CI and PI for regression models

n = 50
x = seq(-1,1, len = n)
f = function(x) 0.3 * x^2
y = f(x) + rnorm(n, sd = 0.2)


par(mfrow = c(1,2))


lmFit <- lm(y ~ x + I(x^2))

plot(x,y, main = "linearRegression")
curve(f, -1, 1, add = T)

pred = predict(lmFit, interval = "confidence")
lines(x, pred[,1], col = 2, lwd = 2)
polygon( c(x, rev(x)), 
         c(pred[,2], rev(pred[,3])), 
         border = F, col = "#FF000022" )

pred = predict(lmFit, interval = "predict")
lines(x, pred[,2], lty = 5, col = 2)
lines(x, pred[,3], lty = 5, col = 2)  


library(mgcv)
gamFit <- gam(y ~ s(x))

plot(x,y, main = "GAM")
curve(f, -1, 1, add = T)

pred <- predict(gamFit, se.fit = T)

lines(x, pred$fit, col = "green", lwd = 2)

polygon( c(x, rev(x)), 
         c(pred$fit + 1.96 * pred$se.fit, rev(pred$fit - 1.96 * pred$se.fit)), 
         border = F, col = "#00FF0022" )