In a forward stepwise regression process, it is actually possible for the R-square value to decline if variables are added to the regression model that do not help to explain the variation in the dependent variable.

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In a forward stepwise regression process, the R-square value either increases or remains the same when new variables are added to the model, because R-square measures the proportion of the variance for the dependent variable that's explained by the independent variables in the model, and adding variables cannot decrease this explained variance, though it may not increase it significantly if the variables do not contribute much explanatory power.

In a Forward Stepwise Regression Process, It Is Actually Possible