How Do I Compute a Correlation Coefficient?

How Do I Compute a Correlation Coefficient?

A correlation coefficient is computed by inserting the proper values into a simple question.

The formula is as follows:

$$r_{xy}=\frac{n\sum XY-\sum X\sum Y}{\sqrt{\left[n\sum X^2-{\left(\sum X\right)}^2\right]\left[n\sum Y^2-{\left(\sum Y\right)}^2\right]},}$$

where

• rxy is the correlation coefficient between X and Y;
• n is the size of the sample;
• X is the individual’s score on the X variable;
• Y is the individual’s score on the Y variable;
• XY is the product of each X score times its corresponding Y score;
• X2 is the individual’s X score, squared; and
• Y2 is the individual’s Y score, squared.

For example, let’s compute the correlation coefficient, represented as a lowercase rxy for the the variables X and Y, using the following data:

With the values substituted, the equation looks like this:

$$r_{xy}=\frac{10(360)-(46)(74)}{\sqrt{[10(238)-{(46)}^2][10(578)-{(74)}^2]}}=.69$$

And the result is that rxy equals .69, a positive or direct correlation.

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