Coefficient of Determination Calculator Formula

Understand the math behind the coefficient of determination calculator. Each variable explained with a worked example.

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Formulas Used

R-squared

r_squared = pow(r, 2)

Variance Explained (%)

r_sq_pct = pow(r, 2) * 100

1 - R-squared

unexplained = 1 - pow(r, 2)

Unexplained Variance (%)

unexplained_pct = (1 - pow(r, 2)) * 100

Variables

VariableDescriptionDefault
rCorrelation Coefficient (r)0.85

How It Works

How to Calculate the Coefficient of Determination

Formula

R-squared = r^2

R-squared is the square of the Pearson correlation coefficient. It represents the proportion of variance in the dependent variable that is predictable from the independent variable. The remaining 1 - R^2 is unexplained variance.

Worked Example

If r = 0.85, how much variance does X explain in Y?

r = 0.85
  1. 01R-squared = 0.85^2 = 0.7225
  2. 02X explains 72.25% of the variance in Y
  3. 03Unexplained variance = 1 - 0.7225 = 0.2775 or 27.75%

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