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The coefficient of determination calculator calculates the coefficient of determination (R^{2}) 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.
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 R^{2} ranges from 0 to 1, if the result is 0 then the outcome of the model is not good, and vice versa.
There are two different ways to calculate R^{2} both are as follows:
The coefficient of determination (R^{2}) can be calculated by following the below steps:
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 R^{2}.
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.
R^{2} = 0.04456
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Coefficient of determination formula | EDUCBA