Quantitative Methods Combining continuous and categorical variables

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

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

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

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

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

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 BACAFTER = BACBEF (Model Formula) (Model) (Fitted Value Equation or Best Fit Equation)

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

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

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

Combining categorical and continuous variables Graphs and equations

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

Combining categorical and continuous variables Graphs and equations

Combining categorical and continuous variables Graphs and equations

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.

Combining categorical and continuous variables Orthogonality

Combining categorical and continuous variables Orthogonality

Combining categorical and continuous variables Orthogonality

Combining categorical and continuous variables Ambivalence

Combining categorical and continuous variables Ambivalence

Combining categorical and continuous variables Ambivalence

Combining categorical and continuous variables Generality of GLM

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