library(faraway)
library(MASS)
data(savings)
g <- lm(sr ~ pop15+pop75+dpi+ddpi,savings)
boxcox(g,plotit=T)
boxcox(g,plotit=T,lambda=seq(0.5,1.5,by=0.1))
data(gala)
g <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent,gala)
boxcox(g,plotit=T)
boxcox(g,lambda=seq(0.0,1.0,by=0.05),plotit=T)
g1 <- lm(sr ~ pop15, savings, subset=(pop15 < 35))
g2 <- lm(sr ~ pop15, savings, subset=(pop15 > 35))
plot(sr ~ pop15,savings,xlab="Pop'n under 15",ylab="Savings Rate")
abline(v=35,lty=5)
segments(20,g1$coef[1]+g1$coef[2]*20,35,g1$coef[1]+g1$coef[2]*35)
segments(48,g2$coef[1]+g2$coef[2]*48,35,g2$coef[1]+g2$coef[2]*35)
lhs <- function(x) ifelse(x < 35,35-x,0)
rhs <- function(x) ifelse(x < 35,0,x-35)
gb <- lm(sr ~ lhs(pop15) + rhs(pop15), savings)
x <- seq(20,48,by=1)
py <- gb$coef[1]+gb$coef[2]*lhs(x)+gb$coef[3]*rhs(x)
lines(x,py,lty=2)
summary(lm(sr ~ ddpi,savings))
summary(lm(sr ~ ddpi+I(ddpi^2),savings))
summary(lm(sr ~ ddpi+I(ddpi^2)+I(ddpi^3),savings))
savings <- data.frame(savings,mddpi=savings$ddpi-10)
summary(lm(sr ~ mddpi+I(mddpi^2),savings))
g <- lm(sr ~ poly(ddpi,4),savings)
summary(g)
g <- lm(sr ~ polym(pop15,ddpi,degree=2),savings)
funky <- function(x) sin(2*pi*x^3)^3
x <- seq(0,1,by=0.01)
y <- funky(x) + 0.1*rnorm(101)
matplot(x,cbind(y,funky(x)),type="pl",ylab="y",pch=18,lty=1)
g4 <- lm(y ~ poly(x,4))
g12 <- lm(y ~ poly(x,12))
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)
matplot(x,bx,type="l")
matplot(x,cbind(y,gs$fit),type="pl",ylab="y",pch=18,lty=1)