Enter your values in the **Coefficient of Determination (R-Squared) Calculator**. Each value should be separated by a comma. Example is included below.

## How to use the Coefficient of Determination Calculator

Let's say that you'd like to calculate the Coefficient of Determination using the values below:

- The X values are: 2, 7, 12
- The Y values are: 4, 11, 15

To start, enter the values in the Coefficient of Determination calculator:

Then, click on the button to execute the calculations. You'll then get the R-Squared of **0.9758 **and the Adjusted R-Squared of **0.9516**:

## How to Manually Calculate the Coefficient of Determination

You may use the following formula to manually calculate the Coefficient of Determination (R-Squared):

` [ Σ [(xi - x̅) * (yi - ȳ)] ]`^{2}
R-Squared (R^{2}) = [Σ(xi - x̅)^{2 }]*[Σ(yi - ȳ)^{2}]

Where:

- x̅ = Average of all the x values
- ȳ = Average of all the y values

For example, let's say that you have the following values:

- 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 R-Squared as follows:

[ [(2 - 7) * (4 - 10)] + [(7 - 7) * (11 - 10)] + [(12 - 7) * (15 - 10)] ]^{2}R^{2}= [(2 - 7)^{2 }+ (7 - 7)^{2 }+ (12 - 7)^{2 }]*[(4 - 10)^{2 }+ (11 - 10)^{2 }+ (15 - 10)^{2 }] = 0.9758

You'll then get the R^{2} of **0.9758**

### Calculate the Adjusted R-Squared

You may use this formula to calculate the Adjusted R-Squared:

` (n-1)*(1 - R`^{2})

Adjusted R-Squared = 1 - (n - k -1)

Where:

- R
^{2}= R-Squared - n = Sample Size
- k = Number of independent variables used in the regression model (for simple linear regression k = 1)

For our example, the Adjusted R-Squared is:

` (3-1)*(1 - 0.9758)`

Adjusted R-Squared = 1 - (3 - 1 - 1) = 0.9516

The Adjusted R-Squared is therefore **0.9516**.