I read some questions about this subject, but I couldn't find an answer.
I'm having trouble interpreting the practical effect of the polynomial predictor variable on the response variable.
My model is:
y ~ poly(x,3) + z
My result is:
Estimate SE Z P (Intercept) -2.851 0.234 -12.173 < 0.0001 poly(x)1 -0.784 1.036 -0.758 0.449 poly(x)2 1.937 0.845 2.293 0.022 * poly(x)3 2.754 0.768 3.587 0.0003 ** z 0.342 0.105 3.268 0.001 *
I think it extremely complicated to describe the curvature just by looking at the parameter estimates. When I plot the model considering only “poly(x,3)”, I observe clear evidence of a curvilinear relationship, like this:
Note that I don't have only one independent variable in my model, so my question is: Can I show the table with all predictor variables together (e.g. y ~ poly(x,3)) and, after that, interpret them separately using graphs?
By the way, my hypothesis is that the responsible variable “y” increases until an optimum level of a gradient of the predictor variable “x”, but decreases after that (I am really interested in this hump-shaped relationship), while presents a positive response to the variable “z”.