Adjusted R-Square

The coefficient of determination established that when an explanatory variable is added to a model, R-Squared decreases - no matter how useless the additional variable is. So, R-Squared is the fraction of variance explained by the model. Ideally, the measure of fit would decrease when useless variables are entered into the model as "explanatory variables". In other words, if the measure of fit decreases every time a useless variable is entered into the model, then the analysts can measure and determine which variables to keep and which to expunge. A statistic widely used to achieve this is the coefficient of determination adjusted for the number of parameters in the model (Adjusted R-Squared). Adjusted R-Squared tells you when the negative affect of the variable outweighs the positive.