Chapter_7.R

library(ISLR)
names(Wage)
# Polynomial Regression
lm.fit = lm(wage~poly(age,4),data = Wage)
coef(summary(lm.fit))
#Orthogonal polynomials from 1 to degree are generated by default
fit2 <- lm(wage~poly(age,4,raw=TRUE),data = Wage)
coef(summary(fit2))
age_grid = seq(25:45)
fit2a = lm(wage~age + I(age^2)+I(age^3)+I(age^4),data = Wage)
fit2b = lm(wage~cbind(age,age^2,age^3,age^4),data = Wage)
agelims = range(Wage$age)
length(agelims)
agelims[1]
agelims[2]
age.grid = seq(from = 20,to = 80,length = 7)
age.grid
preds2 = predict(fit2,newdata = list(age = age.grid),se = TRUE)
preds= predict(fit,newdata = list(age = age.grid),se = TRUE)
max(abs(preds2$fit-preds$fit))
preds$fit
preds$se.fit
out = cbind(preds$fit-2*preds$se.fit,preds$fit,preds$fit+2*preds$se)
length(Wage$wage)
age.grid = seq(from=18, to=80,length = 3000)
par(mfrow = c(1,1), mar = c(1,1,1,1))
plot(x = Wage$age,y = Wage$wage,xlim = agelims,col = "darkgrey")
lines(age.grid,preds$fit,lwd = 2,col = "blue")
sebands = cbind((preds$fit-2*preds$se.fit),(preds$fit+2*preds$se.fit))
matlines(age.grid,sebands,col= 'red',lty = 3)
fit = lm(wage~age, data = Wage)
fit2 = lm(wage~poly(age,2),data = Wage)
fit3 = lm(wage~poly(age,3),data = Wage)
fit4 = lm(wage~poly(age,4),data = Wage)
fit5 = lm(wage~poly(age,5),data = Wage)
anova(fit,fit2,fit3,fit4,fit5)
class.fit = glm(I(Wage$wage>250)~poly(age,4),data = Wage,family= "binomial")
class.fit
preds = predict(class.fit,newdata = list(age=age.grid),se = TRUE)
names(preds)
pred_probs= exp(preds$fit)/(1+exp(preds$fit))
pred_probs = predict(class.fit, newdata = list(age=age.grid),type= 'response')
se.bands.logit =cbind(pred_probs-2*preds$se.fit,pred_probs+2*preds$se.fit)
se.bands = exp(se.bands.logit)/1+exp(se.bands.logit)
se.bands
range(Wage$wage)
plot(jitter(Wage$age) ,I((Wage$wage >250)/5),xlim = agelims,ylim = c(0,0.2),col = "darkgrey")
lines(age.grid,lwd = 2, col= 'blue')
matlines(age.grid,se.bands,lwd=1,col='red')
length(age.grid)
dim(se.bands)
# To fit a step function we use 'cut'
#'cut' fucntion cuts the range of variable evenly. To give our specific
# break points, we can use the 'breaks' option in the cut function.
range(Wage$age)
cut(Wage$age,4)
unique(cut(Wage$age,4))
(80.1-17.9)/4
17.9+15.55+15.55+15.55
piecewise.regfit = lm(wage~cut(age,4),data = Wage)
summary(piecewise.regfit)
breaks <- seq(from =agelims[1],to= agelims[2],length = 7)
agelims[1]
agelims[2]
?cut
lm.piecewis = lm(wage~cut(age,c(30,40,50,60,70)),data = Wage)
summary(lm.piecewis)
test_age = c(45,55,65,75)
predict(lm.piecewis,newdata = list(age=test_age))
# For regression splines, we use the splines library
# The bs function generates the basis function. By default it generates a
#cubic spline. For basis function, use 'bs' with function 'lm'.

library(splines)
spline.fit = lm(wage~bs(age, knots = c(25,40,60)),data = Wage)
names(summary(spline.fit))
predict(spline.fit, newdata = list(age = c(20,30,50)),se= TRUE)
summary(spline.fit)
age.grid
preds  = predict(spline.fit,newdata = list(age = age.grid), se = TRUE)
plot(age.grid,preds$fit,pch = 16)
stderr = cbind(preds$fit-2*preds$se.fit,preds$fit+2*preds$se.fit)
matlines(age.grid,stderr,col = "blue")
#if we do not want to pre-specify knots, we can use df=6 to create knots
#at all 4 quartiles
dim(bs(Wage$age,df = 6))
attr(bs(Wage$age,df=6), "knots")
(bs(Wage$age,df=6))
fit2 = lm(wage~ns(age,df = 4),data = Wage)
summary((fit2))
coef(summary(fit2))
pred2 = predict(fit2,newdata = list(age = age.grid),se = TRUE)
pred2$fit
pred2$se.fit
serr = cbind(pred2$fit-2*pred2$se.fit,pred2$fit+2*pred2$se.fit)
plot(Wage$age,Wage$wage,pch=16,col="darkgrey")
lines(age.grid,pred2$fit,col='blue',lwd = 2)
matlines(age.grid,serr,col='red',led=2)
predict(fit2,newdata = list(age=age.grid),interval = "confidence")

## For a smoothing spline we use the function smooth.spline
fit = smooth.spline(Wage$age,Wage$wage,df= 16)
plot(Wage$age,Wage$wage,xlim = agelims,col = 'darkgrey')
preds = predict(fit,newdata = data.frame(age= age.grid))
fit2 = smooth.spline(Wage$age,Wage$wage,cv = TRUE)
fit2$df
lines(fit,co= "red",lwd =2)
lines(fit2,col= "blue",lwd =2)
legend("topright",legend= c('Df 16','Df 6.8'),c('red','blue'),lwd= 2,cex=0.8)
plot(Wage$age,Wage$wage,xlim= agelims,cex = 0.5, col= "darkgrey")
title('Local Regression')
local.regr = loess(Wage$age,Wage$wage,span=.2)
?loess
local.regr = loess(wage~age , data = Wage , span = 0.2)
summary(local.regr)
names(Wage)
# gam function is a part of the gam library and used to find gam models
install.packages("gam")
library(gam)
gam1= lm(wage~ns(age,5)+ns(year,4)+education,data = Wage[train,],)
gam2 = gam(wage~s(age,4)+year+education, data = Wage[train,])
gam3 = gam(wage~s(age,4)+education,data = Wage[train,])
summary(gam1)
dim(Wage)
train= sample(3000,1500)
test = -train
pred1 = predict(gam1,newdata = Wage[test,])
pred1
actual_y = Wage$wage[test]
length(actual_y)
mse1 = mean((pred1-actual_y)^2)
pred2 = predict(gam2,newdata = Wage[test,])
pred3 = predict(gam3,newdata = Wage[test,])
mse2 = mean((pred2-actual_y)^2)
mse3 = mean((pred3-actual_y)^2)
mse1
mse2
mse3
plot(Wage$age,Wage$wage,col ="darkgrey")
par(mfrow=c(1,3))
plot.gam(gam1,se = TRUE,col = "blue")
plot(gam2,se = TRUE,col = 'red')
plot(gam2,se= TRUE,col= 'blue')
lines(Wage$age[test],gam1$fitted.values,col = 'blue')
length(gam1$fitted.values)
length(train)
length(-train)
test = -train
length(test)
anova(gam1,gam2,gam3)
summary(gam2)
## akima is the package that can be used to plot 2-d figures that use
#smooth splines with local regression
install.packages('akima')
library(akima)
fit.complex = gam(wage~s(age,4)+lo(year,span=0.5),data = Wage)
warnings()
plot(fit.complex)
# To use logistic regression with gam, specify family = 'binomial'
gam.logistic = gam(I(wage>250)~s(age,4)+lo(year,span=0.5+education),data = Wage)
warnings()
plot(gam.logistic)
par(mfrow= c(1,3))
plot(gam.logistic,se = TRUE, col = "green")
table(Wage$education,I(Wage$wage>250))