# Canonical Correlation

Quantitative Results
Statistical Analysis

A canonical correlation is a correlation between two canonical or latent types of variables. In canonical correlation, one variable is an independent variable and the other variable is a dependent variable. It is important for the researcher to know that unlike regression analysis, the researcher can find a relationship between many dependent and independent variables. A statistic called the Wilk’s Lamda is used for testing the significance of this correlation. The work of the canonical correlation is the same as in simple correlation. In both of these, the point is to provide the percentage of the variances in the dependent variable that are explained by the independent variable. So, canonical correlation is defined as the tool that measures the degree of the relationship between the two variates.

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The process of canonical correlation is considered the member of the multiple general linear hypotheses, and therefore the assumptions of multiple regressions are also assumed in this correlation as well.

There are concepts and terms associated with canonical correlation. These concepts and terms will help a researcher better understand. They are as follows:

1. Canonical variable or variate: In canonical correlation is defined as the linear combination of the set of original variables. These variables are a form of latent variables.

2. Eigen values: The value of the Eigen values in canonical correlation are considered as approximately being equal to the square of the value. The Eigen values basically reflect the proportion of the variance in the canonical variate, which is explained by the canonical correlation that relates to the two sets of variables.

3. Canonical Weight: The other name for canonical weight is the canonical coefficient. The canonical weight in canonical correlation must first be standardized. It is then used to assess the relative importance of the contribution of the individual’s variable.

4. Canonical communality coefficient: This coefficient in canonical correlation is defined as the sum of the squared structure coefficients for the given type of variable.

5. Redundancy coefficient, d: This coefficient in canonical correlation basically measures the percent of the variance of the original variables of one set that is predicted from the other sets.

6. Likelihood ratio test: This significance test in canonical correlation is used to carry out the significance test of all the sources of the linear relationship between the two canonical variables.

There are certain assumptions that are made by the researcher for conducting canonical correlation. They are as follows:

1. It is assumed that the interval type of data is used to carry out canonical correlation.

2. It is assumed in canonical correlation that the relationships should be linear in nature.

3. It is assumed that there should be low multicollinearity in the data while performing canonical correlation. If the two sets of data are highly inter-correlated, then the coefficient of the canonical correlation is unstable.

4. There should be unrestricted variance in canonical correlation. If the variance is not unrestricted, then this might make the canonical correlation look unstable.

Most researchers think that canonical correlation is computed in SPSS. However, canonical correlation is obtained while computing MANOVA in SPSS. In MANOVA, canonical correlation is used in data sets where one refers to the one set of variables as the dependent and the other as the covariates.