I have a logistic model where I modeled an independent variable at both first order only and then as a second order polynomial (via the poly function in R). I noticed that the p-value for the IV decreased significantly from 10^-4 to 10^-77. However, when I look at the summary output for both first and second order terms, the first order appears to not be statistically significant (high Pr(>|z|)).
poly(log(x), 2)1 0.420098
poly(log(x), 2)2 0.000322 ***
Does this mean that the first order term should be removed from the model, and if so what is the syntax to do so?