# Examples 1
x <- 2/3
x

sqrt(x)

a <- 2*(x+3)^2
a

y <- t(c(1, 2, 3, 5))
y

y[1]

sum(y)

2 * y

f <- function(y, m=2)  m * y
f

f(y, 2)

f(y, 3)

# Your turn 1
x <- t(c(4, 1, 3, 9))
x

d <- sqrt(x^2 + y^2)
d

2*(d[1] + d[4])

# Loading data
x <- read.csv(file.choose()) # Choose the tips data
head(x)
dim(x)


# Your turn 2
sla <- read.csv(file.choose())
head(sla)

# Examining data
x
head(x)
summary(x)
str(x)
dim(x)

# Data frames
x$bill
x[, "bill"]
x[1,1]
x[1:5,]
x[,1]
x[,c(2,3,5)]
x[1:5,c("tip","day")]
x$tip[1:20]

# Statistical summaries
mean(x$tip)
median(x$tip)
min(x$tip)
max(x$tip)
range(x$tip)
sd(x$tip)
var(x[,2:3])
cor(x[,2:3])
cor(x$tip,x$bill)
summary(x)

# Your turn 3
cor(sla$day,sla$weight)
mean(sla$day)

# Random numbers
runif(10)
runif(10,-100,100)
rnorm(30)
rnorm(10,5,6)
x<-rnorm(30)
mean(x)
sd(x)
rexp(30)
rpois(20,1)
rpois(20,10)

# Your turn 4
x<-rnorm(10)
mean(x)
sd(x)
x<-rnorm(100)
mean(x)
sd(x)
x<-rnorm(100,-8,4)
mean(x)
sd(x)
cor(rnorm(30),runif(30))

# Getting information
?runif
help(package="ggplot2")
?"*"

# Your turn 
?mean
slap <- read.csv(file.choose())
mean(slap$age,na.rm=T)

# Listing R objects
ls()
ls(pos=2)
search()

# Generating sequences
3:10
seq(3, 10)
seq(3, 10, by=1/3)
seq(3, 10, len=8)
rep(3, 10)
rep(1:3, 5)
rep(c(1,2,3,4), c(2,3,2,3))
rep(1:3, rep(2,3))

# Common functions
abs(-2)
sign(-2)
sqrt(2)
exp(1)
log(100)
log10(100)
floor(2.579)
ceiling(2.579)
trunc(2.579)
round(2.579)
signif(2.579, 2)
10%/%3
10%%3
strsplit("10-Oct-99","-")
Sys.Date()
strsplit(as.character(Sys.Date()),"-")
Sys.time()
format(Sys.time(), "%a %b %d %X %Y")
format(Sys.time(), "%X")
strsplit(format(Sys.time(), "%X"),":")

# Options
options(digits=2)
head(sla)
options(digits=5)
head(sla)
head(sla)
options(width=80)
head(sla)

# Functions
std.data <- function(vec) {
  (vec-mean(vec))/sd(vec)
}
x <- std.data(sla$weight)
mean(x)
sd(x)

x <- matrix(rnorm(100, 10, 5), ncol=4)
dim(x)
apply(x, 2, mean)
apply(x, 2, sd)

y <- apply(x, 2, std.data)
dim(y)
apply(y, 2, mean)
apply(y, 2, sd)