statistical computation using R- an intro..

STATISTICAL COMPUTATION
USING R

 Introduction
 R as a statistical software
 Statistical features
 R preliminaries
 Functions in R
 Graphics in R
 Distributions
 Conclusion
 References

Introduction
 programming language and software environment
for statistical computing and graphics.
 S,S PLUS.
 Developed by Ross Ihaka and Robert Gentleman at
the University of Auckland, New Zealand.
 Open source software
 R works fundamentally by the question-and-answer
model
 Can be downloaded from http://R-Project.org

R - as a Statistical software
 It has very good computing performance
 R makes its view especially in colleges &
universities
 It has excellent built in help system
 Its graphical environment is flexible and
powerful
 Easy for new user
 Easy to extend with user written functions
 It provides scripting and interacting facilities
 Vectors as the basic data structure

Statistical features
 R is an interpreted language
 users typically access it through a command-line
interpreter
 Like other similar languages such as APL and
MATLAB, R supports matrix arithmetic
 R's data structures include vectors, matrices, arrays,
data frames (similar to tables in a relational
database) and lists.
 R supports procedural programming with functions
and, for some functions, object-oriented
programming with generic functions.

R-Preliminaries
Common operators:
 Arithmatic Operator
+ Addition
- Subtract
* Multiplication
/ Division
^ Exponential
 Relational Operator
< Lessthan
> Greaterthan
<= Lessthan Equal
>= Greaterthan Equal
== Is Equal to
!= Not Equal

 Logical Operator
! NOT
& AND
| OR
 Assignment Operator
<- Left assignment
-> Right assignment
Eg : x<-2 Assigns the value 2 to the object x
x^2->y Assigns the value x^2 to the object y
Commands will be lines, starting with a # mark.
To display the value of y, we type ‘print(y)’ or ‘y’

Functions
 function name is followed by a set of parentheses
containing one or more arguments.
Eg: plot(height,weight)
 the function name is ‘plot’ and the arguments are
‘height’ and weight.
 positional matching

Method of data input
 C function (concatenate)
Eg: > x <- c(1, 2, 3)
> y <- c(10, 20)
> c(x, y, 5) # R command
[1] 1 2 3 10 20 5
 Sequence function
seq (“sequence”), is used for equidistant series of
numbers.
Eg: > seq(4,9) # R command
[1] 4 5 6 7 8 9

 If you want a sequence in jumps of 2
Eg: > seq(4,10,2)
[1] 4 6 8 10
Sequence operator “:”
> 4:9 # R command
[1] 4 5 6 7 8 9
 Scan function
Used to provide small quantities of data.
variable=scan() # R command
Used for creating data object
Eg: wt=Scan(103,102,108);
[1] 103 102 108

 Rep function
rep (“replicate”), is used to generate repeated
values
y=rep(x,n) # R command
X<-c(rep(1,4),rep(2,2));
 Data frames
o provides the table of data in R
object=data.frame(list of variables); # R command
o Display the content of data frame with row no.
o Column headings can be modified after creation of
frame.
o Colnames(name of data frame)= c(list of column under
double quotes)

Eg:
n<-c(2, 3, 5)
s<-c("aa", "bb", "cc")
b<-c(TRUE, FALSE,TRUE)
df<-data.frame(n, s, b)
df
o/p
n s b
2 aa TRUE
3 bb FALSE
5 cc TRUE

 Matrix function
> x <- 1:12
> dim(x) <- c(3,4)
> x
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
o The dim assignment function sets or changes the dimension
attribute of x, causing R to treat the vector of 12 numbers as a
3 × 4 matrix
o storage is column-major; that is, the elements of the first
column are followed by those of the second, etc.
o Convenient function to provide matrix type data.
o Another function used to create a data frame.
Object=matrix(c(data values) nrow=m,byrow=T/F)
o The byrow=T switch causes the matrix to be filled in a row
wise fashion rather than column wise

 List function
It is sometimes useful to combine a collection of
objects into a larger composite object.This can be
done using lists.
Eg: > list1 <- c(5640,6180,6390,6805,7515)
list2 <- c(3910,3885,5160,5645,7335)
> mylist <- list(before=list1,after=list2)
>mylist
$before
[1] 5640 6180 6390 6515 6805 7515
$after
[1] 3910 3885 5160 5645 7335

 Class function
used to decide the class of the data object
Eg: > a1<-c(‘x’,’y’);
class(a1);
o/p: character
 Built in functions
length() no. of elements of data
max()the maximum element of data
min() the minimum element of data
sort() sorting in increasing magnitude
-sort() “ decreasing “ etc

Graphics in R
 2 types of graphics function
o High level function, which creates a new graph
o Low level function, which adds elements to an already
existing graph
High level ploting functions
plot() Scatter plot
hist() Histogram
boxplot() box & whisker
barplot() bar diagram

Arguments to plot function
Argument explanation
Main= Tittle
Xlab= Label of X axis
Ylab Label of Y axis
Xlim= Specific X limit
Ylim= “ Y limit
Type= type of ‘p’ for points
Pch= Style of points(bw 0&20)
Col= colour

Low level ploting functions
Lines() Draw lines
abline() Lines given by intercept and slopes
points() Points
text() Texts in the plot
legent() List of symbols

 > age<-c(5,10,15,20)
 > freq<-c(10,15,30,20)
>plot(age,freq,xlab=age,ylab=freq,pch=1,col="b
lue",main="age vs frequency")

Probability Distributions
Distribution Rname Additional Argument
Binomial binom size,probability
Poisson pois lamda
Geometric geom probability
Hyper geom hyper m,n,k
Normal norm mean,sd
Uniform unif min,max
Gamma gamma shape,scale
Chi-square chisq df,df2,nCp
F p df1,df2,nCp

 Binomial Distribution
> n<-10
> p<-.5
> pr<dbinom(x,n,p)# for pmf (pbinom for pdf)
Error: object 'pr' not found
> pr<-dbinom(x,n,p)
> pr
[1] 0.009765625 0.117187500 0.246093750 0.009765625
> pmf<-data.frame(x,pr)
> pmf
x pr
1 1 0.009765625
2 3 0.117187500
3 5 0.246093750
4 9 0.009765625
>
plot(x,pr,type="h",main="binomial",lwd=2,xlab="x",ylab="pr")

Conclusion
 R is a flexible programming language designed to facilitate
exploratory data analysis, classical statistical tests, and high-
level graphics.
 R is a full-fledged programming language, with a rich
complement of mathematical functions, matrix operations and
control structures.
 With its rich and ever-expanding library of packages, R is on the
leading edge of development in statistics, data analytics, and
data mining.
 R has proven itself a useful tool within the growing field of big
data and has been integrated into several commercial packages,
such as IBM SPSS and InfoSphere, as well as Mathematica.

References
 Introductory Statistics with R- Peter
Dalgaard(2nd edition)
 Statistical Computing with R- Eric Slud
 Quick-R : Creating Graphs
http://www.statmethods.net/graphs/

statistical computation using R- an intro..

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