Getting started with R:
The information for these R_intro files has been obtained from the R help system, including the books "An Introduction to R", 
"Rlanguage definition", R Data import/export". Introductory files and reference cards have been obtained by R.Boik, K. Newman, and J Robinson-Cox.
Just type in the examples and follow what happens.

Obtaining R:

R can be downloaded from http://lib.stat.cmu/R/CRAN/

Installing R:

Run rw2001.exe from wherever you saved it and follow instructions from Setup Wizard. The source code is available for
programers.

Running R:

It is a good idea to create a subdirectory for each problem you work on.  The workspace will rapidly get cluttered
and slow your computations, and mixing projects can lead to serious mistakes.

Start R by clicking on the program icon onthe desktop, or by using the Windows start menu.

Change to the desired working directory with the command  setwd("yourharddrive:\\yourpath\\yoursubpath")
Note that you cannot use "\" to specify the path, only "\\" or "/" will work.  

Saving your workspace:

save.image(file="mystuff.RData") saves all of your current objects to the file "mystuff.Rdata". Also saved in a file called ".Rhistory" is your command history

Quitting R:

q() quits and asks you whether you want to save your workspace.
q("yes") quits and saves workspace.
q("no") quits and does not save workspace.

Restarting R:

If you double click on the .RData file for a project, R will be started and your workspace reloaded, including your setting ofro the working directory

Getting Help in R:

for a function, type help(functionname) and a new window with a function description, required arguments and examples appears.  Often these files are linked to other help
files and following these links is useful.

help.start() opens your browser to a R help page.  This give you access to anumber of manuals in HTML

In the www.r-project.org web pages, you can find pdf manuals also. Because many mailing lists of "how to do" problems are on the web, sometimes it helps to google 
an R related question. Now, practice the commands below and carefully look at what R gives you


# Simple arithmetic functions

#1. element by element
 x <- 3:12
 abs(x)
 log(x)
 log10(x)
 sqrt(x)  
 exp(x)
 sin(x)

#2. operate on entire vector:
 # returns a scalar value
 sum(x)
 prod(x)  #multiply each term

 #return vector of same length
 cumsum(x)       #x[1], x[1]+x[2], x[1]+x[2]+x[3]
 cumprod(x)      #x[1], x[1]*x[2], x[1]*x[2]*x[3]

#3. conversion to integers, rounding,..
 x <- 103.652
 round(x)
 round(x,1)
 round(x,2)
 trunc(x)     #nearest integer in direction of 0
 trunc(-0.8)
 floor(x)     #nearest integer in direction of negative infinity
 floor(-0.8)
 ceiling(x)   #nearest integer in direction of positive infinity
 ceiling(-0.8) 

#4. max, min related
 x <- c(3,5,5,9)
 y <- c(5,3,5,11)

 max(x)
 min(x)
 range(x)   #useful for setting limits on graph axes
 pmax(x,y)  #per position [i] return maximum of x[i] and y[i]
 pmin(x,y)
 
#5. ordering
 x <- c(12,5,6,6,-1)
 sort(x)
 rev(x)
 order(x)       #returns position of smallest, next smallest, ...
 rev(order(x))  #returns position of largest, next largest,...
 rank(x)        #rank of x[1], then rank of x[2]; useful for ranksum statistics

#6. simple statistics 
 x <- c(8,12,5,4,19,2,1)
 y <- rnorm(length(x),mean=3+2*x,sd=1)
 mean(x)
 var(x)
 median(x)
 quantile(x,probs=c(0.25,0.75))
 summary(x)     #a generic function used on lots of classes of data 




# Arithmetic and logical expressions

#0. Precedence
 #See Table 2.1 on p. 33 of V&R, but some common situtations, highest to lowest:

   function(..)
   ^            #exponentiation
   * /          #multiplication, division
   + -          #addition, subtraction
   > < <= == != #comparison operators
  
#but can always use parentheses to force a precedence
  
  x <- 36
  y <- 7
  sqrt(x)*7-2 <  x+y^2
  (((sqrt(x))*7)-2) < (x+(y^2))  #identical to above but "clear" precedence

#1. element by element operations on two vectors
 x <- 1:10
 y <- 11:20
 x+y
 x-y
 x*y
 x/y
 x^y

#2. recycling: when operating on 2 vectors with unequal length
#   length of output = length of longer vector, recycling the
#   shorter vector's values till match longer vector's length
#   Note!!! This can have unintended consequences if your vectors
#   are of unequal length because of an error in construction

 x <- 2
 y <- 1:6
 x+y       #2+1, 2+2, 2+3, 2+4, 2+5, 2+6
 
 x <- c(2,9)
 x+y       #2+1, 9+2, 2+3, 9+4, 2+5, 9+6

#3. Integer division and modulo reduction
 7 %/% 3       #answer 2, number of times 3 goes into 7
 7 %%  3       #answer 1, 7 - (7 %/% 3)*3

#4 Logical expressions and functions with logical arguments
 x <- c(1,3,5)
 y <- c(2,2,4)

 x < y
 x <= y
 x != y

 any(x<y)  #if any term in vector x<y is T, return T
 all(x<y)  #if all terms in vector x<y is T, return T
 
 (x==3 | y==2)  # union of vector x==3 with vector y==2
                # T|T or T|F or F|T returns T
                # only F|F returns F

 (x==3 & y==2)  # intersection of vector x==3 with vector y==2 
                # only T&T returns T# Arithmetic and logical expressions

#0. Precedence
 #See Table 2.1 on p. 33 of V&R, but some common situtations, highest to lowest:

   function(..)
   ^            #exponentiation
   * /          #multiplication, division
   + -          #addition, subtraction
   > < <= == != #comparison operators
  
#but can always use parentheses to force a precedence
  
  x <- 36
  y <- 7
  sqrt(x)*7-2 <  x+y^2
  (((sqrt(x))*7)-2) < (x+(y^2))  #identical to above but "clear" precedence

#1. element by element operations on two vectors
 x <- 1:10
 y <- 11:20
 x+y
 x-y
 x*y
 x/y
 x^y

#2. recycling: when operating on 2 vectors with unequal length
#   length of output = length of longer vector, recycling the
#   shorter vector's values till match longer vector's length

 x <- 2
 y <- 1:6
 x+y       #2+1, 2+2, 2+3, 2+4, 2+5, 2+6
 
 x <- c(2,9)
 x+y       #2+1, 9+2, 2+3, 9+4, 2+5, 9+6

#3. Integer division and modulo reduction
 7 %/% 3       #answer 2, number of times 3 goes into 7
 7 %%  3       #answer 1, 7 - (7 %/% 3)*3

#4 Logical expressions and functions with logical arguments
 x <- c(1,3,5)
 y <- c(2,2,4)

 x < y
 x <= y
 x != y

 any(x<y)  #if any term in vector x<y is T, return T
 all(x<y)  #if all terms in vector x<y is T, return T
 
 (x==3 | y==2)  # union of vector x==3 with vector y==2
                # T|T or T|F or F|T returns T
                # only F|F returns F

 (x==3 & y==2)  # intersection of vector x==3 with vector y==2 
                # only T&T returns T


I. More on vectors
 1. contain elements of just 1 type, either numeric, logical, or character
  a. numeric
       y <- 18
       y <- c(-3.6,1.58)
       y <- 1:9
       y <- seq(from=0,to=10,by=0.02)     #seq() a function w/ args from, to,..
					  #by argument gives distance
       y <- seq(0,10,by=0.02)             #if know where args are, no need to specify name
					  
       y <- seq(-3,25,length=6)           #length option 
       x <- c(3,3,9,12,1)
       y <- seq(0,10,along=x)             #will return seq w/ length(x)

       y <- rep(x=3,times=7)              #replicate the value in x, namely 3, seven times
       y <- rep(x=c(3,5),times=7)         # same
       y <- rep(x=c(3,5),times=c(2,6))    #repeat 3 two times, then 5 seven times
 
   b. character
       y <- "San Diego"
       y <- c("LA","NY","San Fran")

   c. logical
       y <- T
       y <- c(F,F,T)
       x <- 1:7
       y <- (x<5)

  2. Accessing elements of a vector in 1 of 4 ways
       y <- c(18,32,15,-7,12,19)
   a. position in vector as positive integer
      y[3:5]

   b. excluding elements, position as negative integers
      y[-c(1,5,6)]

   c. by element name
      names(y) <- c("Joe","Bill","Karen","Helen","Ray","Paul")
      y[c("Helen","Ray")]
 
   d. by logical conditions
      y[y<15]

  3. Matrices, arrays, and factors
   a. Matrices
      y <- c(18,32,15,-7,12,19)
      x <- matrix(data=y,nrow=2,ncol=3)           #fill columns first (column major order)
						  #  -the default
      x <- matrix(data=y,nrow=2,ncol=3,byrow=T)   #fill rows first
      dimnames(x) <- list(c("r1","r2"),c("a","b","c"))

   b. Arrays
        # creates a 2 by 4 by 3 array
      y <- c(1:8, 11:18, 111:118)
      x <- array(y, dim = c(2,4,3))    #first dimension changes fastest

   c. Factors
      color <- c("red", "red", "red", "green", "blue")  #character valued vector
      colors <- factor(color, c("red","green","blue"))
      table(colors)  # table counting occurrences of colors
               #one use: when building models where "dummy" variables needed

  4. Vector attributes
   every vector (and object) has 2 "implicit" attributes, mode and length
      some modes, e.g.  "numeric",  "list",  "logical", "NULL"

   other attributes- name, dimension,levels, class
     attributes(y)        #for "plain" vector doesn't report anything
     attributes(x)
     attributes(colors)

II. More on lists
    x <- list(one=c(18:36),two=c("AK","AL","AZ"),three=c(T,T,F,T),four=matrix(1:12,3,4))
  1. access to components
    x[[1]]          #by order
    x$one           #by name

  2. access to elements within components
    x[[1]][3:6]
    x$one[3:6]

  3. unlist()        #convert a list to a vector
    unlist(x)        #handy for printing out returned values from function

  4. attach(what=..)       #makes components of list directly accessible       
    attach(what=x)
    one
    detach(what="x")       #no longer make this direct access possible

    Note- attach(what="mydirectory",position=2) will put a directory named
       mydirectory, say, in the first position of the search list
       - the directory name must be in quotes to distinguish it from an
	 ordinary object

   5. data frames- a special kind of list object; number of elements must
       be the same for all components
	- handy for regression modeling

      muscle <- rnorm(n=10,mean=3,sd=1)
      sex <- factor(rep(c("M","F"),c(6,4)))
      speed  <- rep(0,10)
      speed[1:6] <- rnorm(6,30-2*muscle[1:6],2)
      speed[7:10] <- rnorm(4,40-2*muscle[7:10],2)
      mydata <- data.frame(y=speed,x1=muscle,x2=sex)
      temp <- lm(y~x1+x2,data=mydata)
      summary(temp)

III. More on functions
   1. specified or unspecified arguments
     a. unspecified   c <- function(...)
     b. specified   
	  sd <- function(x) {return(sqrt(var(x)))}

          dumplot <- function(x,y) {
		      plot(x,y)
		      abline(0,1)
		     }

    2. argument passing for specified case
       if don't use names, call function by passing arguments in proper order
          dumplot(my.x,my.y)	   
       if use names, then any order ok
	  dumplot(y=my.y, x = my.x)

    3. default values for specified case
	dumplot <- function(x,y,my.line=T) {
	        plot(x,y)
	       if(my.line) {
		abline(lm(y~x))
               } 
	     }	


#Random variables- generating, distribution functions

#0. random number seed; fix for reproducible simulations
  i <- 5
  set.seed(i)         #i must be between 0 and 1000

  # the same effect can be created by saving .Random.seed and then
  # assigning that value to .Random.seed later.

#1. random sampling
   z <- c(18,22,15,25,36)

   sample(x=z,size=3,replace=F)  #take a SRS w/o replacement from z
   sample(x=z,size=3,replace=T)  #now w/ replacement; as for bootstrap
   sample(x=z,size=3,replace=T,prob=c(0.1, 0.3, 0.2, 0.1, 0.3)) #unequal prob sampling

#2. univariate random variable generation (see p. 164, Table 5.1)
  #beta, binomial, Cauchy, normal, lognormal, gamma, F, poisson, Chi-square

  rbeta(n=10,shape1=3,shape2=4)    # ten obs'ns from Beta(3,4)
  rbinom(n=10,size=100,prob=0.2)   # ten obs'ns from Binomial(100,0.2)
  rnorm(n=10,mean=20,sd=5.1)       # ten obs'ns from Normal(20,5.1^2)
  rpois(n=30,lambda=3)             # ten obs'ns from Poisson(3) 
  
#3. percentages- for P-values in particular; can discard tables in back of stat texts...
  pnorm(q=1.645,mean=0,sd=1)
  1-pf(q=5.7,df1=3,df2=15)

#4. quantiles- for test statistics, for example
  qt(p=0.975,df=21)


#5. density function value; or probability for discrete valued rv
  dnorm(x=0.5,mean=0,sd=1)
  dpois(x=1,lambda=2)