I'm having two linear regression models as follows: $y = a_1x_1 + a_2x_2 + c$ and $y = b_1x_1 + b_2x_3 + c$.
I'm looking for a statistical test for proving which model is better. I've obtained the $R^2$ values. Please suggest a statistical test.
Also I wanted to know how to apply the Likelihood Ratio test for comparing the above models. Is that an appropriate test for the comparison?
Assuming i.i.d. normal errors, comparing the likelihood of these two models would be equivalent to comparing the $R^2$ values.
What would be the null hypothesis of this test? You might consider fitting a model containing all three covariates and separately testing the hypotheses $H_0:\beta_2=0$ and $H_0:\beta_3=0$.