1. Quantitative Methods Combining continuous and categorical variables

2. Combining categorical and continuous variables Reprise of models fitted so far YIELD=FERTIL YIELDM=VARIETY VOLUME=HEIGHT MATHS=ESSAYS SPECIES2=SPECIES1 AMA=YEARS+HGHT FINALHT=INITHT+WATER WGHT=RLEG+LLEG POETSAGE=BYEAR+DYEAR LVOLUME=LDIAM+LHGHT YIELD=BLOCK+BEAN SEEDS=COLUMN+ROW+TREATMT

3. Combining categorical and continuous variables Reprise of models fitted so far YIELD=FERTIL YIELDM=VARIETY VOLUME=HEIGHT MATHS=ESSAYS SPECIES2=SPECIES1 AMA=YEARS+HGHT FINALHT=INITHT+WATER WGHT=RLEG+LLEG POETSAGE=BYEAR+DYEAR LVOLUME=LDIAM+LHGHT YIELD=BLOCK+BEAN SEEDS=COLUMN+ROW+TREATMT ANOVA table - whether x- variables predict y-variable Coefficients table - how x- variables predict y-variable

4. Combining categorical and continuous variables Model formulae, model and fitted values

5. Combining categorical and continuous variables Model formulae, model and fitted values

6. Combining categorical and continuous variables Model formulae, model and fitted values

7. Combining categorical and continuous variables Model formulae, model and fitted values BACAFTER = BACBEF+TREATMNT TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 TREATMNT Coef PREDICTED 1 -1.590 BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 3 2.316 (Model Formula) (Model) (Fitted Value Equation or Best Fit Equation)

8. Combining categorical and continuous variables Model formulae, model and fitted values

9. Combining categorical and continuous variables Model formulae, model and fitted values

10. Combining categorical and continuous variables Model formulae, model and fitted values

11. Combining categorical and continuous variables Graphs and equations

12. Combining categorical and continuous variables FAT =  + *WEIGHT FAT =  + SEX Coeff M  F - FAT =  + SEX Coeff + *WEIGHT M  F - Graphs and equations

13. Combining categorical and continuous variables Graphs and equations

14. Combining categorical and continuous variables Graphs and equations

15. Combining categorical and continuous variables Orthogonality … is a relationship that may hold between two x-variables The general concept is that two x-variables are orthogonal if you can’t predict one when you know the other.

16. Combining categorical and continuous variables Orthogonality

17. Combining categorical and continuous variables Orthogonality

18. Combining categorical and continuous variables Orthogonality

19. Combining categorical and continuous variables Ambivalence

20. Combining categorical and continuous variables Ambivalence

21. Combining categorical and continuous variables Ambivalence

22. Combining categorical and continuous variables Generality of GLM

23. Combining categorical and continuous variables Last words… Next week: Interactions - getting more complex Read Chapter 7 (a long one) Continuous and categorical variables can be freely combined in a model formula Know how to construct the model Know how to construct the fitted value equation Some variables may be treated in either way The GLM encompasses many traditional tests