# Correlation

The Pearson product moment correlation coefficient is often referred to simply as the correlation. It is a measure of the association of two variables and usually designated by the letter r. A correlation matrix between pairs of columns can be produced using the following syntax:

`CORRELATION column,column,column`

To produce a correlation matrix of Tests 1, 2, 3, and 4, type:

`MTB> CORRELATION 'TEST1','TEST2','TEST3','TEST4'`

This would be the result.

TEST1 TEST2 TEST3

TEST2 0.704

TEST3 0.730 0.579

TEST4 0.382 0.237 0.657

Here we see that Test 1 is correlated with Test 2 .704, Test 1 with Test 3 .73, and Test 1 with Test 4 .382. Test 2 is correlated with Test 3 .579, and Test 4 .237. Test 3 is correlated with Test 4 .657. This indicates that the scores on Test 4 are not as closely linearly related to Test 1 and Test 2 as the other tests are to each other.

When the correlation is positive, two columns are closely related the closer the correlation is to 1, and two columns are not closely related the closer the correlation is to 0. When the correlation is negative, two columns are closely related the closer the correlation is to -1, and two columns are not closely related the closer the correlation is to 0.

Test 1 is correlated with Test 2 .704. This means that people who did well on Test 1 tended to do well on Test 2, and people who did poorly on Test 1 tended to do poorly on Test 2. Since the correlation is not exactly 1, this is not a perfect linear relationship. That may mean that a person who did poorly on Test 1 scored better than expected on Test 2.