Training on RFor 3rd and 4th Year Honours Students, Dept. of Statistics, RU

Empowered by

Higher Education Quality Enhancement Project (HEQEP)Department of Statistics

Rajshahi University, Rajshahi-6205, Bangladesh

March 21-23, 2013

Installation and Data Structures of R

Statistical Programming Language S developed at Bell Labs, 1976.

Licensed as S-Plus in 1983.

1990 : R An open source program similar to S

Developed by Robert Gentleman and Ross Ihaka (Auckland, NZ)

1997: Developed international “R-core” team

Updated versions available every couple months

For more: http://cran.r-project.org/mirrors.html

History of R

R is a free computer programming language, developed by renowned Statisticians.

It is open-source and runs on Windows, Linux and Macintosh.

R has excellent graphing capabilities. R has an excellent built-in help system. R's language has a powerful, easy to learn syntax with many

built-in statistical functions. The language is easy to extend with user-written functions.

Advantage of R

To obtain and install R on your computer

Choose the appropriate item from the “Packages” menu

Go to http://cran.r-project.org/mirrors.html to choose a mirror near you

Click on your favorite operating system (Windows, Linux, or Mac)

Download and install from the “base”

To install additional packages

Start R on your computer

Here, CRAN = Comprehensive R Archive Network.

To obtain and install R on your computer

To obtain and install R on your computer

To obtain and install R on your computer

Double Click

To obtain and install R on your computer

To obtain and install R on your computer

To obtain and install R on your computer

Command Prompt

Tools bar

Menu bar

The R Environment

For clear screenctrl + L

The R Environment

>

Creating a Script File

Working in R: As Calculator

Operator SymbolAddition +

Subtraction -Multiplication *

Division /Power ^ or **

Numeric Operators

4 +2 =6 4 – 2 = 2 4 * 2 = 8 4 / 2 = 2 4 ^ 2 = 16

Numeric5, 5.76, etc

Logical Values corresponding to True or False

Character StringsSequences of characters (blue, male, Rahim, etc)

Variables are assigned by the operator <- or = Data type need not to be declared.

a = 5 (or, a <- 5)b = “blue”c = a^2 + 5c > a etc

Variables & Assignment Operator

Data Structure

Vectors Matrices Arrays Factors Lists Data frames

c() to concatenate elements or sub-vectorsrep() to repeat elements or patternsseq() to generate sequences

> c(2, 7, 9)> [1] 2 7 9> a = c(2, 7, 9)> b = c(3, 5, 8, a)> b> [1] 2 7 9 2 7 9

rep(value(s), number of repetition)> rep(5,10) [1] 5 5 5 5 5 5 5 5 5 5> rep(c(2,4,6),3)[1] 2 4 6 2 4 6 2 4 6

VectorHere we introduce three functions, c, seq, and rep, that are used to create vectors in various situations.

seq(initial value, Terminated value, increment)> seq(2, 10, 2)> [1] 2 4 6 8 10

h = c(21,25, 19, 22, 23, 20) # Numeric vectorh [1] 21 25 19 22 23 20

name = c(“Rahim”, “Rani”, “Raju”) # Character vectorname[1] “Rahim” “Rani” “Raju”

c = h > 22 # Logical vectorc[1] FALSE TRUE FALSE FALSE TRUE FALSE

a = c(1,2,3,4,5)a[1] 1 2 3 4 5

a = 1:5a[1] 1 2 3 4 5

Vector

w = c(1, 3, 5, 2, 10)

> w[3] # the third element of w>[1] 5

> w[3:5] # the third to fifth element of w, inclusive>[1] 5 2 10

> w[w>3] # elements in w greater than 3>w[-2] # all except the second element>[1] 1 5 2 10

> w[w>2 & w<=5)# greater than 2 and less than or equal to 5

VectorIndexing

w = c(1, 3, 5, 2, 10)length(w) sum(w)cumsum(w) min(w)max(w) range(w)sum(w) mean(w)median(w) var(w) std(w) summary(w)abs(10-50) sort(w)sort(w, decreasing=T) etc

VectorVector used in functions

Specific R

keyword help(keyword)

?keyword

HTML

> ?mean# information on mean command> help(mean)

> help(median)

> help.start()

CRAN Full Manual help.start()HTML

Finding "vague" topic

help.search(“topic”)

??topic

Working in R: Using help

# Generate a 3 by 4 array> x <- 1:12> dim(x) <- c(3,4)> x [,1] [,2] [,3] [,4][1,] 1 4 7 10[2,] 2 5 8 11[3,] 3 6 9 12

The dim assignment function sets or changes the dimension attribute of x, causing R to treat the vector of 12 numbers as a 3 × 4 matrix.

Notice that the storage is column-major; that is, the elements of the first column are followed by those of the second, etc.

# Generate a 4 by 5 array> A <- array(1:20, dim = c(4,5)) > A [,1] [,2] [,3] [,4] [,5][1,] 1 5 9 13 17[2,] 2 6 10 14 18[3,] 3 7 11 15 19[4,] 4 8 12 16 20

Array & MatrixA matrix in mathematics is just a two-dimensional array of numbers. Matrices and arrays are represented as vectors with dimensions:

Array & MatrixA matrix in mathematics is just a two-dimensional array of numbers. Matrices and arrays are represented as vectors with dimensions:

# 3 x 2 matrix of 0> Y <- matrix(0, nrow=3, ncol=2) > Y [,1] [,2][1,] 0 0[2,] 0 0[3,] 0 0

# Generate a 3 by 2 Matrix > A = matrix(1:12, nrow=3, byrow=T)> A [,1] [,2] [,3] [,4][1,] 1 2 3 4[2,] 5 6 7 8[3,] 9 10 11 12

> A[ ,2] # 2nd column of matrix A[1] 2 6 10

> A[3, ] # 3rd row of matrix A[1] 9 10 11 12

> A[2 ,2] # (2, 2) th element of matrix A[1] 2 6 10

Basic operations – MatrixR command Purpose (output)A+B addition of A and B matricesA * B element by element productsA %*% B product of A and B matrices t(A) transpose of matrix Asolve(A) inverse of matrix Acbind() forms matrices by binding together

matrices horizontally, or column-wise

rbind() forms matrices by binding together matrices vertically, or row-wise

> A.mat <- matrix(c(19,8,11,2,18,17,15,19,10),nrow=3) > A.mat [,1] [,2] [,3][1,] 19 2 15[2,] 8 18 19[3,] 11 17 10

> inv.A <- solve(A.mat) # inverse of matrix A.mat

> t(A.mat) # transpose of matrix A.mat

> A.mat %*% inv.A

Basic operations – Matrix

> a=matrix(1:9,nrow=3)> b=matrix(2:10, nrow=3)

> a [,1] [,2] [,3][1,] 1 4 7[2,] 2 5 8[3,] 3 6 9

> b [,1] [,2] [,3][1,] 2 5 8[2,] 3 6 9[3,] 4 7 10

> cbind(a,b) [,1] [,2] [,3] [,4] [,5] [,6][1,] 1 4 7 2 5 8[2,] 2 5 8 3 6 9[3,] 3 6 9 4 7 10

> rbind(a,b) [,1] [,2] [,3][1,] 1 4 7[2,] 2 5 8[3,] 3 6 9[4,] 2 5 8[5,] 3 6 9[6,] 4 7 10

Basic operations – Matrix

Cov.matrix = cov(b) Cor.matrix = cor(b)Row.mean = apply(b, 1, mean) Col.mean = apply(b, 2, mean)

NOTE: apply(X, MARGIN, FUN)

vector: an ordered collection of data of the same type. > a = c(7,5,1)> a[2][1] 5

list: an ordered collection of data of arbitrary types. > a = list(Name="Rahim",age=c(12, 23,10), Married = F)> a$Name[1] "Rahim"$age[1] 12 23 10$Married[1] FALSE

Typically, vector elements are accessed by their index (an integer), list elements by their name (a character string).

List

Data frames Data frame is supposed to represent the typical data table that

researchers come up with – like a spreadsheet. It is a rectangular table with rows and columns with same length; data

within each column has the same type (e.g. number, text, logical), but different columns may have different types.

Example:> a localisation tumorsize progress1 proximal 6.3 FALSE2 distal 8.0 TRUE3 proximal 10.0 FALSE

We illustrate how to construct a data frame from the following car data.

Make Model Cylinder Weight Mileage TypeHonda Civic V4 2170 33 Sporty

Chevrolet Beretta V4 2655 26 CompactFord Escort V4 2345 33 SmallEagle Summit V4 2560 33 Small

Volkswagen Jetta V4 2330 26 SmallBuick Le Sabre V6 3325 23 Large

Mitsubishi Galant V4 2745 25 CompactDodge Grand Caravan V6 3735 18 Van

Chrysler New Yorker V6 3450 22 MediumAcura Legend V6 3265 20 Medium

Making data frames

Making data frames> Make <- c("Honda","Chevrolet","Ford","Eagle","Volkswagen","Buick","Mitsbusihi",

+ "Dodge","Chrysler","Acura")

> Model <- c("Civic","Beretta","Escort","Summit","Jetta","Le Sabre","Galant", + "Grand Caravan","New Yorker","Legend")

> Cylinder <-c (rep("V4",5),"V6","V4",rep("V6",3))

> Weight <- c(2170, 2655, 2345, 2560, 2330, 3325, 2745, 3735, 3450, 3265)

> Mileage <- c(33, 26, 33, 33, 26, 23, 25, 18, 22, 20)

> Type <- c("Sporty","Compact",rep("Small",3),"Large","Compact","Van", + rep("Medium",2))

Now data.frame() function combines the six vectors into a single data frame.

> Car <- data.frame(Make, Model, Cylinder, Weight, Mileage, Type) > Car

  Make Model Cylinder Weight Mileage Type

1 Honda Civic V4 2170 33 Sporty 2 Chevrolet  Beretta V4 2655 26 Compact 3 Ford Escort V4 2345 33 Small 4 Eagle Summit V4 2560 33 Small 5 Volkswagen Jetta V4 2330 26 Small 6 Buick Le Sabre V6 3325 23 Large 7 Mitsubishi Galant V4 2745 25 Compact 8 Dodge Grand Caravan V6 3735 18 Van 9 Chrysler New Yorker V6 3450 22 Medium 10 Acura Legend V6 3265 20 Medium

Making data frames

> names(Car) [1] "Make" "Model" "Cylinder“ "Weight" "Mileage" "Type"

> Car[1,] Make Model Cylinder Weight Mileage Type 1 Honda Civic V4 2170 33 Sporty

> Car[10,4][1] 3265

> Car$Mileage [1] 33 26 33 33 26 23 25 18 22 20

> mean(Car$Mileage) #average mileage of the 10 vehicles [1] 25.9

> min(Car$Weight) [1] 2170

Making data frames

> table(Car$Type) # gives a frequency table Compact Large Medium Small Sporty Van 2 1 2 3 1 1

> table(Car$Make, Car$Type) # Cross tabulation Compact Large Medium Small Sporty Van Acura 0 0 1 0 0 0 Buick 0 1 0 0 0 0 Chevrolet 1 0 0 0 0 0 Chrysler 0 0 1 0 0 0 Dodge 0 0 0 0 0 1 Eagle 0 0 0 1 0 0 Ford 0 0 0 1 0 0 Honda 0 0 0 0 1 0 Mitsbusihi 1 0 0 0 0 0 Volkswagen 0 0 0 1 0 0

Making data frames

> Make.Small <- Car$Make[Car$Type == "Small"]

> summary(Car$Mileage) # gives summary statistics Min. 1st Qu. Median Mean 3rd Qu. Max. 18.00 22.25 25.50 25.90 31.25 33.00

Making data frames

> b = data.frame(x=rnorm(10), y=rnorm(10), z=rnorm(10))> b x y z1 -1.7651180 0.462309932 0.092309142 -0.7340731 -1.681826091 0.666487913 -0.4968900 1.728658405 -0.682816644 -1.3217873 0.307030157 0.241927455 -0.2070019 0.003892192 1.195918076 -0.9633084 0.060328696 -1.404248437 -1.1323626 1.079521099 1.635529158 -0.7301976 -1.422012899 -0.166958609 0.2979073 0.528152338 0.6599577810 -0.5759655 0.655296337 -0.39156127

> cor(b) x y zx 1.0000000000 0.0007151043 0.12151913y 0.0007151043 1.0000000000 -0.05770153z 0.1215191317 -0.0577015345 1.00000000

> apply(b,1,var) [1] 1.42472853 1.39573092 1.80047438 0.85041478 0.57226442 0.56454121 [7] 2.14379987 0.39516798 0.03357767 0.44098693

Making data frames

> b = data.frame(x=rnorm(10), y=rnorm(10), z=rnorm(10))> b x y z1 -1.7651180 0.462309932 0.092309142 -0.7340731 -1.681826091 0.666487913 -0.4968900 1.728658405 -0.682816644 -1.3217873 0.307030157 0.241927455 -0.2070019 0.003892192 1.195918076 -0.9633084 0.060328696 -1.404248437 -1.1323626 1.079521099 1.635529158 -0.7301976 -1.422012899 -0.166958609 0.2979073 0.528152338 0.6599577810 -0.5759655 0.655296337 -0.39156127

attach(b)lm.D9 <- lm(y ~ x) # Regression of y on xlm.D90 <- lm(weight ~ group - 1) # omitting intercept

anova(lm.D9)summary(lm.D9

Making data frames

Data Entry using Data Editor • R has a Data Editor with spreadsheet-like interface. • The interface quite useful for small data sets.

Suppose we want to construct a data frame based on following data

Roll Bstat101 Bstat1024701 78 804702 75 654703 60 704704 72 68

To do this – type> result <- data.frame(Roll=integer(0), Bstat101=numeric(0),

Bstat102=numeric(0))> result <- edit(result)

Then enter the data in the Data Editor and close Editor

> result # To see the data

> result <- edit(result) # To modify the data

Data Entry using Data Editor

An entire data frame can be read directly with the read.table() function.

# Reading data from Excel .csv File> data1 <- read.table(file= “d:/RFiles/data1.csv", header=T, sep=“,”)> data1 <- read.csv(file= “d:/RFiles/data1.csv", header=T )> data1

# Reading data from text filedata2 <- read.table(file= “d:/RFiles/data3.txt", header=T, sep=“\t” )> data2

> attach(data1)

> detach(data1)

Reading data from File

Importing from other statistical systemsPackage foreign on cran provides import facilities for files produced by the following statistical software.

> read.mtp # imports a `Minitab Portable Worksheet’> read.xport # reads a file in SAS format> read.spss # reads files created by spss

Package Rstreams on cran contain functions

> readSfile # reads binary objects produced by S-PLUS> data.restore # reads S-PLUS data dumps (created by data.dump)

Thanks