R²

Also called "Coefficient of determination".

In Simple  Linear Regression (and Multiple Linear Regression), a number between 0 and 1 that tells of how well the Least Squares line fits the sample :

• R² = 0 means that there is absolutely no linear relationship between the independent variables and the dependent variable. Note that this does not mean that there is no relationship between independent and dependent variables (for more on that, see here).
• R² = 1 means that the relationship between independent and dependent variable is perfectly linear.

For more information on R², please report to the tutorials on Simple and Multiple Linear Regression.

R² (Adjusted)

R² is an optimistic estimation of the quality of a Linear Regression. Provided that some severe assumptions on data are met, a more realistic value, called "Adjusted R²" can be determined by computation only, without resorting to cumbersome validation techniques, .

For more information on R², please report to the tutorials on Simple and Multiple Linear Regression.