Orthogonal polygnomials

orth.R

library(ggplot2)

set.seed(1001)
start <- 2
end <- 20
N <- 100

x <- runif(N, start, end)

y <- x + x^2 + rnorm(N, 0, 5)

d <- data.frame(y, x)

plot(x, y)

m1 <- lm(y ~ x + I(x^2), d)

predN <- 1000
pred1 <- data.frame(x = seq(0, end, length.out = predN),
                   y1 = predict(m1, newdata = data.frame(x = seq(0, end, length.out = predN))))

ggplot(d, aes(x, y)) + 
  geom_point() +
  geom_line(data = pred1, aes(x, y1))





m2 <- lm(y ~ poly(x, 2), d)

pred2 <- data.frame(x = seq(0, end, length.out = predN),
                   y1 = predict(m2, newdata = data.frame(x = seq(0, end, length.out = predN))))

ggplot(d, aes(x, y)) + 
  geom_point() +
  geom_line(data = pred2, aes(x, y1))



summary(m1)
summary(m2)