R is a free software environment for statistical computing and graphics that provides a wide variety of statistical techniques and graphical methods. It includes base functions and packages, and is used through interfaces like RStudio. R represents data using objects like vectors, matrices, and data frames. Common operations include calculations, generating random variables, and visualizing data. R can be used to analyze a glass fragment dataset to visualize compositions and potentially classify an unknown fragment.

1. R Basics and Simulation
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R Basics and Simulation
About R
R is a free software environment for statistical computing and graphics.
Provides a wide variety of statistical and graphical techniques
Many classical and modern statistical techniques have been implemented.
A few of these are built into the base R environment, but many are supplied as packages.
Convinient interface, RStudio. It is an integrated development environment (IDE) for R. It includes a
console, syntax-highlighting editor that supports direct code execution, as well as tools for plotting, history,
debugging and workspace management.
Open R Studio
Frequently Used Data Types and R-Objects
The variables are not declared as some data type.
The variables are assigned with R-Objects and the data type of the R-object becomes the data type of the
variable.
Data Type: Numeric, Integer, Character
## Numeric
## Assign a number to variable num
num <- 3.14
print(num)
## simple calculation by calling the variable
print(num + 1)
## Let's check the data type that has been assigned to num
print(class(num))
## Integer
## Assign the integer part variable num.int
num.int <- as.integer(num)
num.int
## Let's check the data type
class(num.int)
## Character
## Assign the integer part variable num.int
char <- "Hello"

2. R Basics and Simulation
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char
## Let's check the data type
class(char)
R-Objects: Vectors, Matrices, Data Frames
# Create a vector with more than one element
# We use c() function which means to combine the elements into a vector
# create a vector of characters
col <- c('red','green',"yellow")
col
# create a vector of numeric
num <- c(1,2,3)
num
# extract elements from vectors
num[1]
# Create a matrices of vectors
# Several way to do this
# Use cbind() function which means column combines
Mcol <- cbind(num,num,num)
Mcol
# Use rbind() function which means row combine
Mrow <- rbind(num,num,num)
Mrow
# Use matrix function to fill in each element
M <- matrix(1:9,nrow=3,ncol=3)
M
# Now lets try combining numeric vector and character vector into a matrix
Mtry <- rbind(num,col)
class(Mtry) # Do you notice what has been changed here?
# extract elements from a matrix
M[1,3]
# Create a data frame
df <- data.frame(x = col, y = num)
df
# extract element from data frame
df$x
df$y[3]

3. R Basics and Simulation
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Calculation with R: Multiplication, Log, Exponential ,Power, Square Root
and Some Useful Statistics
# for scaler
x <- 2
x*x
# for vector
num
num + num
y <- c(0,1,2,3,4)
log(y)
# for matrix
M <- matrix(1:9,ncol=3,nrow=3)
exp(M)
sqrt(M)
# for data frame
df
df^2 # why is there a warning message?
# Useful statistics
mean(M)
sum(M)
Simulate Random Variables in R
# generate uniform variable between 0,1
u <- runif(10)
# plot to see what it looks like
plot(u)
hist(u)
# generate more data
u <- runif(1000)
plot(u)
hist(u) # Do you see what has changed?
# sample from a vector
# Type help(sample) to see the function arguments
sampx = sample(x = 1:100, size=1, replace=F)
sampx
# sample 10 numbers from 1-100

4. R Basics and Simulation
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sampx = sample(x = 1:100, size=10, replace=F)
sampx
rank(sampx)
# Normal random variable, a very useful random variable used in statistics
n1 <- rnorm(1)
n1
n2 <- rnorm(1)
n2
# Generate a larger sample to see its distribution
n <- rnorm(1000)
plot(n)
hist(n)
plot(density(n), main="Density of n",xlab="n") # remember the shape of the distribution
# set seed to generate the same random number
set.seed(123)
n1 <- rnorm(1)
n1
set.seed(123)
n2 <- rnorm(1)
n2
Why is Normal Distribution so Useful?
# Let's look at some examples
# If we flip 10 coints and count the number of heads.
# what do you think the distribution of the count will look like.
# simulate 30 coin flips
x = sample(c("head","tail"),30,replace = T)
x
# count the number of heads
x == "head"
sum( x == "head" )
# repeat this 1000 times
headcount <- c() # create an empty vector
for (i in 1:1000){
x = sample(c("head","tail"),30,replace = T)
headcount[i] <- sum( x == "head" )
}
hist(headcount,main="Head Count in 30 Coin Flips") # plot the distribution, what do you see?
# How about we simulation from a different distribution?
# simulation from uniform distribution
x = runif(30)
sum(x)

5. R Basics and Simulation
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# repeat this 1000 times
sumunif <- c() # create an empty vector
for (i in 1:1000){
x = runif(30)
sumunif[i] <- sum(x)
}
hist(sumunif,main="Sum of Uniform Random Variables") # plot the distribution, what do you see?
# The beam machine
# install.packages("animation")
# library(animation)
# balls = 200
# layers = 15
# ani.options(nmax=balls+layers-2)
# quincunx(balls, layers)
Data Visualization to Classify Glass Fragment Found on “Crime Scene”
library(MASS)
data(fgl)
# See data description
help(fgl)
# Print out part of the data set
head(fgl)
# Plot each composition versus glass type
plot(RI ~ type, data=fgl, col=c(1:6))
plot(Al ~ type, data=fgl, col=c(1:6))
plot(K ~ type, data=fgl, col=c(1:6))
plot(Ca ~ type, data=fgl, col=c(1:6))
# visualize two compositions versus glass type.
# Pick two composition: "Ca" and "K"
# Pick two class types: vehical window glass "Veh", and vehicle hadlamps "Head"
# Can we distinguish these two types of glass based on these two compositions
fgl_subset = subset(fgl,type %in% c("WinNF", "Veh"))
cols = ifelse(fgl_subset[,"type"]=="Veh","blue","red")
set.seed(12)
# pick one observation, pretending that we don't know the glass type
test = 22
fgl_subset[test,c("Ca","K")]
# remake boxplot with a focus on these two type of glass
plot(Ca ~ type, data=fgl_subset, col=c("blue","red"))
abline(h=fgl_subset[test,c("Ca")])
plot(K ~ type, data=fgl_subset, col=c("blue","red"))
abline(h=fgl_subset[test,c("K")])

6. R Basics and Simulation
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plot(fgl_subset[-test,c("Ca","K")], col=cols, pch=19,main="Glass type by compositions")
# Add the data points that we left out to see where it lands.
points(fgl_subset[test,c("Ca","K")], col="black", pch=17,cex = 1.5)
legend("topright",col=c("red","blue","black"),legend=c("WinNF","Veh","test case"),pch=c(19,19,17))
# Based on these two composition of the test glass. Can you predict what type of glass it is?
print(fgl_subset[test,"type"])