I read through this question to help me with a similar model that I'm working on. Only the coefficient for readcat.L is deemed significant (per p-values):
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 52.7870 0.6339 83.268 <2e-16 ***
readcat.L 14.2587 1.4841 9.607 <2e-16 ***
readcat.Q -0.9680 1.2679 -0.764 0.446
readcat.C -0.1554 1.0062 -0.154 0.877
In this case, is it appropriate to choose
$$\hat{y_i} = \hat{\beta}_0 + \hat{\beta}_L L_i$$
as your model instead of
$$\hat{y_i} = \hat{\beta}_0 + \hat{\beta}_L L_i + \hat{\beta}_Q Q_i + \hat{\beta}_C C_i$$
(where $\hat{\beta}_L$, $\hat{\beta}_Q$, and $\hat{\beta}_C$ are the estimated coefficients for the linear, quadratic, and cubic terms, and $L_i$, $Q_i$, and $C_i$ are the appropriate contrasts for level $i$)?
I'm worried about throwing out the higher-order contrasts, since the values of the lower-order contrasts depend partly on calculating that many at once (right?). Do they have to stick together, or do I keep only the ones with significant coefficients? And if it's okay to get rid of some of them, is it okay to get rid of a lower-order term and keep a higher-order one?
