Question

How can we compare two models with different dependent variables (i.e., Y t and log(Y ) )?

Answer 1

To compare models with different dependent variables, we can calculate the R² for the 2 models to see which model explains the variability in the dependent variable (Yt or log(Y)) better. Higher R-squared would imply the model explains the variability of the particular dependent variable to a greater extent.

In addition, if we want to compare the models to check whether the independent variable is a significant predictor of the different dependent variables, we can check the p-value of the coefficients of the independent variable in the 2 models. If the p-value is less than the significance value for any of the models, this suggests the dependent variable isn't a significant predictor in that model.