect

21. Challenges to Interactions Multicolinearity Interaction terms are typically highly correlated with other terms Inflates errors of parameter estimates Makes potentially significant relationships appear non-significant