ShowCorrelation

ShowCorrelation creates a visual color-coded representation of a given correlation matrix. It also determines whether your correlation matrix is valid ("positive definite") and creates a Principal Components Report. It is server-based: you submit (via HTML form) the correlation as input. The color-coded representation is sorted by three different methods that let you easily see patterns and data groupings.

Data patterns and groupings are much harder to see from a table of numbers -- the usual representation of correlation -- than with the ShowCorrelation color-coded representation.

Here is an example with 7 variables, r1,...r7. The correlation matrix that shows the pairwise correlations of all the variables is (with 0 in the upper diagonals):

r1	r2	r3	r4	r5	r6	r7
1.000	0.000	0.000	0.000	0.000	0.000	0.000
-0.141	1.000	0.000	0.000	0.000	0.000	0.000
-0.100	0.456	1.000	0.000	0.000	0.000	0.000
0.976	-0.329	0.688	1.000	0.000	0.000	0.000
-0.787	-0.272	0.485	-0.507	1.000	0.000	0.000
-0.235	0.273	0.061	-0.229	0.255	1.000	0.000
-0.631	0.278	0.269	-0.745	0.643	0.746	1.000

The ShowCorrelation output is:

Visual Correlation

Visual Correlation

These colors reveal two variable groups: {r7, r5,r6} and {r1, r4} .

Visual Correlation

The other ShowCorrelation output is the Principal Components Report. Here is an example with 4 variables, x1, x2, x3, x4:

Principal Component	Variance (Eigenvalue)	Per Cent Variance	Accumulated Variance	Accumulated % Variance
x1	2.6375	65.938 %	2.6375	65.938 %
x2	1.1710	29.275 %	3.8085	95.213 %
x3	0.1848	4.621 %	3.9934	99.834 %
x4	0.0066	0.166 %	4.0000	100.000 %

This report shows how the variances of the Principal Components are distributed. In this example, 95% of the variance (the "eigenvalues" of the Correlation Matrix) of the original 4 variables are contained in the first 2 Principal Components. This provides additional insights for the Visual Correlation displays.

Note that one of the theoretical properties of a correlation matrix is that all of its eigenvalues must be strictly greater than zero. ShowCorrelation displays these eigenvalues in its Principal Components Report.

The second part of the Principal Components Report lists all Principal Components (the "eigenvectors" of the Correlation Matrix):

x1	x2	x3	x4
0.6092	-0.0287	-0.2999	-0.7336
0.6044	-0.0250	-0.4219	0.6754
0.4224	0.6192	0.6595	0.0569
0.2919	-0.7843	0.5451	0.0503

There are two inputs to ShowCorrelation. The first is an input box that asks for the number of variables; the second is a text area box.

In the text area box you paste a table: the first row of the table contains variable labels, the remainder of the table contains the Correlation Matrix.

The table must be in tab-delimited format: the columns are separated by tabs and the rows are separated by carriage returns. When you copy a table from an Excel spreadsheet to a text area box in the ShowCorrelation dialog, it will automatically be in tab-delimited text.

View the ShowCorrelation Help and Documentation.

To use ShowCorrelation, just post your problem to our server via HTML forms and get the answer immediately. No download or installation is needed. You do need an access license which allows you to pay-by-use as needed.

If you want to see a sample run, click here .

 
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