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Adjusted R-Squared

The adjusted R squared modifies the standard R squared to account for the degrees of freedom used when estimating model parameters

What is Adjusted R-Squared?

The adjusted R2 modifies the standard R2 to account for the degrees of freedom used when estimating model parameters. Adjusted R-Squared can be determined using the sum of squares formula. The degree of freedom is the only difference between R-square and Adjusted R-square equations. An adjusted R-squared value can be derived based on the r-squared value, the number of independent variables (predictors), and the total sample size.

R2 is not comparable across models with different dependent (Y) variables.

Example of Adjusted R-Squared:

The adjusted R2 value is expressed as:

$ R^{2}\, =\, 1\, -\, [(\frac{n-1}{n-k-1})\, \times (1\, -\, R^{2})] $

where:
n = number of observations
k = number of independent variables

Why is calculating Adjusted R-Squared important?

Adjusted R square adds further value to our analysis and assists analysts in analysing whether the newly added factor is bringing more value or not. Hence, it assists analysts in making better-informed risk decisions.

Owais Siddiqui
1 min read
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