The bivariate correlation analysis measures the strength of the relationship between two variables. One may be required to find the strength of the relationship between two sets of variables. In this case, canonical correlation is an appropriate technique for measuring the strength of the relationship between two sets of variables. Canonical correlation is appropriate in the same situations where multiple regression would be, but where there are multiple inter-correlated outcome variables. Canonical correlation analysis determines a set of canonical variates, orthogonal linear combinations of the variables within each set that best explain the variability both within and between sets.

### Examples: Canonical Correlation Analysis

- In medicine, individuals’ lifestyles and eating habits may affect their different health measures determined by several health-related variables such as hypertension, weight, anxiety, and tension level.
- In business, the marketing manager of a consumer goods firm may be interested in finding the relationship between the types of products purchased and consumers’ lifestyles and personalities.

From the above two examples, one set of variables is the predictor or independent while the other set of variables is the criterion or dependent set. The objective of canonical correlation is to determine if the predictor set of variables affects the criterion set of variables.

Note that it is unnecessary to designate the two sets of variables as dependent and independent. In this case, the objective of canonical correlation is to ascertain the relationship between the two sets of variables.

The objective of canonical correlation is similar to conducting a principal components analysis on each set of variables. In principal components analysis, the first new axis results in a new variable that accounts for the maximum variance in the data. In contrast, in canonical correlation analysis, a new axis is identified for each set of variables such that the correlation between the two resulting new variables is maximum.

Canonical correlation analysis can also be considered a data reduction technique as only a few canonical variables may be needed to adequately represent the association between the two sets of variables. Therefore, an additional objective of canonical correlation is to determine the minimum number of canonical correlations needed to adequately represent the association between two sets of variables.