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Properties of R-Square and Adjusted R-Square

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Researcher estimates the following two econometric models
Yt= β1 + β2x2t + β3x3t +ut
Yt= β1 + β2x2t + β3x3t + β4x4t +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

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Solution Summary

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

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(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 (β4) of the additional variable (4t) equals 0 (i.e. 4t is ...

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