Quantitative Methods

Combining continuous and categorical variables

Combining categorical and continuous variables

Reprise of models fitted so far

YIELD=FERTILYIELDM=VARIETY

VOLUME=HEIGHTMATHS=ESSAYSSPECIES2=SPECIES1

AMA=YEARS+HGHTFINALHT=INITHT+WATER

WGHT=RLEG+LLEGPOETSAGE=BYEAR+DYEARLVOLUME=LDIAM+LHGHT

YIELD=BLOCK+BEANSEEDS=COLUMN+ROW+TREATMT

Combining categorical and continuous variables

Reprise of models fitted so far

YIELD=FERTILYIELDM=VARIETY

VOLUME=HEIGHTMATHS=ESSAYSSPECIES2=SPECIES1

AMA=YEARS+HGHTFINALHT=INITHT+WATER

WGHT=RLEG+LLEGPOETSAGE=BYEAR+DYEARLVOLUME=LDIAM+LHGHT

YIELD=BLOCK+BEANSEEDS=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 CoefPREDICTED 1 -1.590BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 3 2.316

(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