What are R-squared and adjusted R-squared, and what is the difference between them?

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Accepted Answer

Adjusted R-squared accounts for the number of predictors, while R-squared does not, potentially leading to misleading interpretations.

R-squared measures the proportion of variance explained by the model, but it can increase with more predictors, even if they are irrelevant.
Adjusted R-squared adjusts the R-squared value based on the number of predictors, providing a more accurate measure of model fit.
For example, if a model with 5 predictors has an R-squared of 0.80, adding a 6th predictor might increase it to 0.82, but the adjusted R-squared may decrease if the new predictor doesn't improve the model significantly.
Adjusted R-squared is particularly useful for model comparison, as it penalizes excessive use of predictors, helping to avoid overfitting.

Accepted Answer

R square explain the explained variation by the total variation in the model. Higher R square indicate better fit and less multicollinearity. R square had its own disadvantages as if we add an insignificant variable to the model it doesn't decrease. R square either increase or stays as it is hence we should see adjusted R square. If u add any insignificant variable adjusted R square decreases.

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What are R-squared and adjusted R-squared, and what is the difference between them?

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