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The value of R square would not decrease when more variables are added to the model. As a result, there is always a temptation to add more variables in the model, because of which problem can arise therefore in that case Adjusted R2 is used as a measure.
This makes it clear that what's being adjusted is [math]R^2[/math] and that the adjustment is based on the sample size ([math]n[/math]), the number of variables, [math]p[/math], and the degree to which the uncorrected model does not fit well ([math]1-R^2[/math]). Take a look at: Coefficient of determination.