 # adjusted r square

Is it possible for Adjusted R^2 to be equal to R^2? I thought adjusted R^2 should be less than R^2 ------- Which of the following statements regarding the R2 is FALSE? A) The R2 of a regression will be greater than or equal to the adjusted-R2 for the same regression. B) The R2 is the ratio of the unexplained variation to the explained variation of the dependent variable. C) 0 ≤ R2 ≤ 1.0. D) The F-statistic for the test of the fit of the model is the ratio of the mean squared regression to the mean squared error. Your answer: A was incorrect. The correct answer was B) The R2 is the ratio of the unexplained variation to the explained variation of the dependent variable. The R2 is the ratio of the explained variation to the total variation.

B. The R2 is the ratio of the EXPLAINED variation to the TOTAL variation of the dependent variable and yes, it’s completely possible to have R^2 >= Adjusted(R^2)

They are only equal if there are no slope parameters, or if R^2 = 1.0

For our purposes adjusted R^2 will always be lower than R^2.

Cool. I thought regression needs at least one independent variable. So, R^2 and adjusted R^2 should never same. I never thought about R^2 to be equal to 1 so that they can be equal. Thanks for replies

They are equal if there is only one coefficient. Adjusted R^2 compensates for the decresing accuracy when additional (more than one) coefficients are added.