# Properties of R-Square and Adjusted R-Square

Need help with the below

Researcher estimates the following two econometric models

Yt= Î²1 + Î²2x2t + Î²3x3t +ut

Yt= Î²1 + Î²2x2t + Î²3x3t + Î²4x4t +vt

Ut and Vt are iid disturbances and x3t is an irrelevant variable which does not enter into the data generating process for Yt. Will the value of (a) R^2, (b) Adjusted R^2, be higher for the second model than the first? Explain your answers

https://brainmass.com/economics/regression/properties-of-r-square-and-adjusted-r-square-579586

#### Solution Preview

(a) The value of R^2 should be higher for the second model as an additional variable (4t) is added to the regression.

The value of R^2 would be identical for two econometric models only if the coefficient (Î²4) of the additional variable (4t) equals 0 (i.e. 4t is ...

#### Solution Summary

Explaining how adding a new independent variable will affect the value of R-Square and Adjusted R-Square