R Code Applied to Statistics

179 Pages·2017·4.45 MB·English

R Code
Applied to Statistics
David Casado de Lucas
Complutense University of Madrid
∟ Faculty of Economic and Business Sciences 24 March 2017
Department of Statistics and Operational Research II
∟
David Casado de Lucas
∟
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▲ Errata and linguistic errors are corrected as soon as
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Contents
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must overwrite Names of sections are
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different name.
Basic Use and Main Functions 5 Hypothesis Tests 102
Mathematical Analysis 28 Tests on the Mean
Equivalence of the Two Methodologies
Functions
Power Function
Interpolation and Approximation Methods
Significance Level
Probability Theory 37
Regression Methods 118
Random Numbers
Simple Linear Regression (SLR)
Plotting Density and Distribution Functions
SLR: Quantity of Data
Inference Theory 47
SLR: Quality of Data
Sampling
SLR: Y independent
Correction Factor
SLR: Robustness
Descriptive Statistics 65
SLR: Transformation of Data
Some Measures and Plots
SLR: Spurious Correlation
Point Estimations 68 Linear Regression Diagnosis
Basic Estimators
Appendixes 135
Statistics to Study the Mean
Framework
Moving Average
Real Data
Autocorrelation Functions
Package stats
Confidence Intervals 94
Package R Commander
Confidence Intervals for the Mean
Some References
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3
Prologue
This file contents the code that I am writing with teaching purposes. Users
are supposed to have little—but some—knowledge about the basic ideas
about what the computer can be used for in Statistics. I wrote some of these
ideas for the practicals (in the appendixes at the end of each chapter) of:
http://www.casado-d.org/edu/NotesStatisticalInference-Slides.pdf
Acknowledgements
This document has been created with Linux, LibreOffice, OpenOffice, GIMP
and R. I thank those who make this software available for free. I donate
funds to these kinds of project from time to time.
Note: In using the built-in functions of R, we assume that the help of the functions will be consulted.
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4
References
– My Documents
[1] A Brief Guide for Students.
http://www.Casado-D.org/edu/GuideForStudents-Slides.pdf
[2] Notes of Probability Theory.
http://www.Casado-D.org/edu/NotesProbabilityTheory-Slides.pdf
[3] Notes of Statistical Inference.
http://www.Casado-D.org/edu/NotesStatisticalInference-Slides.pdf
[4] Solved Exercises and Problems of Statistical Inference.
http://www.Casado-D.org/edu/ExercisesProblemsStatisticalInference.pdf
[5] R Code Applied to Statistics.
http://www.Casado-D.org/edu/CodeAppliedToStatistics-Slides.pdf
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5
Basic Use
and
Main Functions
Some Functions
Some Useful Methods and Prefixes
How to Define Functions
One Variable
Several Variables
Managing Data
Managing Packages
Managing Code
Probability Theory
Descriptive Statistics
Statistical Inference
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Basic Use and Main Functions
Some Functions
; ... ' #
getwd() # To see which is the working directory
setwd() # To set the working directory
help(Distributions) # To consult the help related to 'Distributions'
?Distributions # To consult the help related to 'Distributions'
help.search('test') # To consult the help related to 'test'
??Distributions # To search for the string 'Distributions' in help info.
apropos('print') # To search functions containing 'print' in their name
library(help = 'stats') # To consult the help of the package 'stats'
ls() # To list all the variables existing at the moment
rm(namevariable) # To remove the variable 'namevariable'
remove(namevariable) # To remove the variable 'namevariable'
rm(list = ls()) # To remove all existing variables
length(namevector) # The lenght of the vector
dim(namearray) # The dimensions of the object
names(nameobject) # To access the names of the fields of the object
namefunction # To see the code of the function 'namefunction'
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Basic Use and Main Functions
a:b # To generate the sequence from a to b
seq() # To generate sequences of numbers
rep() # To repeat numbers, strings, etc
max() # To identify the maximum
min() # To identify the minimum
sum() # To sum the elements
sort() # To order the elements
rank() # To obtain the ranks of the elements
x[x>=0] # To identify an select the elements that are nonnegative
which() # To identify the elements verifying a logical condition
vector() # To create a vector
matrix() # To create a matrix
array() # To create an array
is.numeric() # To check whether an element is numeric
as.numeric() # To convert to numeric
is.character() # To check whether an element is a string
as.character() # To convert into a string
is.infinite() # To check whether a variable is the concept infinite
list() # To construct a list
unlist() # To convert a list into a vector
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Basic Use and Main Functions
c(object1,...,objectX) # To combine numbers, strings, etc
c(3,5,NA,4) # There may be missing data ('not available')
cbind(object1,...,objectX) # To combine objects as columns
rbind(object1,...,objectX) # To combine objects as rows
paste() # To combine vectors as strings
apply(x1,n1,function1) # To apply a function to margins of arrays
tapply(x1,list1,function1)
ave(x1,y1)
by()
tabulate() # To create the frequency table of a vector of integer values
table() # To create a contingency table (by using a factor)
cumsum() # To get a a vector whose elements are the cumulative sums,
products, minima or maxima of the elements of the argument
x11() # To open a new window for figures; otherwise, the last one is used
plot() # To plot objects
matplot() # To plot the columns of one matrix against the columns of
another
par(mfcol=c(4,2), lty=1, lwd=3, bty='n') # To change plotting parameters
Sys.sleep() # For the system to suspend executions for a while
call(function, argument1, argument2) # Another way to call a function
eval(expression) # To evaluate literally a string expression
assign('name', value, .GlobalEnv) # To assign a value to a variable in an

environment
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Basic Use and Main Functions
Some Useful Methods and Prefixes
print. as.
plot. is.
summary.
How to Define Functions
f1 = function(x) (1/2)^x
f2 = function(x) { a=2^2; a*x }
f3 = function(x) f1(x)+f2(x)
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Basic Use and Main Functions
Some Functions of Our Own
Now we define some functions that will be used several times throughout this document:
ourSampleMean = function(x) sum(x)/length(x)
ourSampleSD1 = function(x) sqrt(mean((x-mean(x))^2))
ourSampleSD2 = function(x) sqrt(sum((x-sum(x)/length(x))^2)/length(x))
ourSampleQuasiSD1 = function(x) sqrt( mean((x-mean(x))^2)*length(x)/(length(x)-1))
ourSampleQuasiSD2 = function(x) sqrt(sum((x-sum(x)/length(x))^2)/(length(x)-1))
ourSampleSkewness1 = function(x) mean((x-mean(x))^3)/(mean((x-mean(x))^2)^1.5)
ourSampleSkewness2 = function(x) mean((x-mean(x))^3)/(sd(x)^3)
ourSampleKurtosis1 = function(x) mean((x-mean(x))^4)/(mean((x-mean(x))^2)^2)
ourSampleKurtosis2 = function(x) mean((x-mean(x))^4)/(sd(x)^4)
Due to the use of sd(), the second versions of the skewness and the kurtosis provide values
slightly different from the first versions. There exist different estimators of the (population)
skewness and kurtosis, and some of them are biased while others are simpler and “more natural”.
The user must consult the literature before working with one in important tasks.
# Our mass and distribution functions for the negative hypergeometric distribution
#(for future us)
dnhyperOUR = function(x, N, kappa, nu)
{ (choose(x-1,nu-1)*choose(N-x,kappa-nu))/choose(N,kappa) }
pnhyperOUR = function(x, N, kappa, nu) { cumsum(dnhyperOUR(x, N, kappa, nu)) }