# Multiple R-squared and adjusted R-squared for one variable

I understand that adding variables leads to a better representation of random noise, thus a higher R^2, and thus, in multiple regression, it is adjusted for.

In simple linear regression with one variable, there should not be a difference, should there? However, I get different values that are always quite close but not identical.

Is that difference meaningful? Which value is right? For example:

Multiple R-squared: 0.9118, Adjusted R-squared: 0.9109

To answer your first question: if you have even a single predictor, the $$R^2$$ and adj. $$R^2$$ would be different. Check the adj. $$R^2$$ formula below:
$$\bar R^2 = 1 - (1 - R^2)\frac{n-1}{n-p-1}$$
You can see that having a single predictor ($$p$$) would change the denominator and the adj. $$R^2$$.