For the Polynomial Regression Model, A $t$ -Statistics Do Not Have an Asymptotic Normal Distribution

Short Answer

For the polynomial regression model, a. you need new estimation techniques since the OLS assumptions do not apply any longer.
b. the techniques for estimation and inference developed for multiple regression can be applied.
c. you can still use OLS estimation techniques, but the $t$ -statistics do not have an asymptotic normal distribution.
d. the critical values from the normal distribution have to be changed to $1.96 ^ { 2 } , 1.96 ^ { 3 }$ , etc.