1. To see if the variable Xi2 belongs
in the model
Yi=β1+β2Xi+ui,
Ramsey’s RESET test would estimate the linear model, obtaining the
estimated Yi values from this model [i.e.,
Yi=β1+β2Xi
] and then estimating the model
Yi=β1+β2Xi+α3Yi2+ui
and testing the significance of α3. Prove that, if
α3 turns out to be statistically significant in
the preceding (RESET) equation, it is the same thing as estimating
the following model directly:
Yi=β1+β2Xi+β3Xi2+ui