Please enter your values in the Correlation Coefficient Calculator. Each value should be separated by a comma.
How to Use the Calculator
Let's review a simple example to demonstrate how to use the correlation coefficient calculator. Suppose that you have the following data, where:
- The X values are: 2, 7, 12
- The Y values are: 4, 11, 15
To get the correlation coefficient, simply enter the above values in the calculator, and then click on the Calculate Correlation Coefficient button:
You would then get the result of 0.98783:
How to Manually Calculate the Correlation Coefficient
You may use the following equation to calculate the correlation coefficient manually:
Σ [(xi - x̅) * (yi - ȳ)]
Correlation Coefficient (R) = [ Σ(xi - x̅)2 ]0.5 * [ Σ(yi - ȳ)2 ]0.5
For example, you can apply the calculations below to derive the correlation coefficient, where:
- The X values are: 2, 7, 12
- The Y values are: 4, 11, 15
To start, calculate the averages:
2 + 7 + 12
Average ( x̅ ) = 3 = 7
4 + 11 + 15
Average ( ȳ ) = 3 = 10
Finally, calculate the correlation coefficient as follows:
[(2 - 7) * (4 - 10)] + [(7 - 7) * (11 - 10)] + [(12 - 7) * (15 - 10)]
R = [(2 - 7)2 + (7 - 7)2 + (12 - 7)2 ]0.5 * [(4 - 10)2 + (11 - 10)2 + (15 - 10)2 ]0.5 = 0.98783
You'll then get the same result of 0.98783