Adjusted r square

Before starting this please check below r square blog.

R square

Adding a variable to your model increases the r square value. That new variable may or may not be a useful variable to our model. Since r square searches for best fit ,r square doesn’t bother about new variable, it just keeps on increasing whenever you add a new variable.

So question is how can we solve this issue?

Answer: Using adjusted r square

When a useless variable is added

1. “k” increases
2. In turn overall “denominator” gets reduced.
3. We saw Adding a variable to your model increases the r square value, so r square value in equation increases.
4. Which in turn reduces the adjusted r square value.

Logically just by thinking on proportionality(directly or inversely proportional) we can understand how adjusted r square reduces on adding a new useless variable.

So Adjusted R-squared is used to determine how reliable the correlation is and how much it is determined by the addition of independent variables.