R squared and adjusted R squared

kfp22 · May 31, 2014, 2:15am

I got a question from schweser qbank that says if R squared = 0.35: adjusted R squared = 0.29 Then the model suggests that the independent valuables explain 35% of the dependent variable. Why is it not 29%? I thought the adjusted R squared is supposed to be a more accurate version of R squared? Thank you

kaveh_nobari · May 31, 2014, 2:50am

Could you please provide us with the exact format of the question? Adjusted R2 is only more accurate if and only if you use a multiple regression. If the question specified that it was simple linear regression then 0.35 is indeed the correct answer!

kfp22 · May 31, 2014, 3:12am

I don’t remember the exact question but I think you are right! I think it was a simple linear regression. Thanks!

hellind · June 2, 2015, 8:18am

The question is fro the Q bank and yes it is under multiple regression.

S2000magician · June 2, 2015, 2:49pm

R² tells you the fraction of the variability of the dependent variable that is explained by changes in the independent variables.

Adjusted R², by itself, doesn’t tell you anything. Its use is in determining whether adding a new independent variable improves the model or not. Thus, you need to compare the adjusted R² of the model without the new independent variable to the adjusted R² of the model with the new independent variable; you choose the one with the higher adjusted R².

tickersu · June 2, 2015, 3:54pm

I would be careful with this (bold), as it isn’t entirely true. It has more application than you’ve suggested. Many text books and statisticians will tell you that adjusted R-squared is the more appropriate measure in MR, because it is adjusted for the degrees of freedom (as you know). The practical interpretation of adjusted r-squared specifically mentions that it is the proportion of sample variation in the DV explained by the IVs after accounting for the degrees of freedom (it’s almost the same as the unadjusted interpretation, but importantly different). If you compare the adjusted r-squared in the model to the unadjusted r-squared (for the same model) and there is big discrepancy, it indicates that some of your regressors are probably not useful. At this point, we could get into the application you’ve mentioned. If you see a large discrepancy with the unadjusted and adjusted R-squared, you could try adding or removing a regressor (probably remove, since it could be indicating over-specification) and comparing the adjusted R-squared values for the two models.

S2000magician · June 2, 2015, 5:45pm

tickersu:

S2000magician:

R² tells you the fraction of the variability of the dependent variable that is explained by changes in the independent variables.

Adjusted R², by itself, doesn’t tell you anything. Its use is in determining whether adding a new independent variable improves the model or not. Thus, you need to compare the adjusted R² of the model without the new independent variable to the adjusted R² of the model with the new independent variable; you choose the one with the higher adjusted R².

I would be careful with this (bold), as it isn’t entirely true. It has more application than you’ve suggested. Many text books and statisticians will tell you that adjusted R-squared is the more appropriate measure in MR, because it is adjusted for the degrees of freedom (as you know). The practical interpretation of adjusted r-squared specifically mentions that it is the proportion of sample variation in the DV explained by the IVs after accounting for the degrees of freedom (it’s almost the same as the unadjusted interpretation, but importantly different). If you compare the adjusted r-squared in the model to the unadjusted r-squared (for the same model) and there is big discrepancy, it indicates that some of your regressors are probably not useful. At this point, we could get into the application you’ve mentioned. If you see a large discrepancy with the unadjusted and adjusted R-squared, you could try adding or removing a regressor (probably remove, since it could be indicating over-specification) and comparing the adjusted R-squared values for the two models.

You’re correct, of course.

I was speaking in the context of the Level II CFA exam, where the only application of adjusted R² is to determine whether the addition of a new intependent variable improves the model or not.

tickersu · June 2, 2015, 6:08pm

S2000magician:

tickersu:

S2000magician:

R² tells you the fraction of the variability of the dependent variable that is explained by changes in the independent variables.

Adjusted R², by itself, doesn’t tell you anything. Its use is in determining whether adding a new independent variable improves the model or not. Thus, you need to compare the adjusted R² of the model without the new independent variable to the adjusted R² of the model with the new independent variable; you choose the one with the higher adjusted R².

I would be careful with this (bold), as it isn’t entirely true. It has more application than you’ve suggested. Many text books and statisticians will tell you that adjusted R-squared is the more appropriate measure in MR, because it is adjusted for the degrees of freedom (as you know). The practical interpretation of adjusted r-squared specifically mentions that it is the proportion of sample variation in the DV explained by the IVs after accounting for the degrees of freedom (it’s almost the same as the unadjusted interpretation, but importantly different). If you compare the adjusted r-squared in the model to the unadjusted r-squared (for the same model) and there is big discrepancy, it indicates that some of your regressors are probably not useful. At this point, we could get into the application you’ve mentioned. If you see a large discrepancy with the unadjusted and adjusted R-squared, you could try adding or removing a regressor (probably remove, since it could be indicating over-specification) and comparing the adjusted R-squared values for the two models.

You’re correct, of course.

I was speaking in the context of the Level II CFA exam, where the only application of adjusted R² is to determine whether the addition of a new intependent variable improves the model or not.

The real world is a completely different animal than the bubble of the CFA program (or any class you might take). That’s why I’m hesitant to make the statement that it gives you nothing. I do see your point in keeping it strictly to the confines of the exam, especially with time peeling off the clock!