Correlation Coefficients Help
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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.
- 1. Enter the data into a worksheet as shown below The data can be downloaded at this link.
![](https://www.spcforexcel.com/wp-content/uploads/Correlation-Data.jpg)
- 2. Select the data and the headings.
- 3. Select “Correlation” from the “Statistical Tools” panel on the SPC for Excel ribbon.
- 4. Select the “Correlation Coefficients” option and then OK.
- 5. The following input box is used to enter the range containing the data and the headings. The default is the range selected on the worksheet.
![](https://www.spcforexcel.com/wp-content/uploads/Correlation-Coef-Input.jpg)
Select OK to generate the output.
Correlation Coefficient Output
A new worksheet is added with the following table:
![](https://www.spcforexcel.com/wp-content/uploads/Correlation-Coef-Output.jpg)
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
![](https://www.spcforexcel.com/wp-content/uploads/r-equation.jpg)
- n = number of paired data points for the variable x and the variable y
- sx = standard deviation of x
- sy = standard deviation of y
- Xbar= average of x
- Ybar= average of y
p Value
Determined from a two-tailed test using the t distribution with:
![](https://www.spcforexcel.com/wp-content/uploads/t-dist-equation.jpg)