i want to run a second-order polynomial regression where my dependent variable ("y") is a continuous variable while my independent variable ("comp") is a multivariate variable (including two variables).
The sample data in the dependent variable, "comp", look like this;
[,1] [,2]
[1,] 2.277968e-02 -0.0655286426
[2,] -5.865487e-01 -0.1292127584
[3,] -3.120342e-01 -0.2922297149
[4,] .....................
i have been using 'poly' function in r to run such regression.
here is my code:
model <- lm(y~poly(comp,2, raw = TRUE)*factor(x1), data=test)
(aov.health=car::Anova(model, test.statistic="F") )
summary(health)
when i run this model, i get this output;
> summary(model)
Call:
lm(formula = y ~ poly(comp, 2, raw = TRUE) * factor(x1), data = test)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.63428 0.08437 19.371 <2e-16 ***
poly(comp, 2, raw = TRUE)1.0 -0.38673 0.23435 -1.650 0.0994 .
poly(comp, 2, raw = TRUE)2.0 0.89645 0.43803 2.047 0.0412 *
poly(comp, 2, raw = TRUE)0.1 -0.13266 0.52954 -0.251 0.8023
poly(comp, 2, raw = TRUE)1.1 0.80634 0.98185 0.821 0.4118
poly(comp, 2, raw = TRUE)0.2 0.57313 1.45062 0.395 0.6929
factor(x1)2 0.12263 0.09484 1.293 0.1966
poly(comp, 2, raw = TRUE)1.0:factor(x1)2 0.40963 0.25081 1.633 0.1030
poly(comp, 2, raw = TRUE)2.0:factor(x1)2 -1.13142 0.46668 -2.424 0.0156 *
poly(comp, 2, raw = TRUE)0.1:factor(x1)2 -0.45742 0.58463 -0.782 0.4343
poly(comp, 2, raw = TRUE)1.1:factor(x1)2 -0.78708 1.08822 -0.723 0.4698
poly(comp, 2, raw = TRUE)0.2:factor(x1)2 -2.59316 1.61733 -1.603 0.1094
---
I am not sure if I understand the names of the estimates correctly and how do I interpret these numbers. if I have to write these in a mathematical formula for calculating these estimates, what would be those? can somebody help?
question from:
https://stackoverflow.com/questions/65842233/interpretation-of-estimates-from-poly-function-in-r 
