$y=\beta_1+\beta_2x_2+\beta_3x_3+\beta_4x_3^2+\beta_5x_5+\beta_6x_6$ for a sample size of 50.
Doing an F-test for joint significance, t-tests gives that $x_3,x_3^2,x_5$ are not significant. If I remove $x_3^2,x_5$, then $x_3$ becomes significant. Why?
At first I thought of some collinearity, but one is the square of the other. Maybe I have too many regressors for this sample size?
Any help would be appreciated.