1. Regression
Assumptions of OLS

2. Assumptions of multiple regression
Equal probability of selection (SRS)
Linearity (visible and invisible variables)
Independence of observations:
Errors are uncorrelated
The mean of error term is ALWAYS zero:
Mean does not depend on x.
Normality (of the error term)
Homoskedasticity
Variance does not depend on x.
No multicollinearity

3. Homoskedasticity
The variance of the error term is fixed (equal across all cases).
Compliance with this assumption can be empirically checked.
Consequences if violated: SE will be upward biased.

4. Multicollinearity
Has to do with the quality of the information matrix.
No linear combination of independent variables should be able to predict any other independent variable.

5. Multicollinearity - Dx
Tolerance:
VIF: Inverse of tolerance
Indicates inflated standard errors
>2
>2.5
Multiple correlation among IVs

6. Example: Regression with SPSS

7. Regression exercise Maternal aggression Child aggression Paternal
Harsh
parenting

8. Correlations

9. SPSS output

10. SPSS output

11. Regression exercise Maternal aggression Harsh parenting Child
Paternal
aggression

12. SPSS step 1: Harsh parenting

13. Step 2: Direct effects of mom

14. Step 3: Mediated effects of mom

15. Multicollinearity check

16. Including nominal Or ordinal Variables
Regression
Including nominal Or ordinal Variables

17. Categorical variables in regression

18. Association with DV

19. Dummy variables

20. Regression with dummy variables

21. ANOVA UNIANOVA kidagr BY harsh_o WITH momagr dadagr
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/CRITERIA = ALPHA(.05)
/DESIGN = momagr dadagr harsh_o .

22. Regression
Interaction effects

23. Moderated regression Maternal aggression Child aggression Paternal
Harsh
parenting

24. Moderated regression
momdadagr = momagr*dadagr

25. Issues Related to Regression Homework

26. Issues
Interpreting regression coefficients when measurement units are not meaningful
Interval level, different units of measurement
Legend of conceptual framework
Test of mediated effects XYZ
Atheoretical regression models
Write-up
Hypotheses
Less…than
According to conceptual framework
Regression equations in text
Decimal points

27. Regression & ANOVA: Wrap up

28. Common elements All of these models are linear:
DV(s)=b1*IV1 + b2*IV2 + b3*IV3
All of these models assume a interval/ratio level DV.
All of these models can handle categorical or interval/ratio IVs.
All of these models use some form of least squares method (squared deviations from the mean).

29. Common elements
All of these methods assume SRS (independence of observations).
All of these methods assume homoskedasticity.
All of these methods can only model “flat” and unidirectional effects.

30. ANOVA / Regression Differences arise from “traditions.”
ANOVA  Experimental design
Regression  Non-experimental/survey design.
Differences in the yield of information:
Regression is superior.

31. Within Subjects Designs
Regression with fixed or random effects:

32. Factor Analyses
Regression with an “unknown” IV:

33. HLMs
Regression coefficients themselves are DVs.