You have estimated a linear regression model relating $\backslash ($ Y $\backslash )$ to $\backslash ($ X $\backslash ).$ Your professor says, "I think that the relationship between $\backslash ($ Y $\backslash )$ and $\backslash ($ X $\backslash )$ is nonlinear." How would you test the adequacy of your linear regression? $($Check all that apply$)$

A$.$ Compare the fit between of linear regression to the non$-$linear regression model.

B$.$ If adding a quadratic term, you could test the hypothesis that the estimated coefficient of the quadratic term is significantly different from zero.

C$.$ There is evidence in favor of a non$-$linear relationship if there is zero correlation between the dependent and independent variable.

D$.$ All of the above.