I'm having trouble understanding how to interpret the output of polynomial model when the lower order term (linear term) is significant, but the quadratic term is not.
For instance, create a random dataset:
set.seed(10)
x <- 0:51
y <- 1 - 0.7*x + 0.1*x^2 + rnorm(length(x),
7, 10)
testdf <- data.frame(x,y)
testdf$Treat <- c(0, 1)
testdf$Treat <- as.factor(testdf$Treat)
testdf$y <- ifelse(testdf$Treat == 0 &
(testdf$x >= 40 & testdf$x <=
75), testdf$y + 20, testdf$y)
Interaction plot:
library(ggplot2)
ggplot(testdf, aes(x, y, col=Treat)) +
geom_point() + geom_smooth()
Model:
test.mod <- lm(y ~ poly(x,2)*Treat,
data=testdf)
summary(test.mod)
Coefficients:
Estimate Std.Error t-value Pr(>|t|)
(Intercept) 78.913 1.851 42.643 < 2e-16 ***
poly(x, 2)1 524.521 13.382 39.197 < 2e-16 ***
poly(x, 2)2 174.842 13.374 13.073 < 2e-16 ***
Treat1 -4.405 2.617 -1.683 0.09912 .
poly(x, 2)1:Treat1 -54.606 18.924 -2.885 0.00593 **
poly(x, 2)2:Treat1 -11.238 18.914 -0.594 0.55532
Does this mean that the shapes of the curves do not differ between treatments, and so I should try to visualize (conceptually) the interaction in terms of a linear relationship between the groups? In simple terms, how can I explain this result to someone?