f=file.choose()
survey=read.csv(f,header=T)
names(survey)
t.test(text_day~gender,
#1) var.equal = FALSE, data=survey)
by(survey$text_day,survey$gender,mean,na.rm=T)
by(survey$text_day,survey$gender,sd,na.rm=T)
by(!is.na(survey$text_day),survey$gender,sum,na.rm=T)
boxplot(text_day~gender,data=survey,col=c("red","blue"))
girls=survey$text_day[survey$gender=="female"]
boys=survey$text_day[survey$gender=="male"]
par(mfcol=c(2,1))
hist(boys,col="blue",breaks=50*c(0:24),xlim=c(0,1200))
hist(girls,col="red",breaks=50*c(0:24),xlim=c(0,1200))
set.seed(05242012)
nsims=10000
diff.boot=rep(NA,nsims)
girls=survey$text_day[survey$gender=="female" & !is.na(survey$text_day)]
boys=survey$text_day[survey$gender=="male" & !is.na(survey$text_day)]
for(i in 1:nsims){
girls.sample=sample(girls,length(girls),replace=T)
boys.sample=sample(boys,length(boys),replace=T)
diff.boot[i]=mean(girls.sample)-mean(boys.sample)
}
hist(diff.boot,col="slategray2")
mean(diff.boot)
sd(diff.boot)
o=order(diff.boot)
diff.boot.o=diff.boot[o]
c(diff.boot.o[round(0.025*nsims)],diff.boot.o[round(0.975*nsims)])
t.star=qt(0.975,df=min(length(girls),length(boys))-1)
c((mean(girls)-mean(boys))-t.star*sd(diff.boot),(mean(girls)-mean(boys))+t.star*sd(diff.boot))
2*(1-sum(diff.boot>0)/nsims)
#log.girls=log(girls+1)
#log.boys=log(boys+1)
#log.ci=c((mean(log.girls)-mean(log.boys))-t.star*sqrt(var(log.girls)/length(log.girls)+var(log.boys)/length(log.boys)),(mean(log.girls)-mean(log.boys))+t.star*sqrt(var(log.girls)/length(log.girls)+var(log.boys)/length(log.boys)))
#exp(t.test(log.girls,log.boys)$conf.int)
#exp(log.ci)
#2) vs. L1 L2 vs. "L1.5" regression
library(quantmod)
library(quantreg)
getSymbols("SPY", from = "2009-04-01", to = "2012-03-31",auto.assign = T)
SPY.monthret=as.numeric(monthlyReturn(Ad(SPY)))
getSymbols("AFL", from = "2009-04-01", to = "2012-03-31",auto.assign = T)
AFL.monthret=as.numeric(monthlyReturn(Ad(AFL)))
plot(AFL.monthret~SPY.monthret)
#L1.5
L1.5.obj=function(beta,y,x){
b0=beta[1]
b1=beta[2]
return(sum(abs(y-b0-b1*x)^1.5))
}
beta.hat=nlm(L1.5.obj,beta=c(0,1),y=AFL.monthret,x=SPY.monthret)
beta.hat
b1.hat=beta.hat$estimate[2]
lm1=lm(AFL.monthret~SPY.monthret)
rq1=rq(AFL.monthret~SPY.monthret)
abline(lm1,col="red")
abline(rq1,col="blue")
abline(beta.hat$estimate,col="purple",lty=2)
set.seed(05242012)
nsims=10000
slope.boot=rep(NA,nsims)
n=length(AFL.monthret)
for(i in 1:nsims){
sample.indices=sample(1:n,n,replace=T)
AFL.temp=AFL.monthret[sample.indices]
SPY.temp=SPY.monthret[sample.indices]
beta.hat.temp=nlm(L1.5.obj,c(0,1),y=AFL.temp,x=SPY.temp)
slope.boot[i]=beta.hat.temp$estimate[2]
}
hist(slope.boot,col="slategray2")
mean(slope.boot)
sd(slope.boot)
o=order(slope.boot)
slope.boot.o=slope.boot[o]
c(slope.boot.o[round(0.025*nsims)],slope.boot.o[round(0.975*nsims)])
slope.hat=beta.hat$estimate[2]
t.star=qt(0.975,df=n-2)
c(slope.hat-t.star*sd(slope.boot),slope.hat+t.star*sd(slope.boot))