Interpretation
R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1.0 indicates that the regression line perfectly fits the data.
Values of R2 outside the range 0 to 1 can occur where it is used to measure the agreement between observed and modeled values and where the "modeled" values are not obtained by linear regression and depending on which formulation of R2 is used. If the first formula above is used, values can never be greater than one. If the second expression is used, there are no constraints on the values obtainable.
In many (but not all) instances where R2 is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing SSerr. In this case R-squared increases as we increase the number of variables in the model (R2 will not decrease). This illustrates a drawback to one possible use of R2, where one might try to include more variables in the model until "there is no more improvement". This leads to the alternative approach of looking at the adjusted R2. The explanation of this statistic is almost the same as R2 but it penalizes the statistic as extra variables are included in the model. For cases other than fitting by ordinary least squares, the R2 statistic can be calculated as above and may still be a useful measure. If fitting is by weighted least squares or generalized least squares, alternative versions of R2 can be calculated appropriate to those statistical frameworks, while the "raw" R2 may still be useful if it is more easily interpreted. Values for R2 can be calculated for any type of predictive model, which need not have a statistical basis.
Read more about this topic: Coefficient Of Determination