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Coefficient of Determination Calculator


How to use the coefficient of determination calculator?

  • Enter the data set X
  • Enter the data set Y
  • Values must be comma separated.
  • Click on the calculate button.
  • You can erase all inputs by clicking on the reset button.

 






Coefficient of determination calculator:


The coefficient of determination calculator calculates the coefficient of determination (R2) and the correlation coefficient (r) of the entered data sets it also gives the step-by-step solution. Firstly, it calculates “r” stepwise and then takes its square to find out the coefficient of determination.


What is the coefficient of determination?


The coefficient of determination (R²) measures how well a statistical model predicts an outcome. The outcome is represented by the model’s dependent variable.

The R2 ranges from 0 to 1, if the result is 0 then the outcome of the model is not good, and vice versa.


Ways to calculate R2:


There are two different ways to calculate R2 both are as follows:

  • Method 1: Calculate the correlation coefficient “r” and then take its square.
  • Method 2: Use the following formula

            Coefficient of determination formula

  • RSS is the sum of the squares of the residuals.
  • TSS is the total sum.  

How to calculate the coefficient of determination:


The coefficient of determination (R2) can be calculated by following the below steps:

  1. Calculate the correlation coefficient
  • Calculate the mean of the data sets:
  • Calculate the deviation scores
  • Calculate the squared deviations
  • Find out the product of the squared deviations
  • Apply this formula

           Correlation coefficient formula

  1. Take the square of “r”.

Examples:


In this section, the step-by-step solution for calculating the coefficient of determination is given:

Example 1:

If X = 4, 6, 7, 24, 9.5, 2, 37, 13.7 and Y = 3, 35, 64, 223, 91, 44, 9.3, 12 then find out R2.

Solution:

X = 4, 6, 7, 24, 9.5, 2, 37, 13.7

Y= 3, 35, 64, 223, 91, 44, 9.3, 12

Step 1: Calculate the mean of X and Y

x̄ = (4 + 6 + 7 + 24 + 9.5 + 2 + 37 + 13.7) / 8

x̄ = 103.2 / 8

x̄ = 12.9

ȳ = (3 + 35 + 64 + 223 + 91 + 44 + 9.3 + 12) / 8

ȳ = 481 / 8

ȳ = 60.163

x -

y - ȳ

 (x -)2

(y - ȳ)2

(x -)(y - ȳ)

−8.9

−57.163

79.21

3267.609

508.7507

−6.9

−25.163

47.61

633.177

173.6247

−5.9

3.837

34.81

14.723

−22.6383

11.1

162.837

123.21

26515.889

1807.4907

−3.4

30.837

11.56

950.921

−104.8458

−10.9

−16.163

118.81

261.243

176.1767

24.1

−50.863

580.81

2587.045

−1225.7983

0.8

−48.163

0.64

2319.675

−38.5304

 

Sum

996.66

36550.278752

1274.23

 

Step 2: Applying the formula:

r = ∑ ((x - x̄) (y-ȳ)) / √ (∑ (x-x̄)2 ∑ (y-ȳ)2)

Putting the values

r = 1274.23/ √ ((996.66) (36550.278752)) 

r = 0.2111

Step 3: Take the square.

R2 = 0.04456


References:


Coefficient of determination | Statistics Solutions

Coefficient of determination formula | EDUCBA