Introduction to R A free Statistical/Mathematical Softwarewill be ignored in R. Wanhua Su (MacEwan) Introduction toR FDDay, August26, 2015 9/29 VectorAssignment Use c() to create a

Introduction to RA free Statistical/Mathematical Software

Wanhua Su

Department of Mathematics and Statistics

MacEwan University

Wanhua Su (MacEwan) Introduction to R FD Day, August 26, 2015 1 / 29

Outline

1 Package R Commander in RDownload R and R CommanderAbout the R Commander PackageExamples

2 Command-Driven RUsing R or R Studio as a CalculatorFunction and AssignmentVector and MatrixProbability functionsPlot in RWrite Your Own R FunctionExamples


An Introduction to R

This workshop consists of two parts:

R and R commander (a point-and-click interface similar to Minitaband SPSS) and examples.

R is a command-driven software. More details on coding.


An Introduction to R

This workshop consists of two parts:

R and R commander (a point-and-click interface similar to Minitaband SPSS) and examples.

R is a command-driven software. More details on coding.


About R and R Commander

R is a free software for statistical computing and graphics. Created byRoss Ihaka and Robert Gentleman.

R is a modern implementation of S language developed by JohnChambers.

R is a command-driven software including packages contributed byscientists (statisticians) all over the world.

R commander is an R package providing a point-and-click interfacesimilar to Minitab or SPSS.


About R and R Commander

R is a free software for statistical computing and graphics. Created byRoss Ihaka and Robert Gentleman.

R is a modern implementation of S language developed by JohnChambers.

R is a command-driven software including packages contributed byscientists (statisticians) all over the world.

R commander is an R package providing a point-and-click interfacesimilar to Minitab or SPSS.


Obtain the Software

Download R or R Studio: “http://www.r-project.org/ ”.

Install R. Windows, Unix and Macs.

Start R: In Windows and Macs, click “R”; under Unix, type “R”.

For help: use ? or help(). For example, check how to use lm, the Rfunction for linear model. Type ?lm or help(lm).

To quit an R session: In Windows and Macs, close the window; underUnix, type “q()”


Obtain the Software

Download R or R Studio: “http://www.r-project.org/ ”.

Install R. Windows, Unix and Macs.

Start R: In Windows and Macs, click “R”; under Unix, type “R”.

For help: use ? or help(). For example, check how to use lm, the Rfunction for linear model. Type ?lm or help(lm).

To quit an R session: In Windows and Macs, close the window; underUnix, type “q()”


The R Commander Package

The R package Rcmdr provides a point-and-click interface to R whichis a command-driven software.

Install the package: Packages→Install package(s)→choose amirror→double click the package Rcmdr.

Load the package: Type library(Rcmdr) in the console window.

Read data into R: Data from the toolbar, very similar to Minitab.

The R commands are shown in the R Script window.

The toolbar includes Graphs for plots such as histogram, scatterplot,and etc; Statistics for numerical summaries and inferences on means,proportions, and variances; Models for model selections and building;Distributions for probability distributions.


The R Commander Package

The R package Rcmdr provides a point-and-click interface to R whichis a command-driven software.

Install the package: Packages→Install package(s)→choose amirror→double click the package Rcmdr.

Load the package: Type library(Rcmdr) in the console window.

Read data into R: Data from the toolbar, very similar to Minitab.

The R commands are shown in the R Script window.

The toolbar includes Graphs for plots such as histogram, scatterplot,and etc; Statistics for numerical summaries and inferences on means,proportions, and variances; Models for model selections and building;Distributions for probability distributions.


Examples

Example 1: prices of 15 used cars. Two variables: age (year) andprice ($). Import the data set car.txt. Can we use a simple linearregression to model their relationship?

Example 2: An experiment was conducted to measure and comparethe effectiveness of various feed supplements on the growth rate ofchickens. Date set chickwts in R package datasets. Two variables:weight and feed type on 71 chickens.

◮ Side-by-side box plots of weights by feed type.◮ What method would you like to use? Is there any difference between

feed types?◮ Any other analysis to follow up?


Examples

Example 1: prices of 15 used cars. Two variables: age (year) andprice ($). Import the data set car.txt. Can we use a simple linearregression to model their relationship?

Example 2: An experiment was conducted to measure and comparethe effectiveness of various feed supplements on the growth rate ofchickens. Date set chickwts in R package datasets. Two variables:weight and feed type on 71 chickens.

◮ Side-by-side box plots of weights by feed type.◮ What method would you like to use? Is there any difference between

feed types?◮ Any other analysis to follow up?


Using R or R Studio as a Calculator

Arithmetic

> 2+1

[1] 3

> 2^2

[1] 4

> (3-1)*3

[1] 6

> 1-2*3

[1] -5

> 2/3

[1] 0.6666667

Trick 1: Try to save your R code in a .R file. You can copy the linesyou would like to run and paste in the R Console window.

◮ In Windows, go to Menu “File” and choose “New Script ” to create anew .R file or choose “Open Script...” to open the existing one.

◮ In Mac, go to Menu “File” and choose ”New Document” to create anew .R file or choose “Open Document...” to open the existing one.


Function and Assignment

R functions> sqrt(2) #sqrt root of 2

[1] 1.414214

> exp(1) #exponential function

[1] 2.718282

> sin(2) #sin function

[1] 0.9092974

> log(10) #natural logarithms of 10

[1] 2.302585

Assignment: use = or <-> x=2

> x+3

[1] 5

> x<-exp(1)

> x

[1] 2.718282

Trick 2: use # to add some explanation to the R code. Everything after #will be ignored in R.


Vector Assignment

Use c() to create a vector.

> Age=c(1,1,3,4,4)

> Price=c(13990,13495,12999,9500,10495)

Use “,” to separate data.

Combine vectors:◮ to firm a new vector

> c(Age,Price)

[1] 1 1 3 4 4 13990 13495 12999 9500 10495

◮ to firm a matrix

> cbind(Age,Price) > rbind(Age,Price)

Age Price [,1] [,2] [,3] [,4] [,5]

[1,] 1 13990 Age 1 1 3 4 4

[2,] 1 13495 Price 13990 13495 12999 9500 10495

[3,] 3 12999

[4,] 4 9500

[5,] 4 10495


Creating Structured Data

Use :

> 1:10 #1 to 10, increase by 1

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

> 10:1 #10 to 1, decrease by 1

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

Use seq()

> seq(1,9,by=2) #sequence from 1 to 9

[1] 1 3 5 7 9

> seq(1,10,by=2) #commom difference=2

[1] 1 3 5 7 9

> seq(1,9,length=5) #of length 5

[1] 1 3 5 7 9

> seq(1,10,length=5)

[1] 1.00 3.25 5.50 7.75 10.00


Vector Operation in R is Element-wise

> x=c(1,2,3)

> x

[1] 1 2 3

> y=c(5,2,3)

> y

[1] 5 2 3

> x+y # we get 1+5, 2+2, 3+3

[1] 6 4 6

> x/y # we get 1/5, 2/2, 3/3

[1] 0.2 1.0 1.0

> x*y # we get 1*5, 2*2, 3*3

[1] 5 4 9

> x^2 # we get 1^2, 2^2, 3^2

[1] 1 4 9


Functions on Vectors

> vec=c(2,1,3)

> length(vec) #length of a vector

[1] 3

> sum(vec) #sum of the observations in a vector

[1] 6

> mean(vec) #mean of the observations in a vector

[1] 2

> var(vec) #sample variance of 3 observations

[1] 1

> sort(vec) #sort 3 obervations increasingly

[1] 1 2 3

> min(vec) #minimum value of 3 observations

[1] 1

> max(vec) #maximum value of 3 observations

[1] 3

> summary(vec) #summary of the observations

Min. 1st Qu. Median Mean 3rd Qu. Max.

1.0 1.5 2.0 2.0 2.5 3.0


Accessing Data Using Indices

> vec=1:5

> vec[1] #1st element of vec

[1] 1

> vec[1:4] #the first four elements

[1] 1 2 3 4

> vec[c(1,3,5)] #the 1st, 3rd and 5th elements

[1] 1 3 5

> vec[-(1:2)] #all except the first 2 elements

[1] 3 4 5

> vec[vec>3] #all elements of vec greater than 3

[1] 4 5


Create Matrix Using matrix()

Use matrix(a, m, n) to generate a m × n with elements aUse diag(n) to generate a n× n identity matrix.> matrix(1,2,3) #a 2 by 3 matrix with all elements 1

[,1] [,2] [,3]

[1,] 1 1 1

[2,] 1 1 1

> vec=c(1:6)

> matrix(vec,2,3) #create a 2 by 3 matrix by columns

[,1] [,2] [,3]

[1,] 1 3 5

[2,] 2 4 6

> matrix(vec,2,3,byrow=T) #by rows

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 4 5 6

> diag(3) #3 by 3 identity matrix

[,1] [,2] [,3]

[1,] 1 0 0

[2,] 0 1 0

[3,] 0 0 1


Take Elements From a Matrix

> out=cbind(c(1,2,3),c(4,5,6),c(7,8,9))

> out

[,1] [,2] [,3]

[1,] 1 4 7

[2,] 2 5 8

[3,] 3 6 9

> out[1:2,] #Take the 1st row and 2nd row

[,1] [,2] [,3]

[1,] 1 4 7

[2,] 2 5 8

> out[,c(1,3)] #Take the 1st column and 3rd column

[,1] [,2]

[1,] 1 7

[2,] 2 8

[3,] 3 9

>out[1,3] #Take (1,3) element of the matrix out

[1] 7Wanhua Su (MacEwan) Introduction to R FD Day, August 26, 2015 16 / 29

Matrix Operation (1)

> x =cbind(c(1,2),c(3,4)) #combine by column

> x

[,1] [,2]

[1,] 1 3

[2,] 2 4

> y =rbind(c(6,8),c(7,9)) #combine by row

> y

[,1] [,2]

[1,] 6 8

[2,] 7 9

> x+y # return the sum of x and y

[,1] [,2]

[1,] 7 11

[2,] 9 13



> x%*%y # return the matrix product of x and y

[,1] [,2]

[1,] 27 35

[2,] 40 52

>

> x*y # not matrix product of x and y

[,1] [,2]

[1,] 6 24

[2,] 14 36

>

> t(x) # transpose of x

[,1] [,2]

[1,] 1 2

[2,] 3 4



> det(x) #determinant of x

[1] -2

> solve(x) #inverse of x

[,1] [,2]

[1,] -2 1.5

[2,] 1 -0.5

> x%*%solve(x) #check

[,1] [,2]

[1,] 1 0

[2,] 0 1


Obtain Data From a File: Use read.table()Suppose the data have been saved in the file car.txt.

> data=read.table("/Users/wanhuasu/documents/MacEwan/talk/R/car.txt",

header=T)

> data

Age Price

1 1 13990

2 1 13495

3 3 12999

4 4 9500

5 4 10495

6 5 8995

7 5 9495

8 6 6999

9 7 6950

10 7 7850

11 8 6999

12 8 5995

13 10 4950

14 10 4495

15 13 2850


Probability Functions

R has four types of functions for getting information about a family ofdistributions.

◮ “d” function: return the pdf of the distribution;◮ “p” function: return the cdf of the distribution;◮ “q” function: return the quantiles;◮ “r” function: return random observations.

The R names◮ binomial distribution: binom◮ poission distribution: pois◮ normal distribution: norm◮ t-distribution: t◮ F-distribution: F◮ χ2-distribution: chisq

Combine the four functions to each name, then get the four functionsfor each distribution.


Plot a Graph in R

x=seq(-2*pi,2*pi,length=100)

y=sin(x)

z=cos(x)

plot(x,y,type="p") #scatter plot, type=points

plot(x,y,type="l") #scatter plot, type=line

plot(x,y,type="b") #scatter plot, type=line and points

plot(x,y,pch=19,xlab="x",ylab="f(x)")

#plot the points using solid circles

lines(x,y,lty=1,col="red") #add a red solid line

points(x,z,pch=2) #add points using triangles

lines(x,z,lty=2,col="blue") #add a blue dashed line

title("Sin & Cos") #add a title

par(mfrow=c(2,3)) #plot 6 graphs, 2 rows and 3 columns


Two Ways to Save a Graph

Click on the graph, go to the menu ”File”, choose ”Save as”, thenchoose the file type and the place you would like to save.

Use postscript() or pdf() to start the graphics device, plot the graph,and then close the device by dev.off().

> postscript(file="/Users/wanhuasu/documents/MacEwan

/talk/R/plot.ps",height=8,width=8,horizontal=F)

#start the graphic device

> par(mfrow=c(2,1)) #two figures in one plot

> plot(x,y,pch=1,xlab="x",ylab="sin(x)")

> lines(x,y,lty=1,col="red")

> title("Sin(x)") #title of the first figure

> plot(x,z,pch=1,xlab="z",ylab="cos(z)")

> lines(x,z,lty=1,col="blue")

> title("Cos(z)") #title of the second figure

> dev.off() #close the graphic device


Write Your Own R Functions

Write a function to standardize a vector to have mean 0 and variance 1.

> std=function(x){

+ m=mean(x)

+ s=sqrt(var(x))

+ result=(x-m)/s

+ return(result)

+ }

> x=1:5

> y=std(x)

> y

[1] -1.2649111 -0.6324555 0.0000000 0.6324555 1.2649111

> mean(y)

[1] 0

> var(y)

[1] 1


Summarize the Data (Stat 151)

Annual income from 40 U.S. households. Two factors: race (whiteand black) and region (Northeast, Northwest, South, West)

Use hist(), stem(), qqnorm(), boxplot() to plot the data

Use table(), apply(), tapply() to summarize the data

data=read.table("/Users/wanhuasu/documents/MacEwan/stat252/data/income.txt",

sep="",header=T)

attach(data)

hist(income) #histogram of the variable income

stem(income) #stem-and-leaf diagram

boxplot(income~race,data=data) #side-by-side boxplot, by race

> tapply(income,race,mean) #sample means for levels of race

Black White

27.820 41.195

> tapply(income,region,mean) #sample means for region

MWest NEast South West

32.95 37.06 31.38 36.64

> table(race,region) #contingence table by race and region

region

race MWest NEast South West

Black 5 5 5 5

White 5 5 5 5


Linear Regression: Price of Used Cars> data=read.table("/Users/wanhuasu/documents/MacEwan/talk/R

/car.txt",header=T)

> age=data[,1]

> price=data[,2]

> model=lm(price~age,data=data) #fit a linear model

> names(model) #model is an object

[1] "coefficients" "residuals" "effects"

[4] "rank" "fitted.values" "assign"

[7] "qr" "df.residual" "xlevels"

[10] "call" "terms" "model"

> summary(model) #summary of the model

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 14285.95 448.67 31.84 1.01e-13 ***

age -959.05 64.58 -14.85 1.56e-09 ***

The fitted regression is P̂rice = 14285.95 − 959.05 × AgeWanhua Su (MacEwan) Introduction to R FD Day, August 26, 2015 26 / 29

Least Squares Line: Price of Used Cars

plot(age,price,xlab="Age (year)",ylab="Price ($)",cex.lab=1.3)

abline(coef=model$coef,col="red",lwd=2)

title("Scatterplot of Used Car",cex.main=1.5)

2 4 6 8 10 12

4000

6000

8000

1000

012

000

1400

0

Age (year)

Pric

e ($

)

Scatterplot of Used Car


Example: Two-Way ANOVA (Stat 252)Annual income from 40 U.S. households. Two factors: race (white andblack) and region (Northeast, Northwest, South, West)

> data=read.table("/Users/wanhuasu/documents/MacEwan/stat252

/data/income.txt",sep="",header=T)

> model=lm(income~race+region+race*region,data=data)

> anova(model)

Analysis of Variance Table

Response: income

Df Sum Sq Mean Sq F value Pr(>F)

race 1 1788.9 1788.9 10.8733 0.002395 **

region 3 232.7 77.6 0.4715 0.704296

race:region 3 38.8 12.9 0.0787 0.971107

Residuals 32 5264.7 164.5

Conclusions: no interaction effect, no main effect due to region, maineffect due to race is significant.


Acknowledgments

Thanks for your time and attention.

The slides of this talk is available on my webpage:http://academic.macewan.ca/suw3/

More detailed tutorial on R can be found on R webpage:http://www.r-project.org/

Comparison of R and Matlab:http://mathesaurus.sourceforge.net/octave-r.html


Documents

Introduction to R A free Statistical/Mathematical Softwarewill be ignored in R. Wanhua Su (MacEwan) Introduction toR FDDay, August26, 2015 9/29 VectorAssignment Use c() to create a