Question

What is the difference between a coefficient of multiple determination and an adjusted coefficient of multiple determination?

Please explain it in detail with their concepts.

Answer 1

R squared measures the amount of variation in the response variable that can be explained by the predictor variables. The main point is that when we add predictors to our model, the R squared will always increase, as a predictor will always explain some portion of the variance.

Adjusted Rsquared controls against this increase, and will not always increase for the number of predictors in the model. Therefore it shows a balance between the most possible model, and the best fitting model. Generally, if you have a large difference between your multiple and your adjusted Rsquared that indicates you may have overfit your model.

Hence we can say that Adjusted R-squared adds precision and reliability by considering the impact of additional independent variables that tend to skew the results of R-squared measurements.

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