A Gentle Introduction to R for Stat 133 Class

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• A Gentle Introduction to Rfor Stat 133 Class
• by Doods

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Introduction to R

• 1. A few things to know before starting
• access R by launching the corresponding
  executable (RGui.exe under Windows, R under
  Unix).
• the prompt gt indicates that R is waiting for
  your commands.

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1.1 The operator lt-

• R is an object-oriented language the variables,
  data, matrices, functions, results, etc. are
  stored in the active memory of the computer in
  the form of objects which have a name
• one has just to type the name of the object to
  display its content.
• For example, if an object n has value 10
• gt n
• 1 10gt
• The digit 1 within brackets indicates that the
  display starts at the first element of n.

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• The symbol assign is used to give a value to an
  object. This symbol is written with a bracket (lt
  or gt) together with a sign minus so that they
  make a small arrow which can be directed from
  left to right, or the reverse
• gt n lt- 15
• gt n
• 1 15
• gt 5 -gt n
• gt n
• 1 5

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• Can simply type an expression without assigning
  its value to an object, the result is thus
  displayed on the screen but not stored in memory
• Example
• gt (102)5
• 1 60
• 1.2 Listing and deleting the objects in memory
• The function ls() lists the objects in memory
  only the names of the objects are displayed.
  Example
• gt name lt- "Laure" n1 lt- 10 n2 lt- 100 m lt- 0.5
• gt ls()
• 1 "m" "n1" "n2" "name"
• Note the use of the semi-colon "" to separate
  distinct commands on the same line.

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1.3 The on-line help

• The on-line help of R gives some very useful
  informations on how to use the functions. The
• help in html format is called by typing
• gt help.start()
• A search with key-words is possible with this
  html help. Example
• gt help(anova)

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2. Data with R

• 2.1 Lire des données à partir dun fichier
• R can read data stored in text (ASCII) files
  three functions can be used read.table()(which
  has two variants read.csv() and read.csv2()),
  scan() and read.fwf(). We will discuss only
  read.table() and read.fwf()function.
• Example, if we have a file data.dat, one can just
  type
• gt mydata lt- read.table("data.dat")
• Note you can specify your directory example
  read.table(a\data.dat"). The default is a
  library where R is installed..

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• data.dat is a file in table (text) format
  separated by space(s).
• Example mydata.dat has the format below
• A 1.50 1.2
• A 1.55 1.3
• B 1.60 1.4
• B 1.65 1.5
• C 1.70 1.6
• C 1.75 1.1
• Can read with gtread.table(mydat.dat,
  col.namesc(dose, water, relief)) to get
• Dose Water Relief
• A 1.50 1.2
• A 1.55 1.3
• B 1.60 1.4
• B 1.65 1.5
• C 1.70 1.6
• C 1.75 1.1

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• If mydata.dat already has the format
• Dose Water Relief
• A 1.50 1.2
• A 1.55 1.3
• B 1.60 1.4
• B 1.65 1.5
• C 1.70 1.6
• C 1.75 1.1
• Then read this table with
• gt read.table(" mydata.dat", headerT) reads the
  variable name
• Dose Water Relief
• A 1.50 1.2
• A 1.55 1.3
• B 1.60 1.4
• B 1.65 1.5
• C 1.70 1.6
• C 1.75 1.1

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• For read.fwf(), the options are the same than for
  read.table() except widths which specifies the
  width of the fields.
• Example data.txt has the following data
• A1.501.2
• A1.551.3
• B1.601.4
• B1.651.5
• C1.701.6
• C1.751.7, one can read them with
• gt mydata lt- read.fwf("data.txt", widthsc(1,4,3))
• gt mydata
• V1 V2 V3
• 1 A 1.50 1.2
• 2 A 1.55 1.3
• 3 B 1.60 1.4
• 4 B 1.65 1.5
• 5 C 1.70 1.6
• 6 C 1.75 1.

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• The function write(x, file"data.txt") writes an
  object x (a vector, a matrix, or an array) in the
  file data.txt.
• 3. Graphics with R
• R offers a remarkable variety of graphics. To get
  an idea, one can type demo(graphics).
• 3.1 Opening several graphic windows
• When a graphic function is typed, a graphic
  window is open with the graph required. It is
  possible to open another window by typing
• gt x11()
• The window so open becomes the active window, and
  the subsequent graphs will be displayed on it.
  To know the graphic windows which are currently
  open
• gt dev.list()
• windows windows
• 2 3

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• The figures displayed under windows are the
  numbers of the windows which can be used to
  change the active window
• gt dev.set(2)
• windows
• 2
• 3.2 Partitioning a graphic window
• The function split.screen() partitions the active
  graphic window. For instance, split.screen(c(1,2)
  ) divide the window in two parts which can be
  selected with screen(1) or screen(2)
• erase.screen() erases the last drawn graph. Well
  have more on this when we go to linear models.

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4. Generating data

• Regular sequences.
• A regular sequence of integers, for example from
  1 to 30, can be generated with
• gt x lt- 130
• The resulting vector x has 30 éléments. The
  operator has priority on the arithmetic
  operators within an expression
• gt 110-1
• 1 0 1 2 3 4 5 6 7 8 9
• gt 1(10-1)
• 1 1 2 3 4 5 6 7 8 9

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• The function seq() can generate sequences oe real
  numbers as follows
• gt seq(1, 5, 0.5)
• 1 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
• where the first number indicates the start of the
  sequence, the second one the end, and the
• third one the increment to be used to generate
  the sequence. One can use also
• gt seq(length9, from1, to5)
• 1 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

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• It is also possible to type directly the values
  using the function c()
• gt c(1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5)
• 1 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
• which gives exactly the same result, but is
  obviously longer.
• The function rep() creates a vector with
• elements all identical
• gt rep(1, 30)
• 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1

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• The function sequence() creates a series of
  sequences of integers each ending by the
• numbers given as arguments
• gt sequence(45)
• 1 1 2 3 4 1 2 3 4 5
• gt sequence(c(10,5))
• 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5

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5. Statistical analyses with R

• Lots of statistical packages, but will probably
  concentrate on regression only. See the URL
  http//cran.rproject.
• org/src/contrib/PACKAGES.html for extensive list.
  
• Among the most remarkable ones, there are
• gee (generalised estimating equations)
• multiv (multivariate analyses, includes
  correspondance analysis)
• nlme (linear and nonlinear models with
  mixed-effects)
• survival5 (survival analyses)
• tree (trees and classification)
• tseries (time-series analyses)
• lm linear models

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• We will discuss only regression analysis.
• If we have two vectors x and y each with five
  observations, and we wish to perform a linear
  regression of y on x
• gt x lt- 15
• gt y lt- rnorm(5) generates 5 random numbers from
  a normal distribution
• gt lm(yx)
• Call
• lm(formula y x)
• Coefficients
• (Intercept) x
• 0.2252 0.1809

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• As for any function in R, the result of lm(yx)
  can be copied in an object
• gt mymodel lt- lm(yx)
• if we type mymodel, the display will be the same
  as previously. Several functions allow the user
  to display details relative to a statistical
  model, among the useful ones summary() -
  displays details on the results of a model
  fitting procedure residuals()displays the
  regression residuals, predict() displays the
  values predicted by the model, and coef()
  displays a vector with the parameter estimates
• .

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• gt summary(mymodel)
• Call
• lm(formula y x)
• Residuals
• 1 2 3 4 5
• 1.0070 -1.0711 -0.2299 -0.3550 0.6490
• Coefficients
• Estimate Std. Error t value Pr(gtt)
• (Intercept) 0.2252 1.0062 0.224 0.837
• x 0.1809 0.3034 0.596 0.593
• Residual standard error 0.9594 on 3 degrees of
  freedom
• Multiple R-Squared 0.1059, Adjusted R-squared
  -0.1921
• F-statistic 0.3555 on 1 and 3 degrees of
  freedom, p-value 0.593

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• gt residuals(mymodel)
• 1 2 3 4 5
• 1.0070047 -1.0710587 -0.2299374 -0.3549681
  0.6489594
• gt predict(mymodel)
• 1 2 3 4 5
• 0.4061329 0.5870257 0.7679186 0.9488115 1.1297044
• gt coef(mymodel)
• (Intercept) x
• 0.2252400 0.1808929

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• Other statistical functions in R
• func indicates the law of probability, n the
  number of data to generate and p1, p2, ...
  are the values for the parameters of the law.
• Heres a few
• Gaussian (normal) rnorm(n, mean0, sd1)
• exponential rexp(n, rate1)
• gamma rgamma(n, shape, scale1)
• Poisson rpois(n, lambda)
• Weibull rweibull(n, shape, scale1)
• Cauchy rcauchy(n, location0, scale1)
• beta rbeta(n, shape1, shape2)
• Student (t) rt(n, df)

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• Fisher (F) rf(n, df1, df2)
• Pearson (?2) rchisq(n, df)
• binomial rbinom(n, size, prob)
• geometric rgeom(n, prob)
• hypergeometric rhyper(nn, m, n, k)
• logistic rlogis(n, location0, scale1)
• lognormal rlnorm(n, meanlog0, sdlog1)
• negative binomial rnbinom(n, size, prob)
• uniform runif(n, min0, max1)
• Wilcoxons statistics
• rwilcox(nn, m, n), rsignrank(nn, n)

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6. The Plot Function

• Generic X-Y Plotting
• Usage
• plot(x, y, xlimrange(x), ylimrange(y),
  type"p",
• main, xlab, ylab, ...)
• Arguments
• x the coordinates of points in the plot.
  Alternatively, a single plotting structure,
  function or any R object with a plot' method
  can be provided.
• y the y coordinates of points in the plot,
  optional if x' is an appropriate structure.
• xlim, ylim the ranges to be encompassed by the x
  and y axes.

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• type what type of plot should be drawn.
  Possible types are
• "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.
• All other type's give a warning or an error

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• main an overall title for the plot.
• xlab a title for the x axis.
• ylab a title for the y axis.

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6. 1 Plotting Densities

• Normal density curves
• gt plot(dnorm, xlim c(-7, 7), ylim c(0,0.8))
• gt x lt- seq(-7, 7, 0.5)
• gt normdensity1 lt- dnorm(x, mean 0, sd 0.6)
• gt normdensity2 lt- dnorm(x, mean 0, sd 2)
• gt normdensity3 lt- dnorm(x, mean 3, sd 0.8)
• gt lines(x, normdensity1, col "blue")
• gt lines(x, normdensity2, col "red")
• gt lines(x, normdensity3, col "green")

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Plot of Normal Density
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• Gamma density curves
• gt x lt- seq(0, 7, 0.1)
• gt gammadensity1 lt- dgamma(x, shape 1, scale
  1)
• gt gammadensity2 lt- dgamma(x, shape 2, scale
  2)
• gt gammadensity3 lt- dgamma(x, shape 2, scale
  1/3)
• gt gammadensity4 lt- dgamma(x, shape 2, scale
  1)
• gt plot(x, gammadensity1, type "l", ylab
  "Gamma densities", ylim c(0, 1.1))
• gt lines(x, gammadensity2, col "blue")
• gt lines(x, gammadensity3, col "red")
• gt lines(x, gammadensity4, col "green")

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• Exponential density curves
• gt plot(dexp, xlim c(0, 7), ylab exponential
  densities)
• gtx lt- seq(0, 7, 0.1)
• gtexpdensity1 lt- dexp(x, rate 0.5)
• gtexpdensity2 lt- dexp(x, rate 2)
• gtlines(x, expdensity1, col "blue")
• gtlines(x, expdensity2, col "red")

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• Chi-squared densities
• gt x lt- seq(0, 10, 0.1)
• gt chisq1 lt- dchisq(x-1, df 1)
• gt plot(x-1, chisq1, type "l", ylab
  chi-squared densities)
• gt chisq2 lt- dchisq(x, df 2)
• gt chisq3 lt- dchisq(x, df 3)
• gt lines(x, chisq2, col "blue")
• gt lines(x, chisq3, col "red")

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Going back to Regression, etc

• create and embellish simple graphics R.
• The file education.dat contains data about school
  expenditures for each of the 50 states and the
  District of Columbia.
• The variables are school expenditures in 1970
  (SE70), each states citizens average income in
  1968 (PI68), school age population per capita in
  1969 (Y69), urban population per capita in 1970
  (Urban70), and two variables for the states
  location Region (general) and Locale (specific).
  
• We are interested in exploring the relationships
  between SE70 and the other variables.

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• education.dat
• State SE70 PI68 Y69 Urban70 Region Locale
• 1 ME 189 2824 350.7 508 NOREAST NEWENG
• 2 NH 169 3259 345.9 564 NOREAST NEWENG
• .. ...
• Read this data set into a data frame and attach
  to it. (The database is attached to the R search
  path. This means that the database is searched by
  R when evaluating a variable, so objects in the
  database can be accessed by simply giving their
  names. Heres how
• gt edu lt- read.table("education.dat", headerT)
• gt attach(education)
• gt hist(SE70)produces a histogram

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• We can expect that school expenditures will be
  related to the number of students, so lets plot
  Y69 (students) against SE70.
• gtplot(Y69, SE70)
•  

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• Embellishing Plots
• Once you have created a plot, you can embellish
  it in various ways. S-PLUS documentation refers
  to function
• of this sort as low-level graphics functions.
• Adding Titles
• R allows you to add titles at several places in
  the plot a main title (above the picture) and
  x-axis and y-axis titles.
• gt plot(PI68, SE70)
• gt title(main"Income vs. School Expenditures")

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• Adding a Line
• The function abline adds a line of the form y a
  bx to a plot. It also has an lty field to
  allow different line types (dashed, dotted,
  etc.).
• Lets add two lines to the plot of income and
  school expenditures, one including Alaska and the
  other not.
• We can find these lines using regression. The
  first command below says SE70 modelled by PI68
  and the second says SE70 modelled by PI68 using
  all points except the 50th.

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• gt lm(SE70 PI68)
• Output
• Call
• lm(formula SE70 PI68)
• Coefficients
• (Intercept) PI68
• 17.71003 0.05537594
• Degrees of freedom 51 total 49 residual
• Residual standard error 34.9384

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• gt lm(SE70 PI68, subset-50)
• Call
• lm(formula SE70 PI68, subset -50)
• Coefficients
• (Intercept) PI68
• 40.56264 0.04747211
• Degrees of freedom 50 total 48 residual
• Residual standard error 29.93981

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• gt lm(SE70 PI68, subset-50)
• Call
• lm(formula SE70 PI68, subset -50)
• Coefficients
• (Intercept) PI68
• 40.56264 0.04747211
• Degrees of freedom 50 total 48 residual
• Residual standard error 29.93981

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• Now we can use the first equation to plot a solid
  line (line type 1, the default), and the second
  to plot a dotted line (line type 2).
• gt abline(17.71003, 0.05537594, lty1)
• gt abline(40.56264, 0.04747211, lty2)

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• Adding Text
• R allows you to add text to a graph in a few
  different ways. The simplest is with the function
  text.
• The format is text(x,y,"string"), and this plots
  the text string at the coordinates (x,y).
• R also has a somewhat more elegant function,
  legend. This function takes x and y coordinates,
  a
• vector of labels, and a vector of colors or
  line types corresponding to those labels.
• For instance, we could add a legend to the graph
  which labels the two line types, and text to
  write
• Alaska approximately underneath the Alaska data
  point.

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• gt legend(2500, 350, c("With Alaska","Without
  Alaska"), ltyc(1,2))
• gt text(4100, 360, "Alaska")

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Plotting All Pairs of Variables

• You can plot all possible pairs of variables in
  edu by issuing the command.
• gt pairs(edu)
• Try it!

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Multiple Plots per Page

• To see multiple plots on the same page, first
  break the graphics window into multiple sections.
  Lets try a 2 by 2 grid of smaller windows.
• gt par(mfrowc(2,2))
• This has no obvious immediate effect. However,
  the next plot will appear in the upper left hand
  frame of a 2 by 2 matrix of plotting frames.
  Lets fill these frames with plots of predictors
  and SE70, two of which we have already seen.
• gt plot(PI68, SE70)
• gt plot(Y69, SE70)
• gt plot(Urban70, SE70)

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Multiple Plots
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• Heres another one you can try If you create the
  object
• educ.lm lt-lm(SE70 PI68)
• Then you can plot all diagnostics by
• gtpar(mrowc(2,2)) and
• gtplot(educ.lm)

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Diagnostic Plots
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End?!

• Thats probably enough, just read the R manual
  and the others I posted on the internet!