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