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 **