abline(v=35,lty=5)
segments(48,g2$coef[1]+g2$coef[2]*48,35,g2$coef[1]+g2$coef[2]*35)
segments(20,g1$coef[1]+g1$coef[2]*20,35,g1$coef[1]+g1$coef[2]*35)
lines(x,py,type=2)
lines(x,py,lty=2)
summary(lm(sr~ddpi,savings))
summary(lm(sr~ddpi+I(ddpi^2),savings))
plot(savings$ddpi,savings$sr)
summary(lm(sr~ddpi+I(ddpi^2)+I(ddpi^3),savings))
poly(savings$ddpi,3)
g <- lm(sr~poly(ddpi,3),savings)
summary(g)
g <- lm(sr~poly(ddpi,2),savings)
g
x <- model.matrix(g)
t(x) %*% x
weird <- function(x) sin(2*pi*x^3)^3
x <- seq(0,1,by=0.01)
plot(x,weird(x),type="l")
y <- weird(x)+0.1*rnorm(101)
plot(x,y)
g4 <- lm(y~poly(x,4))
g12 <- lm(y~poly(x,12))
matplot(x,cbind(y,g4fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
matplot(x,cbind(y,g4$fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
library(splines)
knots <- c(0,0,0,0,0.2,0.4,0.5,0.6,0.7,0.8,0.85,0.9,1,1,1,1)
bx <- splineDesign(knots,x)
gs <- lm(y~bx)
lines(x,gs$fit,col=3)
lines(x,gs$fit,col=4)
matplot(x,bx,type="l")
gx
summary(gs)
matplot(x,cbind(y,g4$fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
matplot(x,bx,type="l")
matplot(x,cbind(y,g4fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
matplot(x,cbind(y,g4$fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
library(splines)
knots <- c(0,0,0,0,0.2,0.4,0.5,0.6,0.7,0.8,0.85,0.9,1,1,1,1)
bx <- splineDesign(knots,x)
gs <- lm(y~bx)
lines(x,gs$fit,col=3)
lines(x,gs$fit,col=4)
matplot(x,bx,type="l")
gx
summary(gs)
matplot(x,cbind(y,g4$fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
matplot(x,bx,type="l")
matplot(x,cbind(y,g4$fit,g12$fit),type="pll",ylab="y",pch=18,lty=c(1,2))
lines(x,gs$fit,col=4)