Multivariate Analysis: Correlation Analysis

Variables Tab

You can use the Variables tab to specify the numerical variables for the analysis. The Variables tab is shown in Figure 25.2.

The variables in the Y Variables list correspond to variables in the VAR statement of the CORR procedure. The variables in the X Variables (With) list correspond to variables in the WITH statement of the CORR procedure.

The simplest way to analyze correlations is to add the variables of interest to the Y Variables list, as in the example earlier in this chapter.

If the X Variables (With) list is empty, the correlation matrix is symmetric. If you request a matrix of pairwise scatter plots (on the Plots tab), you will get plots for pairs of variables in the lower triangular portion of the matrix.

If the X Variables (With) list is not empty, the correlation matrix is not symmetric. If you specify $C_1, \ldots C_ m$ as the Y variables and $R_1, \ldots R_ n$ as the WITH variables, then the (i, j) cell of the correlation matrix will be the correlation of $R_ i$ with $C_ j$. If you request a matrix of pairwise scatter plots, you will get $nm$ plots, arranged in n rows and m columns.

The Partial list is rarely used. The variables in this list correspond to variables in the PARTIAL statement of the CORR procedure. A partial correlation measures the strength of a relationship between two variables, while controlling the effect of other variables. The Pearson partial correlation between two variables, after controlling for variables in the PARTIAL statement, is equivalent to the Pearson correlation between the residuals of the two variables after regression on the controlling variables.

If there are variables in the Partial list, then the following conditions hold:

  • You cannot request Hoeffding’s D correlation statistic.

  • Observations with missing values are excluded from the analysis.