1. Multivariate Description

2. What Technique? Response variable(s)... Predictors(s) No Predictors(s) Yes... is one distribution summary regression models... are many indirect gradient analysis (PCA, CA, DCA, MDS) cluster analysis direct gradient analysis constrained cluster analysis discriminant analysis (CVA)

3. Raw Data

4. Linear Regression

5. Two Regressions

6. Principal Components

7. Gulls Variables

8. Scree Plot

9. Output > gulls.pca2$loadings Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Weight -0.505 -0.343 0.285 0.739 Wing -0.490 0.852 -0.143 0.116 Bill -0.500 -0.381 -0.742 -0.232 H.and.B -0.505 -0.107 0.589 -0.622 > summary(gulls.pca2) Importance of components: Comp.1 Comp.2 Comp.3 Standard deviation 1.8133342 0.52544623 0.47501980 Proportion of Variance 0.8243224 0.06921464 0.05656722 Cumulative Proportion 0.8243224 0.89353703 0.95010425

10. Bi-Plot

11. Male or Female?

12. Linear Discriminant > gulls.lda <- lda(Sex ~ Wing + Weight + H.and.B + Bill, gulls) lda(Sex ~ Wing + Weight + H.and.B + Bill, data = gulls) Prior probabilities of groups: 0 1 0.5801105 0.4198895 Group means: Wing Weight H.and.B Bill 0 410.0381 871.7619 115.1143 17.62524 1 430.6118 1054.3092 125.9474 19.50789 Coefficients of linear discriminants: LD1 Wing 0.045512619 Weight 0.001887236 H.and.B 0.138127194 Bill 0.444847743

13. Discriminating

14. Relationship between PCA and LDA

15. CVA