Training on R For 3 rd and 4 th 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, Licensed as S-Plus in : 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: 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 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

Double Click

Command Prompt Tools bar Menu bar The R Environment

For clear screen ctrl+ L The R Environment

> Creating a Script File

Working in R: As Calculator OperatorSymbol Addition+ Subtraction- Multiplication* Division/ Power^ or ** Numeric Operators  4 +2 =6  4 – 2 = 2  4 * 2 = 8  4 / 2 = 2  4 ^ 2 = 16

 Numeric 5, 5.76, etc  Logical Values corresponding to True or False  Character Strings Sequences 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 + 5 c > aetc Variables & Assignment Operator

Data Structure  Vectors  Matrices  Arrays  Factors  Lists  Data frames

c() to concatenate elements or sub-vectors rep() to repeat elements or patterns seq() to generate sequences > c(2, 7, 9) > [1] > a = c(2, 7, 9) > b = c(3, 5, 8, a) > b > [1] rep(value(s), number of repetition) > rep(5,10) [1] > rep(c(2,4,6),3) [1] Vector Here 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]

h = c(21,25, 19, 22, 23, 20)# Numeric vector h [1] name = c(“Rahim”, “Rani”, “Raju”) # Character vector name [1] “Rahim” “Rani” “Raju” c = h > 22 # Logical vector c [1] FALSE TRUE FALSE FALSE TRUE FALSE a = c(1,2,3,4,5) a [1] a = 1:5 a [1] 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] > w[w>3] # elements in w greater than 3 >w[-2]# all except the second element >[1] > w[w>2 & w<=5)# greater than 2 and less than or equal to 5 Vector Indexing

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 Vector Vector 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,] [2,] [3,]  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,] [2,] [3,] [4,] Array & Matrix A matrix in mathematics is just a two-dimensional array of numbers. Matrices and arrays are represented as vectors with dimensions:

Array & Matrix A 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,] [2,] [3,] > A[,2] # 2nd column of matrix A [1] > A[3, ] # 3rd row of matrix A [1] > A[2,2] # (2, 2) th element of matrix A [1]

Basic operations – Matrix R commandPurpose (output) A+B addition of A and B matrices A * Belement by element products A %*% Bproduct of A and B matrices t(A)transpose of matrix A solve(A)inverse of matrix A cbind()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,] [2,] [3,] > 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,] [2,] [3,] > b [,1] [,2] [,3] [1,] [2,] [3,] > cbind(a,b) [,1] [,2] [,3] [,4] [,5] [,6] [1,] [2,] [3,] > rbind(a,b) [,1] [,2] [,3] [1,] [2,] [3,] [4,] [5,] [6,] 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] $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 progress 1 proximal 6.3 FALSE 2 distal 8.0 TRUE 3 proximal 10.0 FALSE

We illustrate how to construct a data frame from the following car data. MakeModelCylinderWeightMileageType HondaCivicV Sporty Chevrolet BerettaV Compact FordEscortV Small EagleSummitV Small VolkswagenJettaV Small BuickLe SabreV Large MitsubishiGalantV Compact DodgeGrand CaravanV Van ChryslerNew YorkerV Medium AcuraLegendV Medium 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 Car MakeModelCylinderWeightMileageType 1 HondaCivicV Sporty 2 Chevrolet BerettaV Compact 3 FordEscortV Small 4 EagleSummitV Small 5 VolkswagenJettaV Small 6 BuickLe SabreV Large 7 MitsubishiGalantV Compact 8 DodgeGrand CaravanV Van 9 ChryslerNew YorkerV Medium 10 AcuraLegendV Medium Making data frames

> names(Car) [1] "Make" "Model" "Cylinder“ "Weight" "Mileage" "Type" > Car[1,] Make Model Cylinder Weight Mileage Type 1 Honda Civic V Sporty > Car[10,4] [1] 3265 > Car$Mileage [1] > mean(Car$Mileage) #average mileage of the 10 vehicles [1] 25.9 > min(Car$Weight) [1] 2170 Making data frames

> table(Car$Type) # gives a frequency table Compact Large Medium Small Sporty Van > table(Car$Make, Car$Type) # Cross tabulation Compact Large Medium Small Sporty Van Acura Buick Chevrolet Chrysler Dodge Eagle Ford Honda Mitsbusihi Volkswagen Making data frames

> Make.Small <- Car$Make[Car$Type == "Small"] > summary(Car$Mileage) # gives summary statistics Min. 1st Qu. Median Mean 3rd Qu. Max Making data frames

> b = data.frame(x=rnorm(10), y=rnorm(10), z=rnorm(10)) > b x y z > cor(b) x y z x y z > apply(b,1,var) [1] [7] Making data frames

> b = data.frame(x=rnorm(10), y=rnorm(10), z=rnorm(10)) > b x y z attach(b) lm.D9 <- lm(y ~ x)# Regression of y on x lm.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 RollBstat101Bstat

 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 file data2 <- read.table(file= “d:/RFiles/data3.txt", header=T, sep=“\t” ) > data2 > attach(data1) > detach(data1) Reading data from File

Importing from other statistical systems Package 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