# Fitting a regression model with spurious variables: do they vanish with large samples?

I am fitting the usual linear regression model

$$y_j = x_j^T\beta + e_j,$$ where the errors $$e_j$$ are iid normal with unknown variance. If the vector of covariates $$x_j$$ contain spurious variables, will they always vanish with large samples? This is, the corresponding estimators converge to zero when the sample grows? What if my model is incorrect (like the true model is non linear)?

• More details on "spurious variables"? In "will they always vanish with large samples", who is "they"? – user158565 Jul 18 at 21:35