Statistics/Multivariate Data Analysis/Canonical Correlation Analysis

From Wikibooks, open books for an open world
< Statistics
Jump to navigation Jump to search

CANONICAL ANALYSIS This analysis can be used incase of measurable and non-measurable variables for the purpose of simultaneously predicting a set of dependent variables from their joint covariance with a set of independent variables. Both metric and non-metric data can be used in the context of this multivariate technique. The procedure is to followed is to obtain a set of weights for the dependent independent variables in such a way that linear composite of the criterion variables has a maximum correlation with the linear composite of the explanatory variables The main objective of canonical correlation analysis is to discover factors separately in the two sets of variables such that the multiple correlations between sets of factors will be the maximum possible. Mathematically, the weight of two sets y= a1*y1 + a2*y2 + ... + ap*yp

           x=b1*x1 + b2*x2 + ... + bq*xq

Have common variance. The resulting canonical correlation solution then gives an overall description of the presence or absence of a relationship between the two sets of variables.