Coefficient of Determination Calculator
The coefficient of determination formula calculates the value R2, which is used to analyze how differences in one variable can be explained by a difference in a second variable. The coefficient of determination is also known as the R squared formula.
What is a Coefficient of Determination Calculator?
'Coefficient of Determination Calculator' is an online tool that helps in calculating the coefficient of determination and correlation coefficient for a given data set. Just enter the values given in the data set and find the coefficient of determination in a few seconds.
How to Use Coefficient of Determination Calculator?
Please follow the below steps to find the coefficient of determination:
- Step 1: Enter the values of x and y (separated by comma) in the given input boxes.
- Step 2: Click on the "Calculate" button to find the coefficient of determination and correlation coefficient of the given dataset.
- Step 3: Click on the "Reset" button to clear the fields and enter the different values.
How to Find a Coefficient of Determination?
To find the coefficient of determination or r squared value, we calculate the square of the coefficient of correlation, R. The r squared formula is given as:
\(\large R^{2}=\left[\frac{N\sum xy-\sum x \sum y}{\sqrt{\left[N\sum x^{2}-\left(\sum x\right)^{2}\right]\left[N\sum y^{2}-\left(\sum y\right)^{2}\right]}}\right]^2\)
Where,
- R = Coefficient of correlation
- N = No of scores given
- ∑ XY = Sum of paired product
- ∑ X = X score sum
- ∑ Y = Y score sum
- ∑ X2 = square of X score sum
- ∑ Y2 = square of Y score sum
Solved Example:
Calculate the coefficient of determination using the r squared formula for given data:
X = 5, 6 ,12, 15 and
Y = 7, 14, 20, 25
Solution:
We will first construct a table to get the required values for the coefficient of determination formula:
| X | Y | X2 | Y2 | XY |
|---|---|---|---|---|
| 5 | 7 | 25 | 49 | 35 |
| 6 | 14 | 36 | 196 | 84 |
| 12 | 20 | 144 | 400 | 240 |
| 15 | 25 | 225 | 625 | 375 |
| ∑X=38 | ∑Y=66 | ∑X2=430 | ∑Y2=1,270 | ∑XY=734 |
The coefficient of correlation is given by,
\(\large R=\frac{N\sum xy-\sum x \sum y}{\sqrt{\left[N\sum x^{2}-\left(\sum x\right)^{2}\right]\left[N\sum y^{2}-\left(\sum y\right)^{2}\right]}}\)
\( \begin{align*} r &= \frac{ 4\times 734 - (38)(66) }{\sqrt{[4 \times 430 - (38)^2][4 \times 1,270 - (66)^2]}} \\ &= \frac{2,936 - 2,508}{ \sqrt{[1,720 - 1,444][5,080 - 4,356]}} \\ &= \frac{428}{447.02} \\ &= 0.9574 \end{align*}\)
Using r squared formula, coefficient of determination = R2 = 0.9167
Answer: Coefficient of determination for the given data = 0.9167
Similarly, you can try the calculator and find the coefficient of determination for the following:
- Calculate the coefficient of determination using the r squared formula for given data:
X = 1,3, 5 ,10, 12 and
Y = 6, 15, 22, 25