Usage of R^2 and adjusted R^2

[chiaaugu]

Hi all

I was reviewing the regressor (Stock and Watson Chapter 4-7) and have a query regarding Rsquare

My original thoughts around R^2 is a measure of how well the indepedent variable(regressor) explains the dependent variable. Adjusted R^2 is used when we have multiple regressor as adding a regressor would always increase the vanilla R^2. At the end of Chapter7, we ran into a whole range of "what a high R^2" doesn't mean (for example, it doesn't mean we got the best regressors etc)

So what is R^2 used for? is it just a numerical value for us to compare how good various indepdent variables are at predicting a dependent variable?

 

[ShaktiRathore]

Hi,
Yes R^2 is just a numerical value for us to compare how good various independent variables are at predicting a dependent variable.Do not get confused with Adjusted R^2 ,we have Adjusted R^2 to overcome deficiency of R^2 that always increases with addition of independent variable,Adjusted R^2 accounts for this deficiency that's it.
thanks

 

[chiaaugu]

Thanks @ShaktiRathore

Was studying Diebold Chapter 5 and noticed Diebold mentioned that R^2 may lead to a model that doesn't provide an apt "out of sample" forecast?

Would you know why this is the case?

 

[ShaktiRathore]

Hi,
R^2 is determined using the sample data its not necessary that the high R^2 applies to out of sample data also sometimes this is called in-sample over fitting. Therefore the model may not be accurate when applied to out of sample. Thus new measures are required to overcome this like the MSE(Mean square error).As these new measures ,S^2 and other as AIC and SIC criterons apply the penalty factor and adjust for increase in the number of independent variables(R^2 doesnt) therefore they are better in identfying a more truer model and this increases out of sample forecast accuracy as is empirically verified.
thnks