Multivariate Regression

1. Multivariate Regression 11/20/2012

2. Readings • Chapter 8 Correlation and Linear Regression (Pollock) (pp 187-199) • Chapter 9 Dummy Variables and Interaction Effects (Pollock Workbook)

3. Homework • Homework Due 11/29 • Chapter 8 • Question 1: A, B,C,D • Question 2: A, B, C, D, E • Question 3: A, B, C • Question 4: A, B, C, D • Question 5: A, B, C, D, E, G

4. Opportunities to discuss course content

5. Office Hours For the Week • When • Monday 11-1:00 • Tuesday 8-12

6. Course Learning Objectives • Students will be able to interpret and explain empirical data. • As this course fulfills the Computational Skills portion of the University degree plan, students will achieve competency in conducting statistical data analysis using the SPSS software program. • Students will learn the basics of polling and be able to analyze and explain polling and survey data

7. Ratio and Intervals! Regression analysis

8. Rules for Regression • If you have a Ratio/Interval Dependent variable that takes on at least 11 values • You need ratio level independent variables (some argue that you can use ordinals, but be careful) • If you have 30 or more cases (N>30) • If you have a linear relationship. It will not work with curvilinear or exponential relationships.

9. What we can do with it • Test the significance, strength and direction of more than one independent variable on the dependent variable, while controlling for the other independent variables. • We can compare the strength of each independent variable against each other • We can examine an entire model at one time!

10. The Model • Y is the dependent variable • a is the constant • b1x1- first beta coefficient and first independent variable • b2x2- Second beta coefficient and Second independent variable

11. Regression Outputs • These have 3 parts • The Model Summary • ANOVA • The Variables/Model

12. Part I Things that Begin with “r”

13. With So Many, How do we know? • There are many R's out there: • lower case "r" for correlation • upper case "R" for regression

14. What the R’s look like The R Square Adj R-Square

15. Part II The Analysis of variance (ANOVA)

16. ANOVA and The F-Score • It is like a chi-square for Regression. • If the F-Score is not significant, we accept the null hypothesis (no relationship). • It usually tells us at least one of our variables is significant. • It is a way of examining the entire regression.

17. The F-Score • We look at the Sig value and use the p<.05 measurement • In the model above, our p value is .001 • We Reject the null hypothesis • At least one variable is significant

18. Part III The Model

19. The Model • What it tells us • Variable relationships and direction • Variable significance • Variable Strength

20. Standardized Beta Coefficients • They show us the variables which have the greatest influence. • These are measured in absolute value • The larger the standardized beta, the more influence it has on the dependent variable.

21. Looking at our Model T-Score- Significance Beta Values

22. Trying it out

23. Another One • D.V.Palin_therm-post (Feeling thermometer for Palin 0-100) • IV's • enviro_jobs (Environment vs. jobs tradeoff) 0=envir, 1=middle, 2=jobs • educ_r- education in years • Gunown- do you own a gun (1=yes, 5=no) • relig_bible_word (Is Bible actual word of God?) 1=yes, 0=No

24. Another one from the states • Gay Rights involves many concepts. The Lax-Phillips index uses content validity to address this issue at the state level. It examines the support for the following issues • Adoption • Hate Crimes legislation • Health Benefits • Housing Discrimination • Job Discrimination • Marriage Laws • Sodomy Laws • Civil Unions • It then averages these to get a statewide level

25. State Example • Dependent Variable- gay_support (higher is more supportive on Lax-Phillips) • Independent Variables • relig_import (% of people in state that say religion provides a great deal of guidance) • south (1=south, 0= NonSouth • abortlaw (restrictions on abortion)

26. Tautology • it is tempting to use independent variables that are actually components of the dependent variable. • How you will notice this: • if the dependent variables seem to be measures of each other (human development vs. education) they probably are, (female literacy and literacy rate) • High Adj. R-Squares (above .900)

27. Multicolinearity • Your independent variables should not only be independent of the d.v. (non tautological) but they should be independent of each other! • Picking independent variables that are very closely related, or are actually part of the same measure What can happen here is these variables will negate the influence of each other on the dependent variable.

28. Symptoms of Multicolinearity • the multiple regression equation is statistically significant (big R values, even a significant ANOVA), but none of the t-ratios are statistically significant • the addition of the colinear independent variable radically changes the values of the standardized beta coefficients (they go from positive to negative, or weak to strong), without a corresponding change in the ADJ R-square. • Variables, that you would swear on a stack of bibles should be related, are not

29. Solving Tautology and Multicolinearity • Solving tautology- Drop the independent variable • What to do About Multicolinearity • run bivariate correlations on each of your variables. If the r-square value is >.60. • You will want to drop one of the variables, or combine them into a single measure.

30. Data collection

31. Collecting Primary Data • Direct Observation • Document Analysis • Interview Data

32. Document Analysis

33. Document Analysis (The Written Record) • What is it • When to use it

34. Types of Document Analysis • The Episodic Record • The Running Record

35. Limitations and Advantages

36. Observation

37. Observation • What is it • Types of Observation

38. Problems of Observation • Reactivity • Ethics