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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.
Simply put, R is the correlation between the predicted values and the observed values of Y. R square is the square of this coefficient and indicates the percentage of variation explained by your regression line out of the total variation. This value tends to increase as you include additional predictors in the model.