hello Manoj  Kumar,

I want to compare the adjusted R-squared of two competing models. i am looking for a test that to apply that would help me determine whether the difference in R-squared is significant or not. Thank you

You can compare AIC's of these models and select the smaller one. If models are nested then you could make use of an F test.

Adjusted R squares are adjusted, so you can compare them numerically as you compare AICs. I am not aware of and do not expect a statistical test for comparing them.

I added two relevant links.

https://www.researchgate.net/post/Comparing_R-squared_values_in_two_models_any_help

https://www.researchgate.net/post/What_does_R_square_Adjusted_R_and_R_indicate_in_terms_of_Multiple_Regression_Analysis

thank you

you can compare adjusted r squares across board but word of caution make sure the dependent variable of the models are the same (e.g when both dependent variables are in logs or not but not when one is in log and the other is not.)

sure, all the dependents variables are the same. i want a formal test that can help me determine whether the difference in adj R2 is significant or not. I have heard about tests such as Vuong(1989) and Cramer(1987) test but i seem to be lost as to how to apply them.

thank you Lawrence

the Vuong (1989) test worked perfectly 

Thank you all