Combining continuous and categorical variables Quantitative Methods Combining continuous and categorical variables

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

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

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

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

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

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 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 (Model) TREATMNT Coef PREDICTED 1 -1.590 BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 3 2.316 (Fitted Value Equation or Best Fit Equation)

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

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

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

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

Combining categorical and continuous variables Graphs and equations

Combining categorical and continuous variables Graphs and equations

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.

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

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)