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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.

 


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Coefficient of Determination Calculator


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 () 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:


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