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 (R2) = [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 R2 = [(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 R2 of 0.9758
Calculate the Adjusted R-Squared
You may use this formula to calculate the Adjusted R-Squared:
(n-1)*(1 - R2)
Adjusted R-Squared = 1 - (n - k -1)
Where:
- R2 = 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.