# Agenda of Week VII Review of Week VI Multiple regression Canonical correlation.

## Presentation on theme: "Agenda of Week VII Review of Week VI Multiple regression Canonical correlation."— Presentation transcript:

Agenda of Week VII Review of Week VI Multiple regression Canonical correlation

Review of Week VI Inference on MV Mean Vector Two populations Inference on MV Mean Vector Multi-populations: MANOVA

Multiple Regression Basic assumptions Linearity X is an n by K matrix with rank K Regression Homoscedasticity

Multiple Regression Hypotheses By ANOVA When the null hypothesis is rejected, For all i.

Multiple Regression OLS model OLS solution

Multiple Regression ANOVA table

Multiple Regression t-statistics (d.f. = n-k) Where S kk is the k th diagonal element of (XX) -1 Standard error of the regression

Multiple Regression Standard error of coefficient

Canonical Correlation Correlation structure between a group of independent variables and a group of dependent variables A kind of multiple regression with more than two dependent variables Example: Physical size group vs. Exercise group How much explained the variation of a group of variables by other group of variables?

Canonical Correlation Basic model Group of independent variables Group of dependent variables Covariance matrixes

Canonical Correlation Basic model LC of two groups of variables Correlation between V and W

Canonical Correlation Correlation testing Hypotheses Correlation between V and W

Canonical Correlation Objective: To find α and β maximizing ρ or r.

Canonical Correlation 1 st canonical variable k th canonical variable

Canonical Correlation 1 st canonical correlation coefficient k th canonical coefficient coefficient

Canonical Correlation