Data Management and Statistical Analysis - Basic R Graphics

8/8/2019 Data Management and Statistical Analysis - Basic R Graphics

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BASIC R GRAPHICSBASIC R GRAPHICS

Leilani A. NoraLeilani A. NoraLeilani A. NoraLeilani A. NoraLeilani A. NoraLeilani A. NoraLeilani A. NoraLeilani A. NoraAssistant ScientistAssistant Scientist

Introduction to R:Introduction to R:

Data Manipulation and StatisticalData Manipulation and Statistical

AnalysisAnalysis

OVERVIEWOVERVIEW

One of the best things about R is the abilityOne of the best things about R is the abilityto create publicationto create publication--quality graphsquality graphs

To get an idea you can browse throughTo get an idea you can browse through

Understanding the graphics will facilitateUnderstanding the graphics will facilitateunderstanding R programming in generalunderstanding R programming in general

How a plotting function deals with data oftenHow a plotting function deals with data oftendepends on the data type (e.g. matrix,depends on the data type (e.g. matrix,factor, vector) given to it.factor, vector) given to it.

> demo(graphics)> demo(graphics)

> demo(persp)> demo(persp)

OVERVIEWOVERVIEW

Types of basic graphics that will beTypes of basic graphics that will bediscussed are:discussed are:

-- HistogramHistogram

-- BoxplotBoxplot-- ScatterplotScatterplot

-- Line GraphLine Graph

-- Bar charts / Bar GraphBar charts / Bar Graph

-- Error BarsError Bars

PLOTTING COMMANDSPLOTTING COMMANDS

HighHigh--level plotting functions:level plotting functions:

create a new plot on the graphics devicecreate a new plot on the graphics device

LowLow--level plotting functions:level plotting functions:add more information on existing plotadd more information on existing plot(extra points, lines, and labels)(extra points, lines, and labels)

Interactive graphics functions:Interactive graphics functions:

allow you interactively add information toallow you interactively add information toan existing plot using a pointing devicean existing plot using a pointing device

such as mouse.such as mouse.


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HIGHHIGH--LEVEL PLOTTING FUNCTIONSLEVEL PLOTTING FUNCTIONS

Produces new graph on the graphics deviceProduces new graph on the graphics device

Selected high level plotting functionsSelected high level plotting functions

LOWLOW--LEVEL PLOTTING FUNCTIONSLEVEL PLOTTING FUNCTIONS

Add additional information to an existingAdd additional information to an existinggraphgraph

Selected lowSelected low--level plotting functionslevel plotting functions

GRAPHICAL PARAMETERS: par()GRAPHICAL PARAMETERS: par()

The graphs can be modified with the function par()The graphs can be modified with the function par()

There are 73 graphical parameters, some of themThere are 73 graphical parameters, some of themhave very similar functions.have very similar functions.

The exhaustive list of these parameters can be readThe exhaustive list of these parameters can be readwith ?parwith ?par

Some par elements can be modified from within highSome par elements can be modified from within highand low level plotting functionsand low level plotting functions

> par(bg=> par(bg=yellowyellow))

## bgbg all subsequent plots will have a yellowall subsequent plots will have a yellowbackgroundbackground

GRAPHICAL WINDOWGRAPHICAL WINDOW

When a graphical function is executed, RWhen a graphical function is executed, Ropens the graphical window and displays theopens the graphical window and displays thegraphgraph

To generate a graphic in a new window, useTo generate a graphic in a new window, usethe command:the command:

-- x11() in Linuxx11() in Linux

-- windows() in Windowswindows() in Windows


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SUMMARY OF GRAPHICS ANDSUMMARY OF GRAPHICS AND

DATA FILEDATA FILE

ggdatadata1.csv1.csvError BarsError Bars

gdata3.csv and ggdata3.csv and gdatadata2.csv2.csv(matrix)(matrix)

Bar GraphBar Graph

gdata2.csvgdata2.csvLinegraphLinegraph

gdata2.csvgdata2.csvScatterplotScatterplot

ggdatadata1.csv1.csvBoxplotBoxplot

ggdatadata1.csv1.csvHistogramHistogram

DATA FILEDATA FILEGRAPHICSGRAPHICS

HISTOGRAMHISTOGRAM

DATAFRAME :DATAFRAME :gdata1gdata1.csv.csv

Consider theConsider the

data from Splitdata from Split

plot design withplot design with

Nitrogen as MPNitrogen as MPand Variety asand Variety as

SP, replicated 4SP, replicated 4times.times.

DATA FRAME:DATA FRAME: gdata1gdata1

Read data fileRead data file gdata1gdata1.csv.csv

>>gdata1gdata1

gdata1gdata1

Nitrogen Variety Rep Yield

1 0 C4-63 1 3464

2 60 C4-63 1 4768

3 90 C4-63 1 6224

4 120 C4-63 1 5792

. . .

47 90 Peta 3 414648 120 Peta 3 3638


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HISTOGRAM :HISTOGRAM : hist()hist()

Histogram is an important tool forHistogram is an important tool for

exploratory data analysis that provides aexploratory data analysis that provides a

graphical summary of the shape or datagraphical summary of the shape or datassdistribution.distribution.

The generic function hist() computes aThe generic function hist() computes a

histogram of the given data values.histogram of the given data values.

Details ofDetails ofhist()hist() function.function.> hist(x,> hist(x, ))

## xx a vector of valuesa vector of values

DATAFRAME gdata : hist()DATAFRAME gdata : hist()

Ex1. To obtain histogram for YEx1. To obtain histogram for Y

> hist(gdata> hist(gdata11$Yield)$Yield)

Displays theDisplays thehistogram of Yieldhistogram of Yield

at Graphicsat Graphicswindowwindow

Ex2. Modifying HistogramEx2. Modifying Histogram

> hist(gdata1$Yield, main='Histogram> hist(gdata1$Yield, main='Histogram

of Yield', col=of Yield', col=yellow2',yellow2',

border=border= blue', xlab= blue', xlab=Y ClassY Class,,

ylab="Frequency",ylab="Frequency",xlim=c(0,10000),ylim=c(0, 11))xlim=c(0,10000),ylim=c(0, 11))

# main# main -- main title of the histogrammain title of the histogram

# col# col -- color of filled barscolor of filled bars

# border# border -- foreground colour of barsforeground colour of bars

# ylab# ylab y axis labely axis label# xlim / ylim# xlim / ylim x and y axis limitx and y axis limit

GRAPHICAL parGRAPHICAL par EXAMPLE : hist()EXAMPLE : hist()


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BOXPLOTBOXPLOT

boxplot()boxplot()

Produce a boxProduce a box--andand--whisker plot(s) of the givenwhisker plot(s) of the given(grouped) values.(grouped) values.

Details ofDetails ofboxplot()boxplot() function.function.

> boxplot(formula, data=NULL,> boxplot(formula, data=NULL, ,,

na.action=NULL)na.action=NULL)

formulaformula a formula, such as y~grpa formula, such as y~grp

wherewhere :: yy -- is a numeric vector of datais a numeric vector of datavalues to be split into groupsvalues to be split into groups

according to the grouping variable,according to the grouping variable,

grp (factor)grp (factor)

Ex1. To obtain boxplot of YEx1. To obtain boxplot of Y

> boxplot(gdata> boxplot(gdata11$Yield)$Yield)

DATAFRAME gdataDATAFRAME gdata11 : boxplot(): boxplot() Ex2. To obtain boxplot of Y by SiteEx2. To obtain boxplot of Y by Site

> boxplot(gdata1$Yield~> boxplot(gdata1$Yield~

gdata$Variety)gdata$Variety)


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SCATTERPLOTSCATTERPLOT

plot()plot()

plot(x,y) or plot(y~x)plot(x,y) or plot(y~x)

-- x and y are the variables to be used forx and y are the variables to be used for

the x and y axes, respectivelythe x and y axes, respectively

-- x and y are both numeric variablesx and y are both numeric variables

DATAFRAME :DATAFRAME :gdata2gdata2.csv.csv

Nitrogen x Variety Summary of MeansNitrogen x Variety Summary of Means



>>gdata2gdata2gdata2gdata2

Nitrogen C463 IR5 IR8 Peta

1 0 3183 4306 4253 4481

2 60 5443 5982 5672 4816

3 90 5987 6259 6400 4812

4 120 6014 6895 6733 3816

5 150 6687 6951 7563 2047

6 180 6065 6540 8701 1881


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> attach(gdata2)> attach(gdata2)> plot(> plot(NitrogenNitrogen,, C463C463,,main=main=PlotPlot

of Yield at Different Nitrogenof Yield at Different Nitrogen

RateRate,, xlab=xlab=Nitrogen RateNitrogen Rate",",

ylab=ylab=Grain Yield,Grain Yield, col="Red")col="Red")

# x# x NitrogenNitrogen## yy C463C463

Ex1Ex1. Scatter plot of GY and. Scatter plot of GY and Nitrogen RateNitrogen Rate

SCATTERPLOT: plot()SCATTERPLOT: plot()SCATTER PLOTSCATTER PLOT

PLOTTING CHARACTERPLOTTING CHARACTERSS::

plot(plot(pchpch==))

# - same content as Ex1

# pch# pch plotting character that controlsplotting character that controls

the type of symbol.the type of symbol.

Can either be an integer from 1Can either be an integer from 1--2525and character (and character (**,, ??,, ..,, ))

> plot(> plot(, pch=19), pch=19)

Ex2. With graphical parameter pchEx2. With graphical parameter pch

PLOTTING CHARACTERSPLOTTING CHARACTERS

ColoColouurs cars cann be obtained with optionsbe obtained with optionscol=col=blueblue, bg=, bg=yellowyellow (only for the(only for thesymbols 21symbols 21--25)25)


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STYLE OF AXES LABELS:STYLE OF AXES LABELS:

plot(plot(laslas==))

# - same content as Ex1

# las - style of axis labels

0: always parallel to the axis [default],

1: always horizontal2: always perpendicular to the axis,

3: always vertical.

> plot(> plot(,,pch=19,pch=19, las=3las=3))

Ex3. With graphical parameter lasEx3. With graphical parameter las

CUSTOMIZING A PLOTCUSTOMIZING A PLOT


> par(cex=> par(cex=0.90.9, bg=, bg=lightyellowlightyellow,,

col.axis=col.axis=blueblue,,

mar=c(4,4,2.5,0.5))mar=c(4,4,2.5,0.5))

> plot(> plot())

# par# par modify graphical parameters such as bg,modify graphical parameters such as bg,

col.axis and marcol.axis and mar

# cex# cex controls the size of the textcontrols the size of the text

# bg# bg background colorbackground color

# col.axis# col.axiscolor of the numbers on the axescolor of the numbers on the axes

# mar# mar-- use to set the margin size specified inuse to set the margin size specified in

inches of the form c(bot, left, top, right).inches of the form c(bot, left, top, right).-- The default is mar=c(5, 4, 4, 2)The default is mar=c(5, 4, 4, 2)



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LINE CHARTLINE CHART

LINE CHART : plot(type=)LINE CHART : plot(type=)

# type =# type = pp # point# point

== ll # line# line

== oo # overplotted point and line# overplotted point and line== bb # points joined by line# points joined by line

== ss # stair steps# stair steps

== hh # histogram like vertical line# histogram like vertical line

== nn # does not produce points or line# does not produce points or line

> plot(Nitrogen, C463, main=> plot(Nitrogen, C463, main=Plot ofPlot of

Yield at Different Nitrogen RateYield at Different Nitrogen Rate,,

xlab=xlab=Nitrogen Rate", ylab=Nitrogen Rate", ylab=GrainGrain

Yield, col="RedYield, col="Red,,pch=19, las=3,pch=19, las=3,

xlim=c(0,180), ylim=c(1000,8000),xlim=c(0,180), ylim=c(1000,8000),

type=type=oo, lty=1, lty=1))

ExEx11.. Connecting points using plot()Connecting points using plot()

LINE CHART : plot(lty=)LINE CHART : plot(lty=)

ExEx11.. Connecting points using plot()Connecting points using plot()

# lty - style of axis labels option to change

line type. The default value is 1.

LINE CHART : plot()LINE CHART : plot()


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lineslines()()

Use to create line charts that addsUse to create line charts that adds

information to a graphinformation to a graph

> lines(x,y, type=> lines(x,y, type= ))

> lines(y~x, type=> lines(y~x, type= ))

## x and yx and y numeric vectors of points to connectnumeric vectors of points to connect

ADDING LINE CHARTADDING LINE CHART

ExEx22.. Adding line charts to plot()Adding line charts to plot()

> lines(IR5~Nitrogen, pch=19,> lines(IR5~Nitrogen, pch=19,

col="blue", type="o", lty=1)col="blue", type="o", lty=1)

> lines(IR8~Nitrogen, pch=19,> lines(IR8~Nitrogen, pch=19,

col=col=green", type="o", lty=1)green", type="o", lty=1)

> lines(Peta~Nitrogen, pch=19,> lines(Peta~Nitrogen, pch=19,

col=col=brownbrown", type="o", lty=1)", type="o", lty=1)

ADDING LINE CHARTADDING LINE CHART ADDING A LEGEND : legend()ADDING A LEGEND : legend()

Adds legends to plots.Adds legends to plots.

> legends(x, legend, pch, col,> legends(x, legend, pch, col,

lty,lty, ))

## xx use to position the legend that can be ause to position the legend that can be a

single keyword from the list,single keyword from the list, bottomrightbottomright,,

bottombottom,, bottomleftbottomleft,, leftleft,, toplefttopleft,, toptop,,

toprighttopright,, rightright andand centercenter

## legendlegend a charactera character


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ExEx33.. Adding a legendAdding a legend

>>legendlegend("topleft", legend=c("C4("topleft", legend=c("C4--

63", "IR5", "IR8", "Peta"),63", "IR5", "IR8", "Peta"),pch=1:4, bty="n")pch=1:4, bty="n")

> detach(gdata2)> detach(gdata2)

ADDING A LEGEND : legend()ADDING A LEGEND : legend()

## pchpch plotting symbols appearing in the legendplotting symbols appearing in the legend

## colcol color of points or lines appearing in thecolor of points or lines appearing in the

legendlegend

## ltylty line types and widthsline types and widths appearing in theappearing in the

legendlegend

ADDING A LEGENDADDING A LEGEND

ExEx44.. Suppressing plot of axesSuppressing plot of axes

SUPPRESSING PLOT OF AXESSUPPRESSING PLOT OF AXES

# xaxt and yaxt# xaxt and yaxt a character which specifies thea character which specifies the

xx--axis and yaxis and y--axis type. Specifyingaxis type. Specifying nn

suppresses plotting of the axis.suppresses plotting of the axis.

> plot(Nitrogen, C463, main=> plot(Nitrogen, C463, main=Plot ofPlot of

Yield at Different Nitrogen RateYield at Different Nitrogen Rate,,

xlab=xlab=Nitrogen Rate", ylab=Nitrogen Rate", ylab=GrainGrainYield, col="RedYield, col="Red,,pch=19, las=3,pch=19, las=3,

type=type=oo, lty=1,, lty=1, xaxt=xaxt=nn, yaxt=, yaxt=nn))

ADD AN AXIS : axis()ADD AN AXIS : axis()

Adds an axes to the current plotAdds an axes to the current plot

>>axisaxis((sideside,, at,at, ))

## sideside an integer specifying which side of thean integer specifying which side of the

axis is to be drawn on.axis is to be drawn on.

side = 1 : belowside = 1 : below side = 3 : aboveside = 3 : above

side = 2 : leftside = 2 : left side = 4 : rightside = 4 : right

# at# at points at which tickpoints at which tick--marks are to be drawnmarks are to be drawn


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ADD AN AXIS : axis()ADD AN AXIS : axis()

Ex5. Adds an axes to the current plotEx5. Adds an axes to the current plot

> plot(> plot()) # same as Ex4# same as Ex4

> axis> axis((side=1side=1,, at=seq(0,180,30))at=seq(0,180,30))

>>axisaxis((side=2side=2,, at=seq(3000,7000,500))at=seq(3000,7000,500)) BAR GRAPH / BAR PLOTBAR GRAPH / BAR PLOT

barplot()barplot()

barplot(height, # vector or matrix of values describing# the bars which make up the plot.

beside = FALSE, # stacked by default. If# TRUE bars will be side

# by side

density = NULL, # a vector giving the density of# shading lines, in lines per inch,

# for the bars or bar components.

# The default value of NULL

# means that no shading lines are

# drawn.

xlab = NULL, # label for x-axis

ylab = NULL, # label for y-axis

ylim = NULL) # limit for y-axis

DATAFRAME :DATAFRAME : gdata3gdata3.csv.csv

Summary of Variety MeansSummary of Variety Means


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>>gdata3gdata3gdata3gdata3

Variety Yield

1 V1 4.7559

2 V2 5.0410

3 V3 5.0581

SIMPLE BAR PLOT : gdata3SIMPLE BAR PLOT : gdata3

>>barplot(gdata3$Yield)barplot(gdata3$Yield)

WITH LABELS AND COLORSWITH LABELS AND COLORS

> barplot(> barplot(gdata3$gdata3$Yield, xlab="Variety",Yield, xlab="Variety",

ylab="Grain Yield",ylab="Grain Yield",

nnames.arg=c(ames.arg=c(V1V1",",V2V2",",V3V3),),

col=c(col=c(pink",pink", llightblue",ightblue",

yellowgreenyellowgreen))))

# names.arg# names.arg a vectora vector

of names to be plottedof names to be plotted

below each bar or groupbelow each bar or group

of barsof bars

DATA FRAMEDATA FRAME FOR GROUPEDFOR GROUPED

BAR PLOT : gdata2.csvBAR PLOT : gdata2.csv


> gdata4 gdata4 gdata4 < t(as.matrix(gdata4))> gdata4 < t(as.matrix(gdata4))

0 60 90 120 150 180

C463 3183 5443 5987 6014 6687 6065

IR5 4306 5982 6259 6895 6951 6540

IR8 4253 5672 6400 6733 7563 8701

Peta 4481 4816 4812 3816 2047 1881

GROUPED BAR PLOTGROUPED BAR PLOT d t 4d t 4


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GROUPED BAR PLOTGROUPED BAR PLOT gdata4gdata4

> barplot(> barplot(gdata4gdata4, beside=T,, beside=T,

xlab="Variety", ylab="Grain Yield",xlab="Variety", ylab="Grain Yield",

ccol=c("pink", "lightblue",ol=c("pink", "lightblue",

"yellowgreen"yellowgreen,, redred))))

ADD LEGENDADD LEGEND

> legend("topleft", Vlevel, bty="n",> legend("topleft", Vlevel, bty="n",

fill=c("pink", "lightblue",fill=c("pink", "lightblue",

"yellowgreen", "red"))"yellowgreen", "red"))

ERROR BARSERROR BARS

PACKAGEPACKAGE sciplotsciplot

A collection of functions that createsA collection of functions that creates

graphs with error bars for data collectedgraphs with error bars for data collected

from onefrom one--way or higher factorial designs.way or higher factorial designs.

It has three available functions:It has three available functions:

> bargraph.CI()> bargraph.CI()

> lineplot.CI()> lineplot.CI()

>>sse()e()

BARGRAPH WITH ERROR BARS


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BARGRAPH WITH ERROR BARS:BARGRAPH WITH ERROR BARS:

bargraph.CI()bargraph.CI()

Use to obtain barplot of the mean and standardUse to obtain barplot of the mean and standard

error of a response variable.error of a response variable.

Usage:Usage:

> bargraph.CI(x.factor, response,> bargraph.CI(x.factor, response,

group,group, ))

# x.factor# x.factor a factor whose levels will form thea factor whose levels will form the

xx--axisaxis

# response# response numeric response variablenumeric response variable

# group# group grouping factor whose levels willgrouping factor whose levels will

form groups of bars for each level of x.factorform groups of bars for each level of x.factor

BARGRAPH WITH ERROR BARS:BARGRAPH WITH ERROR BARS:

bargraph.CI()bargraph.CI()

Usage:Usage:

> bargraph.CI(x.factor, response,> bargraph.CI(x.factor, response,group, density, angle, legend,group, density, angle, legend,

x.leg, cex.legx.leg, cex.leg ))

# x.leg, y.leg# x.leg, y.leg to over ride the default legendto over ride the default legend

placementplacement

# cex.leg# cex.leg character expansion value forcharacter expansion value forlegend valueslegend values

BARGRAPH WITH ERROR BARS:BARGRAPH WITH ERROR BARS:gdata1gdata1

> bargraph.CI(Nitrogen, Yield,> bargraph.CI(Nitrogen, Yield,

group=Variety, data=group=Variety, data=gdata1gdata1,,

density=45, col=c("pink",density=45, col=c("pink",

"lightblue", "yellowgreen"lightblue", "yellowgreen,,redred), legend=T, x.leg=1,), legend=T, x.leg=1,

cex.leg=0.8)cex.leg=0.8)

BARGRAPH WITH ERROR BARSBARGRAPH WITH ERROR BARS

LINEGRAPH WITH ERROR BARSLINEGRAPH WITH ERROR BARS


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LINE PLOT WITH ERROR BARS:LINE PLOT WITH ERROR BARS:

lineplot.CI()lineplot.CI()

Use to obtain lineplot of the mean and standardUse to obtain lineplot of the mean and standard

error of a response variable.error of a response variable.

Usage:Usage:

> lineplot.CI(x.factor, response,> lineplot.CI(x.factor, response,

group,group, typetype))

# group# group grouping factor whose levels willgrouping factor whose levels will

formform the tracesthe traces

## typetype the type of plot: lines, points, or boththe type of plot: lines, points, or both


> lineplot.CI(Nitrogen, Yield,> lineplot.CI(Nitrogen, Yield,

group=Variety, data=group=Variety, data=gdata1gdata1,,

density=45, col=c(density=45, col=c(red",red", blue",blue",

"green"), legend=T, x.leg=1,"green"), legend=T, x.leg=1,

cex.leg=0.8, xlab=cex.leg=0.8, xlab=NitrogenNitrogen

RateRate, pch=c(15:18)), pch=c(15:18))


GRAPHICAL DEVICESGRAPHICAL DEVICES

GRAPHICAL DEVICEGRAPHICAL DEVICE


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GRAPHICAL DEVICEGRAPHICAL DEVICE

Before you create your graphs, you can decideBefore you create your graphs, you can decideon a format for output. The format is called aon a format for output. The format is called adevice.device.

A graphical device is a graphical window or aA graphical device is a graphical window or afilefile..

Some commonly usedSome commonly used graphicalgraphical devicedevice

Produces a bitmap JPEG fileProduces a bitmap JPEG filejpeg()jpeg()

Produces a bitmap PNG fileProduces a bitmap PNG filepngpng()()

Produces PDF fileProduces PDF filepdfpdf()()

jpeg(filename=jpeg(filename=plot.jpgplot.jpg, width=480,, width=480,

height=480, pointsize=12,height=480, pointsize=12,

units=units=pxpx))

png()png() same parameters as jpegsame parameters as jpeg

pdf(file=pdf(file=plot.pdfplot.pdf, width=7,, width=7,

height=7, paper =height=7, paper = a4a4))

USAGE OF GRAPHICS DEVICEUSAGE OF GRAPHICS DEVICE

##

filenamefilename

--

the name of the output filethe name of the output file

## width and heightwidth and height width and height of the devicewidth and height of the device

USAGE OF GRAPHICS DEVICEUSAGE OF GRAPHICS DEVICE

When you have finished with a device, be sureWhen you have finished with a device, be sure

to terminate the device driver by using dev.off()to terminate the device driver by using dev.off()

graphics.off() closes all open graphics devices.graphics.off() closes all open graphics devices.

## pointsizepointsize defaultdefault pointsize of plotted text,pointsize of plotted text,

interpreted as big points(1/72 inch)interpreted as big points(1/72 inch) atat res dpires dpi

## unitsunits The units in which height and width areThe units in which height and width are

given. Can be px(pixels), in, cm or mm.given. Can be px(pixels), in, cm or mm.

jpeg(jpeg(,,pointsize=12pointsize=12,, units=units=pxpx))

Plots in JPEG and PNG format can easilyPlots in JPEG and PNG format can easily

converted to many other bitmap formats.converted to many other bitmap formats.

PNG format is lossless and is best for linePNG format is lossless and is best for line

diagrams. While JPEG format is lossydiagrams. While JPEG format is lossy

InIn pdfpdf() m() multiple graphics can be saved in oneultiple graphics can be saved in onefile.file.

COMPARISONS OF GRAPHICSCOMPARISONS OF GRAPHICSDEVICEDEVICE


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SAVING GRAPHS IN FILESSAVING GRAPHS IN FILES

Ex. Saving histogram in png deviceEx. Saving histogram in png device

> png(filename=> png(filename=hist.pnghist.png))

> hist(gdata$Y)> hist(gdata$Y)> dev.off()> dev.off()

THANK YOU!THANK YOU!

Please do Exercise CPlease do Exercise C

Data Management and Statistical Analysis - Basic R Graphics

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