# R square and adjusted R square

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• #3762

I am confused about the difference between R square and adjusted R square. I’ve 11% R square and 2% adjusted R square of my model. I’ve one dependent and two independent variables in my model. How I can interpret and differentiate R square and adjusted R square for my model?

Thanks

#3764

The problem with R square is that it’s biased upwards as a population estimate.  Imagine that the true (population) correlation is exactly zero.   Now sample data from that population.  You won’t get a correlation of zero – you’ll sometimes get a correlation that’s positive (too high) and sometimes negative (too low).    However, if you were to sample lots of times, on average you would get a correlation of zero.  So the correlation is an unbiased estimate of the population correlation.

If the population correlation is 0, then the population R-squared is also zero.  But what happens when we sample and get a positive correlation?  We get a positive R-squared.  And if we sample and get a negative correlation, we square that to get R-squared.  So, on average, the R-squared is positive when the true R-squared is zero.  Hence R-squared is biased.

To remove this bias, you can use adjusted R-squared.  This makes R-squared smaller, and the effect is larger when you have more variables, and smaller when you have fewer people.  If you only have two predictor variables, and R-squared is going down that much , you don’t have many predictors.

Use R-squared for R-squared.  Don’t worry about adjusted R-squared, unless you’re going to do precise prediction.

#3763

Thank You very much dear Miles

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