# What is Adjusted R-Squared

Adjusted R-Squared is a modified form of **R-Squared** whose value increases if new predictors tend to improve models performance and decreases if new predictors does not improve performance as expected. R-squared is a comparison of **Residual sum of squares** (SSres) with total sum of squares(SStot). It is calculated by dividing **sum of squares of residuals** from the regression model by total sum of squares of errors from the average model and then subtract it from 1.

Unlike R-squared, the **Adjusted R-squared** would penalize you for adding features which are not useful for predicting the target. It takes into account the number of **independent variables** used for predicting the target variable.

where,

- N = number of records in the data set.
- p = number of independent variables.

For a simple representation, you can rewrite the above formula like the following:

**Adjusted R-squared = 1 — (x * y)**

where,

- x = 1 — R Squared
- y = (N-1) / (n-p-1)

Adjusted R-squared can be negative when R-squared is close to zero.

Adjusted R-squared value always be less than or equal to R-squared value.