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Quantitative Methods

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

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Quantitative Methods

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  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 ANOVA table - whether x-variables predict y-variable Coefficients table - how x-variables predict y-variable 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

  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. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 TREATMNT Coef PREDICTED 1 -1.590 BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 32.316 Combining categorical and continuous variables Model formulae, model and fitted values BACAFTER = BACBEF+TREATMNT (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. FAT = m + SEX Coeff + b*WEIGHT M g F -g FAT = m + SEX Coeff M g F -g Combining categorical and continuous variables Graphs and equations FAT = m + b*WEIGHT

  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… • 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)

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