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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.
R-sqrd is the amount of variance in Y explained by the set of X variables. It is expressed as a percentage and thus goes from values of 0 - 100% (or 0 - 1 when expressed in decimal form). Adjusted R-sqrd is adjusted for the number of X variables (k in the formula) and the sample size (n in the formula).