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Correlation Coefficients Help

The linear correlation coefficient, R, is a measure of the association between two variables. The maximum value for R is + 1. The minimum value for R is – 1. In both these cases, all sample points fall on a straight line. As R approaches +1 or -1, the stronger the correlation between x and y. The square of this coefficient indicates the fraction of variation in y that is associated with x. An example of this technique is given below.

An engineer wants to know if there is a linear correlation between the hardening temperature, the tempering temperature, and the hardness of steel part. The data that has been collected is shown below.

Select OK to generate the output.

Correlation Coefficient Output

A new worksheet is added with the following table:

The variables are listed in the first row across and down the first column. For each pair of variables, the correlation coefficient is given on one row and the p value is given on the row below it. If the p value is < 0.05, it is highlighted in red. The two calculations are shown below.

Pearson’s Correlation Coefficient

p Value

Determined from a two-tailed test using the t distribution with:

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