introduction on r

7/31/2019 Introduction on R

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package R is a free software environment forstatistical computing and graphics

R is an integrated suite of softwarefacilities for data manipulation,simulation, calculation and graphical

display. It handles and analyzes data very

effectively and it contains a suite of

operators for calculations on arraysand matrices.


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Note:

1. R is case sensitive2. all alphanumeric symbols are

allowed plus . and _

3. a name must start with . or a letter,and if it starts with . the secondcharacter must not be a digit

example : Names starting with adigit is not accepted. You caninstead use .


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3. Commands are separated either bya semi-colon (;), or by a newline.

4. Comments can be put almost

anywhere, starting with a hashmark(#), everything to the end of the lineis a comment

5. Do not use names of variables in adata-frame as names of objects. If youdo so, the object will shadow the

variable with the same name in

Note:


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For example, suppose the followingrepresents eight tosses of a fair die:

2 5 1 6 5 5 4 1

COMMAND:

> dieroll dieroll

[1] 2 5 1 6 5 5 4 1

A Simple Example: the c()

Function


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When entering commands in R,

you can save yourself a lot of typingwhen you learn to use the arrowkeys effectively. Each command

you submit is stored in the Historyand the up arrow will navigatebackwards along this history and

the down arrow forwards. The leftand right arrow keys movebackwards and forwards along the

command line.


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The Workspace

All variables or objects created in Rare stored in whats called theworkspace. To see what variables are

in the workspace, you can use thefunction ls() to list them (this functiondoesnt need any argument between

the parentheses).


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Currently, we only

have:> ls()

[1] "dieroll

The Workspace


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If we define a new variable a simplefunction of the variable dieroll it willbe added to the workspace:

> newdieroll newdieroll

[1] 1.0 2.5 0.5 3.0 2.5 2.5 2.00.5

> ls()

[1] "dieroll" "newdieroll"

The Workspace


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To remove objects from theworkspace (youll want to do thisoccasionally when your workspace gets

too cluttered), use the rm() function:

> rm(newdieroll) # this was a sillyvariable anyway

> ls()

[1] "dieroll"

The Workspace


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Get in the habit of savingyour work it will

probably help you in thefuture.


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Getting Help

using the function help()

> help(log)


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Call help for matrix.


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> a A A[,1] [,2] [,3] [,4]

[1,] 1 3 5 7[2,] 2 4 6 8


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> b B B

[,1] [,2] [,3] [,4][1,] 2 6 10 14


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> a A A

[,1] [,2]

[1,] 1 6

[2,] 2 7

[3,] 3 8[4,] 4 9

[5,] 5 10


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> B B

[,1] [,2]

[1,] 1 2

[2,] 3 4

[3,] 5 6[4,] 7 8

[5,] 9 10


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> C C[,1] [,2] [,3] [,4] [,5]

[1,] 1 2 3 4 5

[2,] 6 7 8 9 10


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Exercises #1

1. Use the help system to findinformation on the R functions meanand median.

2. Get a list of all the functions in Rthat contains the string test.

3. Create the vector myselfcontaininginfo of your age, height (in inches/cm),and phone number.

4. Create the vector myfamilycontaining the names of your father,mother brothers & sisters.

1 0 0

0 1 0

0 0 1


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DataManagem

ent


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Data Management

>myclassmates myclassmates[1] "Stephen""Christopher"


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SequencesSometimes we will need to

create a string of numericalvalues that have a regularpattern. Instead of typing thesequence out, we can define thepattern using some special

operators and functions.1. Colon operator

2. Sequence function seq()


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Sequences

The colon operator creates avector of numbers (between

two specified numbers) thatare one unit apart:

> 1:9

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


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Sequences

> c(1.5:10,10)

[1] 1.5 2.5 3.5 4.5

5.5 6.5 7.5 8.5 9.510.0


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Sequences

The sequence function cancreate a string of values with

any increment you wish. Youcan either specify theincremental value or the

desired length of thesequence:


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Sequences

> seq(1,5) #same as 1:5

[1] 1 2 3 4 5

> seq(1,5,by=.5) #increment by 0.5

[1] 1.0 1.5 2.0 2.5 3.0 3.5


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Sequences

> seq(1,6,by=.5)

[1] 1.0 1.5 2.0 2.5 3.03.5 4.0 4.5 5.0 5.5 6.0


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Sequences

The replicate functioncan repeat a value or asequence of values aspecified number oftimes


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Sequences

How to repeat the value10 ten times?

> rep(10,10)

[1] 10 10 10 10 10 10 10

10 10 10


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Sequences

How to repeat the stringA,B,C,D twice?

>rep(c("A","B","C","D"),2)

[1] "A" "B" "C" "D" "A""B" "C" "D"


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Sequences

How to make a 4x4 matrixof zeroes?

> matrix(rep(0,16),nrow=4)

[,1] [,2] [,3] [,4][1,] 0 0 0 0

[2,] 0 0 0 0


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Reading in Data: SingleVectors

Data can be read directlyfrom encoded by using

the scan() function. Sinceusing c() can sometimes

be tiresome.


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Suppose that we count thenumber of passengers (not

including the driver) in thenext 10 automobiles at anintersection:

2 4 0 1 1 2 3 1 04


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> passengers


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How to print out thevalues of passengers?

> passengers

[1] 2 4 0 1 1 2 3 10 4


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How to Create DataFrames?

Individual variables aredesignated as columns of

the data frame and haveunique names. However, all

of the columns in a dataframe must be of the samelength.


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Suppose that in the lastexperiment we also

recorded the seatbelt use ofthe driver: Y = seatbelt

worn, N = seatbelt notworn. Data:

Y , N, Y, Y, Y, Y, Y, Y, Y

C


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Note: Since these data are textbased, we need to put quotesaround each data value.

>seatbelt seatbelt

[1] "Y" "N" "Y" "Y" "Y" "Y"

H C D


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How to combine thevariables passengers and

seatbelts into a single dataframe ?

> car.dat


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>car.dat

passengers seatbealt

1 2 Y

2 4 N

3 0 Y4 1 Y

5 1 Y

6 2 Y

7 3 Y

8 1 Y


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NOTE: when using dataframe all of thecolumns in a dataframe must be of thesame length.

ANOTHER WAY OF


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ANOTHER WAY OFENCODING DATA

How to usespreadsheet?

You can access the

editor by using eitherthe edit() or fix()

command ANOTHER WAY OF


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ANOTHER WAY OFENCODING DATA

> new.data new.data


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Encode the educatorsdata. Use the followingvariables only

job sex carsalary


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> educators educators


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I want to edit my data. Whatshould I do?

> new.data educators


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How to save file?

Click the save

icon.

H t l d bj t i th


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How to load object in thenext session?

Click on the File, then LoadWorkspace.

Click on the file you want to open.

Then, type

anyname


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SUMMARIZI

NG DATA


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Numerical SummariesName Operation

mean() arithmetic mean

median() sample median

fivenum() five-number summarysummary() generic summary function fordata and model fits

min(), max() smallest/largest valuesquantile() calculate sample quantiles(percentiles)

var(), sd() sample variance, sample


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When using the data set use

> attach(object)

# add data with objectto search path


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Numerical Summaries

> mean (salary)[1] 62350.79

> table(sex)

sex0 1

8 6


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Numerical Summaries

If there are missing valuesuse:

mean(x,na.rm="true")


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GRAPHS


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Type

>sex.freqsex.freq

sex

0 18 6


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> cbind(sex.freq)

>sex.freq

0 81 6


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>barplot(sex.freq)


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>pie(sex.freq)


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>attach(educators)

>sexfreqbarplot(sexfreq)


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>hist(car,right=FALSE)


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>boxplot(salary,vertical=TR

UE)


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>boxplot(salary,horizontal=T

RUE)


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Statistical

Inference

How to access built in


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How to access built indatasets?

Type

>data()

Output



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Is there a dataset withfilename trees?

Use the dataset trees

Type:

> data(trees)



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> treesGirth Height Volume

1 8.3 70 10.3

2 8.6 65 10.3

3 8.8 63 10.24 10.5 72 16.4

5 10.7 81 18.8


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One sample ttest

Using the trees dataset, testthe hypothesis that the mean

black cherry tree heightis 70ft. versus a two-sidedalternative.

> data(trees)

> t.test(trees$Height,

=


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One sample ttest

One Sample t-test

data: Height

t = 5.2429, df = 30, p-value = 1.173e-05

alternative hypothesis: true mean is notequal to 70

95 percent confidence interval:

73.6628 78.3372

sample estimates:

Two-sample ttest


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Two-sample ttest

The recovery time (in days) is measured

for 10 patients taking a new drug andfor 10 different patients taking aplacebo6. We wish to test the

hypothesis that the mean recovery timefor patients taking the drug is less thanfort those taking a placebo (under anassumption of normality and equalpopulation variances). The data are:

With drug: 15, 10, 13, 7, 9, 8, 21, 9,14, 8


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Two-sample ttest

> drug plac t.test(drug, plac,alternative = "less",var.equal = T)


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Two-sample ttest

Two Sample t-testdata: drug and plac

t = -0.5331, df = 18, p-value = 0.3002

alternative hypothesis: true difference inmeans is less than 0

95 percent confidence interval:

-Inf 2.027436

sample estimates:

mean of x mean of y


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Two-sample ttest


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Paired ttest

An experiment was performed todetermine if a new gasoline additivecan increase the gas mileage of cars.

In the experiment, six cars areselected and driven with and withoutthe additive. The gas mileages (in

miles per gallon, mpg) are givenbelow.

Car 1 2 3 4 5

6

i d


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Paired ttest

> add noadd t.test(add, noadd,paired=T, alt ="greater")

Paired t test


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Paired t-test

data: add and noaddt = 3.9994, df = 5, p-value =0.005165

alternative hypothesis: truedifference in means is greater than0

95 percent confidence interval:0.3721225 Infsample estimates:

mean of the differences

ANOVA


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ANOVA

> aov(x ~ a) # one-wayANOVA model

> aov(x ~ a + b) # two-wayANOVA with no interaction

>aov(x ~ a + b + a:b) # two-

way ANOVA withinteraction

> aov(x ~ a*b) # exactly the

ANOVA


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ANOVA

The strength of three different rubbercompounds; four specimens of eachtype were tested for their tensile

strength (measured in pounds persquare inch):

ANOVA


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ANOVA> str type type type

[1] A A A A B B B B C C C C

ANOVA


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ANOVA

To calculate the sample meansof the subgroups, type

> tapply(str,type,mean) A B C

3213.75 3330.00 3552.50

ANOVA


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ANOVA

To calculate the variances:

> tapply(str,type,var)

A B C

6172.917 6733.333

2541.667

ANOVA


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ANOVA

>anova.fit


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ANOVA

To extract the ANOVAtable, use the Rfunction summary():

>summary(anova.fit)

ANOVA


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ANOVA

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

type 2 237029 118515 23.020.000289 ***

Residuals 9 46344 5149

---

Signif. codes: 0 *** 0.001 ** 0.01 *0.05 . 0.1 1

M lti l i t t


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Multiple comparison test

>TukeyHSD(anova.

fit)

Tukey multiple comparisons of


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y p pmeans

95% family-wise confidence level

Fit: aov(formula = str ~ type)

$type

diff lwr upr p adj

B-A 116.25 -25.41926 257.9193

0 1085202

LINEAR REGRESSION


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LINEAR REGRESSION

> lm(y ~ x) # simple linearregression (SLR) model

> lm(y ~ x1 + x2) # a regression

plane

> lm(y ~ x1 + x2 + x3) # linearmodel with three regressors

> lm(y ~ x 1) # SLR w/ anintercept of zero

> lm(y ~ x + I(x^2)) # quadratic

LINEAR REGRESSION


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LINEAR REGRESSION

Consider the cars dataset.The data give the speed

(speed) of cars and thedistances (dist) taken tocome to a complete stop. Fita linear regression modelusing speed as the

independent variable and


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names(car

s)

LINEAR REGRESSION


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LINEAR REGRESSION

>fit fit


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Call:

lm(formula = dist ~ speed)

Coefficients:

(Intercept) speed

-17.579 3.932

LINEAR REGRESSION


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LINEAR REGRESSION

>

summary(fit

)

Call:


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lm(formula = dist ~ speed)

Residuals:

Min 1Q Median 3Q Max

-29.069 -9.525 -2.272 9.215 43.201

Coefficients:

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

(Intercept) -17.5791 6.7584 -2.601 0.0123 *

speed 3.9324 0.4155 9.464 1.49e-12 ***

---

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1


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> anova(fit)

ow o re r eveEMPLOYEEALL data from txt


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EMPLOYEEALL data from txt

file?>emp


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How to rename a variable?

> names(emp)

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