# Correlation Coefficient Calculator

Please enter your values in the Correlation Coefficient Calculator. Each value should be separated by a comma.

X Values (each value separated by comma): Y Values (each value separated by 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