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 **