Workshop in Methods and Indiana Statistical Consulting Center Introduction to R

Transcription

1 Workshop in Methods and Indiana Statistical Consulting Center Introduction to R R Basics Leslie M. Blaha 23 January 2010 WIM and ISCC Intro to R R Basics 1 / 12

2 A Short History of R The R Project for Statistical Computing R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R. WIM and ISCC Intro to R R Basics 2 / 12

3 The Comprehensive R Archive Network (CRAN) The CRAN website is where you can: Download the latest version of R Find additional packages Search documentation manuals Get access to the user listservs Search for help WIM and ISCC Intro to R R Basics 3 / 12

4 The R Graphical User Interface (GUI) Command Window Script Window Plot Window WIM and ISCC Intro to R R Basics 4 / 12

5 Working Directory What is my current working directory? getwd() Mac Menu: Misc Get Working Directory Windows Menu: File Change dir... WIM and ISCC Intro to R R Basics 5 / 12

6 Working Directory What is my current working directory? getwd() Mac Menu: Misc Get Working Directory Windows Menu: File Change dir... Changing the working directory setwd() Mac Menu: Misc Change Working Directory... Windows Menu: File Change dir... WIM and ISCC Intro to R R Basics 5 / 12

7 A Note on Path Names In R, you can specify a path name with either forward slash or backslash. However, if you use backslashes, you must use two of them. These will both set the working directory: e.g. setwd( C:/Program Files/R/R ) or setwd( C:\\ Program Files\\ R\\ R ) WIM and ISCC Intro to R R Basics 6 / 12

8 Clearing the Console Clear the Console (Command Window): Mac Menu: Edit Clear Console Windows Menu: Edit Clear console WIM and ISCC Intro to R R Basics 7 / 12

9 Clearing the Console Clear the Console (Command Window): Mac Menu: Edit Clear Console Windows Menu: Edit Clear console Removing variables from memory: rm() or remove() e.g. create a variable X < 4 Remove variable X: rm(x) To remove all variables in the current memory: rm(list=ls()) WIM and ISCC Intro to R R Basics 7 / 12

10 Getting Help Several help commands: If you know the function name: help()? If you are not sure: help.search() WIM and ISCC Intro to R R Basics 8 / 12

11 Documentation Let s open a sample documentation file:?sum Elements of a documentation file: Function name and the package containing it e.g. sum{base} indicates the sum() function in the base package Description Usage Arguments Details Value: describes what the function will return, may contain a list of object components (for example,?lm) Additional Notes and References See Also indicates related functions Example(s) WIM and ISCC Intro to R R Basics 9 / 12

12 Online Resources and Help R listservs Quick-R tutorial: R Tutor: UCLA Statistical Computing: Google! WIM and ISCC Intro to R R Basics 10 / 12

13 Packages Packages are available for many different types of analyses over 2000 listed on the CRAN website! The basic R program contains some basic packages, including base, graphics, stats, utils Installing a package: On Mac: Packages & Data Package Installer Find the package you want with Package Search and hit Install Selected Try to find and install the package MASS. After installing a package, you MUST call it into active memory with the library() command in order to use its functions. e.g. library(mass) WIM and ISCC Intro to R R Basics 11 / 12

14 Exercise 1 1 From the command window find your current working directory. Change the working directory to be the My Documents folder under your Username. 2 Save the commands for finding and changing the working directory in a script file. 3 Using the various help commands, try to find the documentation for the following functions: plot a function for creating tables from a set of data a function for finding the eigenvalues of a matrix 4 Locate and install the package psych for use later in the workshop. WIM and ISCC Intro to R R Basics 12 / 12

15 Workshop in Methods and Indiana Statistical Consulting Center Introduction to R Working with Data Leslie M. Blaha 23 January 2010 WIM and ISCC Intro to R Working with Data 1 / 15

16 Manually Creating or Entering Data in R Combine items into vector or list: c() e.g. A < c(1,2,3,4,5,6) e.g. c(1,2,3,4,5,6) > A e.g. A = c(1,2,3,4,5,6) WIM and ISCC Intro to R Working with Data 2 / 15

17 Manually Creating or Entering Data in R Combine items into vector or list: c() e.g. A < c(1,2,3,4,5,6) e.g. c(1,2,3,4,5,6) > A e.g. A = c(1,2,3,4,5,6) Repeat a number or a sequence of numbers: rep() e.g. rep(1,5) e.g. rep(c(2,5,7), 3) WIM and ISCC Intro to R Working with Data 2 / 15

18 Manually Creating or Entering Data in R Combine items into vector or list: c() e.g. A < c(1,2,3,4,5,6) e.g. c(1,2,3,4,5,6) > A e.g. A = c(1,2,3,4,5,6) Repeat a number or a sequence of numbers: rep() e.g. rep(1,5) e.g. rep(c(2,5,7), 3) Sequence generation: seq() e.g. seq(1, 10) e.g. seq(1, 10,.5) WIM and ISCC Intro to R Working with Data 2 / 15

19 Manually Creating or Entering Data in R Combine R objects by columns: cbind() A <- rep(1, 4) B <- rep(2, 4) AB <- cbind(a, B) Combine R objects by rows: rbind() A <- rep(1, 4) B <- rep(2, 4) AB <- rbind(a, B) WIM and ISCC Intro to R Working with Data 3 / 15

20 Manually Creating or Entering Data in R Create a matrix: matrix() Let s look at the Usage of matrix(): matrix(data=na, nrow=1, ncol=1, byrow=false, dimnames=null) Create a column vector: matrix(c(2,3,2,6,2,8), ncol=1) WIM and ISCC Intro to R Working with Data 4 / 15

21 Manually Creating or Entering Data in R Create a matrix: matrix() Let s look at the Usage of matrix(): matrix(data=na, nrow=1, ncol=1, byrow=false, dimnames=null) Create a column vector: matrix(c(2,3,2,6,2,8), ncol=1) Create a 2x3 matrix: matrix(c(2,3,2,6,2,8), nrow=2, ncol=3) WIM and ISCC Intro to R Working with Data 4 / 15

22 Manually Creating or Entering Data in R Create a matrix: matrix() Let s look at the Usage of matrix(): matrix(data=na, nrow=1, ncol=1, byrow=false, dimnames=null) Create a column vector: matrix(c(2,3,2,6,2,8), ncol=1) Create a 2x3 matrix: matrix(c(2,3,2,6,2,8), nrow=2, ncol=3) Create a 2x3 matrix filling in across the row first: matrix(c(2,3,2,6,2,8), nrow=2, ncol=3, byrow=true) WIM and ISCC Intro to R Working with Data 4 / 15

23 Manually Creating or Entering Data in R Create a matrix: matrix() Let s look at the Usage of matrix(): matrix(data=na, nrow=1, ncol=1, byrow=false, dimnames=null) Create a column vector: matrix(c(2,3,2,6,2,8), ncol=1) Create a 2x3 matrix: matrix(c(2,3,2,6,2,8), nrow=2, ncol=3) Create a 2x3 matrix filling in across the row first: matrix(c(2,3,2,6,2,8), nrow=2, ncol=3, byrow=true) Create a 2x3 matrix with row and column names: matrix(c(2,3,2,6,2,8), nrow=2, ncol=3, dimnames = list(c( row1, row2 ),c( Col1, Col2, Col3 ))) WIM and ISCC Intro to R Working with Data 4 / 15

24 Types of Data Structures Matrix is.matrix() as.matrix() Data Frame is.data.frame() as.data.frame() List is.list() as.list() WIM and ISCC Intro to R Working with Data 5 / 15

25 Reading a Data File into R Most general function: read.table() e.g. read.table( /Users/Leslie/Documents/R Workshop/SwissNotes.csv, sep=,, header=true) filename is in quotes, double or single must include file extension filename is case sensitive sep defines the separator, like,, \t or be sure to correctly identify header=true or header=false read.table() creates a data frame WIM and ISCC Intro to R Working with Data 6 / 15

26 Reading a Data File into R Most general function: read.table() e.g. read.table( /Users/Leslie/Documents/R Workshop/SwissNotes.csv, sep=,, header=true) filename is in quotes, double or single must include file extension filename is case sensitive sep defines the separator, like,, \t or be sure to correctly identify header=true or header=false read.table() creates a data frame For csv files: read.csv() e.g. read.csv( /Users/Leslie/Documents/R Workshop/SwissNotes.csv, header=true) For tab delimited files: read.delim() WIM and ISCC Intro to R Working with Data 6 / 15

27 Reading a Data File into R The function file.choose() can be used to let you search for a file: > Y<-read.table(file=file.choose()) file.choose() pops up an open file dialogue box WIM and ISCC Intro to R Working with Data 7 / 15

28 Variable Names To identify the list of variable names in your data set: >data <- read.table( /Users/Leslie/Documents/R Workshop/ SwissNotes.csv, sep=",",header=true) >names(data) [1] "Length" "LeftHeight" "RightHeight" "LowerInner.Frame" [5] "UpperInner.Frame" "Diagonal" "Type" If your data file does not contain variable names, you can create them with the command names(). > names(data) <- c("length", "LeftHeight", "RightHeight", "LowerInner.Frame", "UpperInner.Frame", "Diagonal", "Type") WIM and ISCC Intro to R Working with Data 8 / 15

29 A Side Note - Data Description Data compiled by Bernard Flury Dataset contains measurements on 200 Swiss bank notes, 100 genuine and 100 counterfeit notes. WIM and ISCC Intro to R Working with Data 9 / 15

30 The attach() and detach() Commands The attach() function allows you to take the set of variables in a data set and attach each one to its own object in the R search path. In the SwissNote data, if I want to refer to the variable Type, I can use > data$type or >data[,type] If I use attach(), I can refer to Type on its own, like its own variable: > attach(data) > Type [1] Genuine Genuine Genuine... WIM and ISCC Intro to R Working with Data 10 / 15

31 The attach() and detach() Commands The detach() command reverses attach(), and detaches objects from the search path. Variables are now only part of their original data set. They are no longer separate objects. > detach(data) > Type Error: object "Type" not found WIM and ISCC Intro to R Working with Data 11 / 15

32 Subsets of Data In general, you can refer to any entry in an object by [row, column] e.g. > data[1,5] [1] 9.7 WIM and ISCC Intro to R Working with Data 12 / 15

33 Subsets of Data In general, you can refer to any entry in an object by [row, column] e.g. > data[1,5] [1] 9.7 To select an entire row, leave the column blank e.g. > data[1, ] WIM and ISCC Intro to R Working with Data 12 / 15

34 Subsets of Data In general, you can refer to any entry in an object by [row, column] e.g. > data[1,5] [1] 9.7 To select an entire row, leave the column blank e.g. > data[1, ] To select a set of rows: Rows 1-10: data[1:10,] Rows 3, 6, and 7: data[c(3,6,7),] All rows except the first row data[-1,] WIM and ISCC Intro to R Working with Data 12 / 15

35 Subsets of Data In general, you can refer to any entry in an object by [row, column] e.g. > data[1,5] [1] 9.7 To select an entire row, leave the column blank e.g. > data[1, ] To select a set of rows: Rows 1-10: data[1:10,] Rows 3, 6, and 7: data[c(3,6,7),] All rows except the first row data[-1,] Similar commands can be used for columns or sets of columns. WIM and ISCC Intro to R Working with Data 12 / 15

36 Subsets of Data Data can also be selected by names of variables. For example, if I just want the LeftHeight data for all the bank notes: > data[,"leftheight"] [1] Note that this is similar to > data$leftheight WIM and ISCC Intro to R Working with Data 13 / 15

37 Subsets of Data We can also specify a condition to select data. For example, if I just want the data for only Genuine bank notes > data[data$type=="genuine",] Equivalently, > attach(data) > data[type=="genuine",] Length LeftHeight RightHeight LowerInner.Frame WIM and ISCC Intro to R Working with Data 14 / 15

38 Exercise 2 1 Enter the following data into R: CHI FRA GER JPN SWE USA Is the data set you created in (1) a data.frame or matrix? What happens if you switch the format? 3 On OnCourse in the Data Sets folder, download the data file cardiac2.txt. This is a tab delimited data set. Read this data into R. 4 cardiac2.txt includes several measurements taken to predict cardiac events, including heart attacks. Select the data for the male participants only. 5 For the male participants, select only the data for basal hear rate (bhr) and peak heart rate (pkhr). WIM and ISCC Intro to R Working with Data 15 / 15

39 Workshop in Methods and Indiana Statistical Consulting Center Introduction to R Data Visualization Leslie M. Blaha 23 January 2010 WIM and ISCC Intro to R DataVisualization 1 / 16

40 The plot() Function plot() is the primary plotting function. Calling plot will open a new plotting window Let s look at the documentation of plot():?plot WIM and ISCC Intro to R DataVisualization 2 / 16

41 The plot() Function Let s try a basic plot of two variables, LeftHeight and RightHeight > plot(leftheight,rightheight) RightHeight LeftHeight WIM and ISCC Intro to R DataVisualization 3 / 16

42 The plot() Function Let s change the symbols to squares specifying the parameter pch = For details on color options, see the Color Specification section in?par. > plot(leftheight,rightheight, pch=22) RightHeight LeftHeight WIM and ISCC Intro to R DataVisualization 4 / 16

43 The plot() Function Let s change the color of the symbols with the parameter col = To see a list of possible color names: > colors() Let s do our scatterplot with red circles. > plot(leftheight,rightheight, col="red") RightHeight LeftHeight WIM and ISCC Intro to R DataVisualization 5 / 16

44 The plot() Function Say we decide we don t want a scatterplot. With the type parameter, we have the following options: "p" for points, "l" for lines, "b" for both, "c" for the lines part alone of "b", "o" for both overplotted, "h" for histogram like (or high-density) vertical lines, "s" for stair steps, "S" for other steps, see Details below, "n" for no plotting. WIM and ISCC Intro to R DataVisualization 6 / 16

45 The plot() Function For example, if we decide we want points and lines, we can try > plot(leftheight,rightheight, type="o") RightHeight LeftHeight WIM and ISCC Intro to R DataVisualization 7 / 16

46 Scatterplots for Multiple Groups We know in our data we have two types of bank notes, Genuine and Counterfeit. How can we distinguish them in the plot? We can use plot together with points to separately plot the two groups in the same plot. > plot(leftheight[type=="genuine"], RightHeight[Type=="Genuine"], col="red") > points(leftheight[type=="counterfeit"], RightHeight[Type=="Counterfeit"], col="blue") RightHeight[Type == "Genuine"] LeftHeight[Type == "Genuine"] WIM and ISCC Intro to R DataVisualization 8 / 16

47 Scatterplots for Multiple Groups Notice the labels on the x and y axis are simply whatever we identified the x and y data to be. We can change the axis labels and other plot titles. In your plot command call, you can do the following: Specify the x-axis label: xlab = X Label Specify the y-axis label: ylab = Y Label Specify the plot title: main = Main Title Specify a subtitle: sub = Subtitle WIM and ISCC Intro to R DataVisualization 9 / 16

48 Plot Titles and Labels > plot(leftheight[type=="genuine"], RightHeight[Type=="Genuine"], col="red", main="plot of Bank Note Heights", sub = "Measurements are in mm", xlab="height of Left Side", ylab="height of Right Side") > points(leftheight[type=="counterfeit"], RightHeight[Type=="Counterfeit"], col="blue") Plot of Bank Note Heights Height of Right Side Height of Left Side Measurements are in mm WIM and ISCC Intro to R DataVisualization 10 / 16

49 Adding a Legend > legend("topleft",c("genuine Notes","Counterfeit Notes"), pch=c(21,21),col=c("red","blue")) Plot of Bank Note Heights Height of Right Side Genuine Notes Counterfeit Notes Height of Left Side Measurements are in mm WIM and ISCC Intro to R DataVisualization 11 / 16

50 Adding Lines to a Scatterplot We can use the abline() function to add different types of straight lines to our plot. Horizontal line: abline(h= ) Vertical Line: abline(v= ) Line given by slope (b) and intercept (a): abline(a =, b = ) Line given by slope (b) and intercept (a): abline(coef = c(a, b)) WIM and ISCC Intro to R DataVisualization 12 / 16

51 Adding Lines to a Scatterplot > abline(coef=c( , )) Plot of Bank Note Heights Height of Right Side Genuine Notes Counterfeit Notes Height of Left Side Measurements are in mm WIM and ISCC Intro to R DataVisualization 13 / 16

52 Histograms Histograms are another popular plotting option. > hist(length) Histogram of Length Frequency Length WIM and ISCC Intro to R DataVisualization 14 / 16

53 Exploring Data with the pairs() Function Using the SwissNote data > pairs(data) Length LeftHeight RightHeight LowerInner.Frame UpperInner.Frame Diagonal Type WIM and ISCC Intro to R DataVisualization 15 / 16

54 Exercise 3 Using the cardiac data set, create the following plots: 1 Create a scatterplot of age versus peak heart rate (pkhr). Be sure to label your axes and title the plot. 2 Using information available on the points documentation page, adjust your scatterplot to have symbols that are filled blue diamonds with a green border. 3 In your age versus peak heart rate scatterplot, plot the males and females with different symbols and different colors. Add a legend to your plot. 4 Create histograms for the basal blood pressure (basebp) data and the systolic blood pressure (sbp) data. WIM and ISCC Intro to R DataVisualization 16 / 16

55 Workshop in Methods and Indiana Statistical Consulting Center Introduction to R Basic Data Analysis: Descriptive Statistics Leslie M. Blaha 23 January 2010 WIM and ISCC Intro to R Descriptive Statistics 1 / 11

56 Mean or Average mean() > mean(data[, Length ]) > mean(data) WIM and ISCC Intro to R Descriptive Statistics 2 / 11

57 Mean or Average mean() > mean(data[, Length ]) > mean(data) rowmeans() > rowmeans(data[,1:6]) WIM and ISCC Intro to R Descriptive Statistics 2 / 11

58 Mean or Average mean() > mean(data[, Length ]) > mean(data) rowmeans() > rowmeans(data[,1:6]) colmeans() > colmeans(data[,-7]) WIM and ISCC Intro to R Descriptive Statistics 2 / 11

59 Variability Variance: var() > var(data[, Length ]) > var(data) WIM and ISCC Intro to R Descriptive Statistics 3 / 11

60 Variability Variance: var() > var(data[, Length ]) > var(data) Covariance: cov() > cov(data) WIM and ISCC Intro to R Descriptive Statistics 3 / 11

61 Variability Variance: var() > var(data[, Length ]) > var(data) Covariance: cov() > cov(data) Correlation: cor() > cor(data[,1:6]) WIM and ISCC Intro to R Descriptive Statistics 3 / 11

62 Five-number Summary > summary(data[1:3]) Length LeftHeight RightHeight Min. :213.8 Min. :129.0 Min. : st Qu.: st Qu.: st Qu.:129.7 Median :214.9 Median :130.2 Median :130.0 Mean :214.9 Mean :130.1 Mean : rd Qu.: rd Qu.: rd Qu.:130.2 Max. :216.3 Max. :131.0 Max. :131.1 WIM and ISCC Intro to R Descriptive Statistics 4 / 11

63 Creating Tables The function table() allows for crosstabulation of factors or categorical variables. Using the cardiac data: > table(cardiac[,7:9]),, newmi = 0 chestpain gender ,, newmi = 1 chestpain gender WIM and ISCC Intro to R Descriptive Statistics 5 / 11

64 Descriptive Statistics: Using the psych package The psych package offers a summary function describe for gathering descriptive statistics for your data: > describe(data) var n mean sd median trimmed... Length LeftHeight RightHeight LowerInner.Frame UpperInner.Frame Diagonal Type* WIM and ISCC Intro to R Descriptive Statistics 6 / 11

65 Comparing Two Groups: The Univariate t-test The function t.test() can perform 1-sample and 2-sample (paired or independent) t-tests. 1-sample t-test > t.test(x, alternative= two.sided, mu = 0, conf.level=0.95) WIM and ISCC Intro to R Descriptive Statistics 7 / 11

66 Comparing Two Groups: The Univariate t-test The function t.test() can perform 1-sample and 2-sample (paired or independent) t-tests. 1-sample t-test > t.test(x, alternative= two.sided, mu = 0, conf.level=0.95) 2 independent samples t-test > t.test(x, y, alternative= two.sided, mu = 0, paired=false, var.equal=false, conf.level=0.95) WIM and ISCC Intro to R Descriptive Statistics 7 / 11

67 Comparing Two Groups: The Univariate t-test The function t.test() can perform 1-sample and 2-sample (paired or independent) t-tests. 1-sample t-test > t.test(x, alternative= two.sided, mu = 0, conf.level=0.95) 2 independent samples t-test > t.test(x, y, alternative= two.sided, mu = 0, paired=false, var.equal=false, conf.level=0.95) 2 paired samples t-test > t.test(x, y, alternative= two.sided, mu = 0, paired=true, var.equal=true, conf.level=0.95) WIM and ISCC Intro to R Descriptive Statistics 7 / 11

68 Example: 2 Independent Samples t-test Let x be the Diagonal measurements for the Genuine banks notes and y be the Diagonal measurements for the Counterfeit bank notes. H 0 : µ x = µ y v. H 1 : µ x > µ y > x<-data[type=="genuine","diagonal"] > y<-data[type=="counterfeit","diagonal"] > t.test(x,y,alternative="greater",mu=0, paired=false,var.equal=true) WIM and ISCC Intro to R Descriptive Statistics 8 / 11

69 Example: 2 Independent Samples t-test > t.test(x,y,alternative="greater",mu=0, paired=false,var.equal=true) Two Sample t-test data: x and y t = , df = 198, p-value < 2.2e-16 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: Inf sample estimates: mean of x mean of y WIM and ISCC Intro to R Descriptive Statistics 9 / 11

70 Generating Random Numbers R contains functions for generating random numbers from many well-known distributions. A random number from a standard normal distribution: > rnorm(1, mean = 0, sd = 1) [1] A set of random numbers from a uniform distribution: > runif(3, min=0, max=1) [1] WIM and ISCC Intro to R Descriptive Statistics 10 / 11

71 Exercise 4 Using the cardiac data: 1 Find the descriptive statistics for all variables the cardiac data. Note that the first 6 variables are continuous and the last 6 are categorical. 2 Using the appropriate t-tests, test the following hypotheses H0 : µ age = 72 v. H 1 : µ age < 72 For peak heart rate (pkhr), H0 : µ male = µ female v. H 1 : µ male > µ female For peak heart rate, H 0 : µ no chest pain = µ chest pain v. H 1 : µ no chest pain µ chest pain WIM and ISCC Intro to R Descriptive Statistics 11 / 11

72 Workshop in Methods and Indiana Statistical Consulting Center Introduction to R Supplemental Material: Matrix Algebra Leslie M. Blaha 23 January 2010 WIM and ISCC Intro to R Matrix Algebra 1 / 1

73 Matrices > A <- rbind(c(2,1),c(1,3)) > A [,1] [,2] [1,] 2 1 [2,] 1 3 > B <- rbind(c(1,4,2),c(5,0,3)) > B [,1] [,2] [,3] [1,] [2,] > C <- rbind(c(1,4),c(3,2)) > C [,1] [,2] [1,] 1 4 [2,] 3 2 WIM and ISCC Intro to R Matrix Algebra 2 / 1

74 Add or Subtract Matrices > A+C [,1] [,2] [1,] 3 5 [2,] 4 5 > A-C [,1] [,2] [1,] 1-3 [2,] -2 1 WIM and ISCC Intro to R Matrix Algebra 3 / 1

75 Matrix Multiplication To multiply the corresponding elements in two matrices of the same dimensions: > A*C [,1] [,2] [1,] 2 4 [2,] 3 6 To do matrix multiplication of two matrices > A%*%C [,1] [,2] [1,] 5 10 [2,] > C%*%B [,1] [,2] [,3] [1,] [2,] WIM and ISCC Intro to R Matrix Algebra 4 / 1

76 Matrix Transpose > t(a) [,1] [,2] [1,] 2 1 [2,] 1 3 > t(b) [,1] [,2] [1,] 1 5 [2,] 4 0 [3,] 2 3 WIM and ISCC Intro to R Matrix Algebra 5 / 1

77 Inverse Matrix To find the inverse of a square matrix, if an inverse exists, > solve(a) [,1] [,2] [1,] [2,] > solve(c) [,1] [,2] [1,] [2,] WIM and ISCC Intro to R Matrix Algebra 6 / 1

78 Matrix Diagonals To extract the diagonal elements of a matrix: > diag(a) [1] 2 3 > diag(b) [1] 1 0 We can use diag() to create a diagonal matrix, like an identity matrix > diag(rep(1,3)) [,1] [,2] [,3] [1,] [2,] [3,] WIM and ISCC Intro to R Matrix Algebra 7 / 1

79 Singular Value Decomposition > svd(c) $d [1] $u [,1] [,2] [1,] [2,] $v [,1] [,2] [1,] [2,] WIM and ISCC Intro to R Matrix Algebra 8 / 1

80 Eigenvectors and Eigenvalues > eigen(a) $values [1] $vectors [,1] [,2] [1,] [2,] WIM and ISCC Intro to R Matrix Algebra 9 / 1

81 Workshop in Methods and Indiana Statistical Consulting Center Introduction to R Supplemental Material: Function Writing & Control Programming Leslie M. Blaha 23 January 2010 WIM and ISCC Intro to R Functions & Programming 1 / 1

82 if loop > n <- rnorm(1) > if (n < 0){ n <- abs(n) } WIM and ISCC Intro to R Functions & Programming 2 / 1

83 for loop > foo <- rep(0,10) > for (i in seq(1,10)){ foo[i] <- i+1 } > foo [1] WIM and ISCC Intro to R Functions & Programming 3 / 1

84 while loop > n <- 1 > while (n < 10){ n <- n+1 } WIM and ISCC Intro to R Functions & Programming 4 / 1

85 Define a New Function test.function <- function(input arguments){ commands to execute } WIM and ISCC Intro to R Functions & Programming 5 / 1

86 source() a Function into Working Memory source("pathname/test.function.r") WIM and ISCC Intro to R Functions & Programming 6 / 1