Question at position 17 Suppose the regression summary includes: Multiple R-squared: 0.241, Adjusted R-squared: 0.233 What does the Adjusted R-squared value tell you?The model explains all of the variance in the dependent variable.The predictors are highly correlated with each other.The model is not statistically significant.The model cannot be interpreted without the F-statistic.About 24% of the variance in desirability is explained by the predictors, adjusted for the number of predictors.Clear my selection

Question

BlackTom AI · Accepted Answer

When interpreting regression output, there are several statements to evaluate for accuracy based on what Adjusted R-squared conveys.
Option 1: 'The model explains all of the variance in the dependent variable.' This is incorrect. Even with a relatively high R-squared, it rarely (if ever) explains all variance; an R-squared of 0.241 means about 24% of the variance is accounted for, not everything.
Option 2: 'The predictors are highly correlated with each other.' This would suggest multicollinearity, which is a separate issue assessed by diagnostics like VIF, not by the value of Adjusted R-squared itself. Adjusted R-squared does not directly indicate multicollinearity.
Option 3: 'The model is not statistically significant.' Significance is assessed by the F-statistic and its p-value, not by the Adjusted R-squared alone. A model can have a low or moderate Adjusted R-squared yet still be statistically significant, or vice versa depending on sample size and variance.
Option 4: 'The model cannot be interpreted without the F-statistic.' While the F-statistic helps determine overall model significance, Adjusted R-squared provides information about explained variance after penalizing for extra predictors; interpretation can proceed with both metrics, but this statement overstates dependence on the F-statistic.
Option 5: 'About 24% of the variance in desirability is explained by the predictors, adjusted for the number of predictors.' This correctly reflects what Adjusted R-squared represents: a proportion of variance explained, adjusted for model complexity (the number of predictors), here roughly 0.233, which rounds to about 24%.

Summarizing the reasoning in a different light, note that Adjusted R-squared increases only if a new predictor improves the model more than would be expected by chance, and it can decrease when unnecessary predictors are added. This nuance explains why option 5 is the accurate interpretation, while the others either misinterpret what R-squared or Adjusted R-squared measure, or confuse statistical significance with explained variance.

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