How to correctly extract the regression equation from `stat_smooth` or a regression model in R

Question

I plot the equation extracted from stat_smooth, but it mismatches the origin one.

I tried draw a regression line with stat_smooth, and again draw the formula of regression use stat_function, but the 2 curves are obviously different. What I did wrong?

I can't post pictures yet, so I provide an example with ggpmisc package:

ggplot(mtcars, aes(x = mpg, y = disp)) + geom_point() +
  ggpmisc::stat_poly_line(formula = y ~ poly(x, degree = 2)) +
  ggpmisc::stat_poly_eq(aes(label = after_stat(eq.label)), 
                        formula = y ~ poly(x, degree = 2))

ggplot(mtcars, aes(x = mpg, y = disp)) + geom_point() +
  ggpmisc::stat_poly_line(formula = y ~ poly(x, degree = 2)) +
  ggpmisc::stat_poly_eq(aes(label = after_stat(eq.label)), 
                        formula = y ~ poly(x, degree = 2)) +
  stat_function(fun = \(x) 231 - 585 * x + 190 * x ^ 2)

Answer 1

Your x value is transformed into an orthogonal polynomial when you use poly(x, 2).

When you use x in stat_function, your x value is the original x values and not your polynomial x values.

Here's a workaround:

# Compute your polynomial a priori
polynomial <- poly(mtcars$mpg, 2)

# Compute your equation using the polynomials
mtcars$newY <- 231 - 585 * polynomial[,"1"] + 190 * polynomial[,"2"]

# Plot
ggplot(mtcars, aes(x = mpg, y = disp)) + geom_point() +
  ggpmisc::stat_poly_line(formula = y ~ poly(x, degree = 2)) +
  ggpmisc::stat_poly_eq(aes(label = after_stat(eq.label)), 
                        formula = y ~ poly(x, degree = 2)) +
  geom_line(data = mtcars, aes(x = mpg, y = newY))