1. Combining continuous and categorical variables
Quantitative Methods
Combining continuous and categorical variables

2. Reprise of models fitted so far
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. Reprise of models fitted so far
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. Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values

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

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

7. Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values
BACAFTER = BACBEF+TREATMNT
(Model Formula)
TREATMNT Coef 1
BACAFTER = m + bBACBEF  
1 -2
(Model)
TREATMNT Coef
PREDICTED
BACAFTER = BACBEF
(Fitted Value Equation or
Best Fit Equation)

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

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

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

11. Combining categorical and continuous variables
Graphs and equations

12. Graphs and equations Combining categorical and continuous variables
FAT = m + b*WEIGHT
FAT = m + SEX Coeff
M g
F g
FAT = m + SEX Coeff + b*WEIGHT
M g
F g

13. Combining categorical and continuous variables
Graphs and equations

14. Combining categorical and continuous variables
Graphs and equations

15. Orthogonality Combining categorical and continuous variables
… 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. Next week: Interactions - getting more complex
Combining categorical and continuous variables
Last words…
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
Next week: Interactions - getting more complex
Read Chapter 7 (a long one)