I am investigating a curvilinear effect between X and Y by using a hierarchic regression analysis. To test for curvilinear effects, the squared term for X was computed (I mean center also variable X).
In model 1, the control variables were entered. In Model 2, X (linear) was entered. In Model 3, X (quadratic) was entered.
In Model 2, X linear is significant. When the squared term is entered in Model 3, the quadratic term is significant but the linear term is not. Does this prove a curvilinear effect? Or is it essential that in Model 3 both (linear and quadratic) are significant?
When I do not mean center the independent variable, Model 3 stated X linear and X quadratic significant. The problem here is multicollinearity issues.