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###
###         Answers of exercises
###         Chapter 8 and 9
###



##### Ex. 1

test <- 481
test2 <- "this is a test"

objects()
ls()

objects(pattern="s*")


##### Ex. 2

x1 <- c(1,3.5,0.7,5)
data.class(x1)
x2 <- as.integer(x1)
x3 <- round(x1)
is.integer(x3)


##### Ex. 3

y1 <- 1:10
y2 <- y1 > 5
sum(y2)


##### Ex. 4

y1 <- c("high", "low", "high", "high", "low")
y2 <- as.factor(y1)
levels(y2)

## first transform y2 to an ordered factor
y2 <- ordered(y2,levels=c("low","high"))
y3 <- as.integer(y2)
y3


##### Ex. 5

x <- 1:100
y <- seq(0,500,by=5)  or y <- (0:100)*5
z1 <- rep(1:50,each=3)  or z1 <- rep(1:50, rep(3,50))
z2 <- rep(1:10,1:10)

tmp <- rep(c(1,2),25)
z3 <- rep(1:50,tmp)


##### Ex. 6

x <- rnorm(100)

y <- cut(x,breaks=c(-Inf,-1.5,1.5,Inf),labels=c("low","average","high"))

## y is still a numeric vector

y <- as.factor(y)


##### Ex. 7

x <- rnorm(100)
test <- x > 1.96 | x < -1.96

(1:100)[test]


##### Ex. 8

tmp <- rnorm(100)
mat1 <- matrix(tmp,ncol=10)

tmp1 <- 1:10
tmp2 <- 10:1
mat1 <- rbind(tmp1,mat1,tmp2)

tmp1 <- 1:12
mat1 <- cbind(mat1,tmp1)


##### Ex. 9

tmp1 <- rnorm(1000)
tmp2 <- 1:1000
tmp3 <- rep(1:10,100)

testdf <- data.frame(Values=tmp1, number=tmp2,Group=tmp3)


##### Ex. 10

vec <- rnorm(10)
testlist <- list(vec=vec,df=testdf)

res <- rnorm(10)
testlist2 <- list(res=res,tl=testlist)
names(testlist2)

testlist2$tl$df$Group


##### Ex. 11

x <- 1:98

tmp <- (1:14)*7
y <- rep(tmp,each=2)

## subtract 1 from elements of tmp which have an odd subscript.

oddsubscripts <- (1:14)*2 -1
y[oddsubscripts] <- y[oddsubscripts]-1
y

tmp <- match(x,y)
x <- x[tmp=="NA"]
x

### The dates function start to count at zero and x starts at 1 so subtract 1 from x
dates(x-1,origin=c(m=6,d=5,y=2000))  
## or use the timeDate function
timeDate(julian=x-1,in.origin=c(month=6,day=5,year=2000))

##### Ex. 12

test <- car.test.frame$Price > 9500
cars1 <- car.test.frame[test,]

test <- car.test.frame$Price > 9500 & car.test.frame$Type == "Sporty" & car.test.frame$Country != "Japan"
cars2 <- car.test.frame[test,]

tmp <- row.names(car.test.frame)
test <- regexpr("[cv]",tmp)
test <- test > 0
cars3 <- car.test.frame[test,]


##### Ex. 13

x <- 1:20
y <- runif(20)
plot(x,y)
title("My Plot")

ymax <- max(y)
xc <- x[y==ymax]
text(xc,ymax,"highest y value")

plot(x,y,xlab="day number", ylab="stock price")
lines(x,y)

##### Ex. 14

x <- seq(-2*pi,2*pi,l=100)
y1 <- sin(x)
y2 <- cos(x)
y3 <- tan(x)

plot(x,y1,type="l")
lines(x,y2,lty=2)
lines(x,y3,lty=3)

## or set the y range larger, because the tan function has a wider y range

plot(x,y1,type="l",ylim=c(-8,8))
lines(x,y2,lty=2)
lines(x,y3,lty=3)


##### Ex. 15

pairs(air)
hist(air$temperature,breaks=c(min(air$temperature),65,75,85,max(air$temperature)))


##### Ex. 16

## zet layout op 2 bij 2
par(mfrow=c(2,2))

t <- seq(0,2*pi,l=100)
z1 <- sin(3*t)
z2 <- sin(6*t)
plot(z1,z2,type="l")
z1 <- sin(3*t)
z2 <- sin(8*t)
plot(z1,z2,type="l")
z1 <- sin(3*t)
z2 <- sin(11*t)
plot(z1,z2,type="l")
z1 <- sin(7*t)
z2 <- sin(8*t)
plot(z1,z2,type="l")


##### Ex. 17

x <- seq(0,2*pi,l=50)
y <- x
z <- outer(x,y,FUN=function(x,y){sin(x)+cos(y)})
persp(x,y,z)


##### Ex. 18

cars.aov <- aov(Price~Type,data=car.test.frame)
summary(cars.aov)

mcType <- multicomp(cars.aov)
mcType
plot(mcType)


##### Ex. 19

## there are 60 rows in car.test.frame
test <- sample(1:60,size=15,replace=F)
cars2 <- car.test.frame[test,]


##### Ex. 20

testdf3 <- data.frame(x=rnorm(500),y=rnorm(500),z=rnorm(500))
out1 <- lm(z~x,data=testdf3)
out2 <- lm(z~x+y,data=testdf3)
anova(out1,out2)

st.res <- out2$residuals
st.res <- (st.res - mean(st.res))/stdev(st.res)

test <- order(st.res)
## case numbers of 5 smallest standardized residuals
test[1:5]

## case numbers of 5 largest standardized residuals
test[(length(test)-4):length(test)]


##### Ex. 21

cars.lm <- lm(Price ~ Weight + Mileage,data=car.test.frame)
newcars <- data.frame(Mileage=c(33,40,43),Weight=c(3000,2500,2800))
predict(cars.lm,newcars)


##### Ex. 22

tmean <- function(x,n){
	n1 <- length(x)
	tmp <- sort(x)
	mean(tmp[ (1+n) : (n1-n) ])
}

tmean(rnorm(100),5)

tmean <- function(x,n){
	n1 <- length(x)
	if(n > n1/2){
		return("Invalid n")
	}
	tmp <- sort(x)
	mean(tmp[ (1+n) : (n1-n) ])
}

tmean(rnorm(100),51)


##### Ex. 23

lissajous <- function(a,b){
	t <- seq(0,2*pi,l=1000)
	z1 <- sin(a*t)
	z2 <- sin(b*t)
	plot(z1,z2,type="l")
}

lissajous(11,13)