Coefficient of Determination Calculator
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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.

# Coefficient of Determination Calculator

## Coefficient of determination calculator:

The coefficient of determination R2 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

• 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

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 - x̄ y - ȳ (x - x̄)2 (y - ȳ)2 (x - x̄)(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

10 months ago