1. B&A 448-452; and http://www.youtube.com/watch?v=1b18fO9Vt50
REGRESSION - ANCOVA
B&A ; and

2. Technique: Statistics of the straight line
We have multiple data points (not just two)
We need to find a line that best fits them
Define “best fit” – Minimum squared deviations
slope
intercept
Independent variable
Error
Dependent variable
Regression coefficients

3. Technique: Statistics of the straight line
The line that “best fits” has the following slope:
Standard deviation of y
Standard deviation of x
Regression coefficient of y on x.
Correlation coefficient of x and y
The line that “best fits” has the following intercept:

4. Standard error of prediction
Regression does not provide an exact prediction
At each value of x, we expect that the value of y will be between two values, most of the time
We can estimate a confidence interval for predicted values of y, if we assume that at each value of x, the values of y will be distributed normally with a given standard deviation.
Standard deviation of all possible predicted y values obtained from all possible samples.
Confidence interval of prediction:

5. Components of the total variance
Standard deviation of all possible predicted y values obtained from all possible samples.
Variance that cannot be accounted for by regression
Variance that can be accounted for by regression
Total variance

6. Things to know
A significant regression coefficient does not “prove” causality
A regression can provide “predicted” values
Predicted values are “point” estimates
Confidence intervals around the point estimates provide very important information

7. THIS IS A TABLE YOU SHOULD KNOW BEFORE ANALYZING YOUR DATA AND THE FINAL
Dependent Variable
Independent Variable(s)
Method
Nominal/Ordinal
Chi-Square test
Interval/Ratio
T-test (2 groups) or ANOVA (3+ groups)
Multifactorial ANOVA (2+ IVs)
Regression
Interval/Ratio AND
ANCOVA/GLM

8. Example Analyses Using all Information

9. Regression exercise with 2008 SOCI 301 data
Attitudes towards marriage will be influenced by gender role attitudes. Gender role attitudes will be influenced by sex and maternal education.
Sex
Negative attitudes towards marriage
Non egalitarian gender role attitudes
Maternal education

10. Are gender role attitudes correlated with the attitudes towards marriage

11. Sex differences in gender role attitudes

12. Maternal education differences in gender role attitudes

13. Sex and maternal education differences in gender role attitudes

14. Differential effects of maternal education depending on sex?

15. Profile plot

16. Do gender role attitudes influence the attitudes towards marriage?

17. Can I do this in GLM UNIANOVA?
Attention:
You must ask for parameter estimates from GLM
You must specify interval/ratio IV s as “covariates”

18. Can we do the same in GLM (UNIANOVA)?

19. Can we include the nominal/ordinal variables too?
Attention:
You must include nominal/ordinal variables as “fixed factors”
You must specify interval/ratio IV s as “covariates”

20. ANCOVA Model

21. Assumptions
The interval/ratio level independent variable has a LINEAR association with the DV.
Error term has FIXED variance (same as regression).

22. Is the covariate desirable?
What if the factor is a predictor of the covariate?
Current example
What is the factor is independent of the covariate?
Covariate adds information to the model