An introduction to R

1. BCBB Workshop
An introduction to R
Kui Shen, PhD
Bioinformatics and Computational Biosciences Branch (BCBB)
National Institute of Allergy and Infectious Diseases (NIAID)

2. OCICB Bioinformatics and Computational
Biosciences Branch (BCBB)
§ Part of NIAID
§ Group of ~40
§ Software developers
§ Computational biologists
§ Project management &
analysis professionals
§ Biostatistics, phylogenetics,
genomics, structural
biology, programming

3. What will we learn today?
§ R basics
• Arithmetic
• Matrix algebra
• Graphics
• Statistical tests
• Importing and exporting data
• Installing packages
§ Basic statistics with R
• Descriptive statistics
• General linear regression

4. What’s R?
• R is a language and environment for statistical computing and
• graphics. It is an open-source and free software package.

5. What can R do? -- Importing and
manipulating data
§ Importing data.
• Basic text files. (read.table).
• Excel files. ( read.xls in the gdata package).
§ Manipulating data.
• Indexing and subsetting.
• Merging and Reshaping.
An example: from wide format to long format (help('reshape'))

6. What can R do? -- Data analysis
§ Statistical data analysis
• Descriptive statistics
• One- and two-sample tests
• Regression and correlation
• Analysis of variance
• Tabular data
• Power and sample size estimation
• Mixed model
§ Genetic and genomic data analysis (Bioconductor)
• Microarray
• Next generation sequencing

7. What can R do? -- Visualization

8. What can R do? -- Visualization
xyplot(Counts~Status|sample,data=dat)

9. What can R do? – Generating reports 1
An example of Sweave code:
documentclass[a4paper]{article}
title{Sweave=R+LaTeX}
author{Kui Shen}
begin{document}
maketitle
<<LM, eval=TRUE, echo=T,fig=TRUE,
include=TRUE>>=
library(MASS)
data(cats)
mylm = lm(Hwt ~ Bwt,data=cats)
plot(Hwt ~ Bwt,data=cats, main='Linear
regression')
abline(mylm)
@
This is the embedded figure.
end{document}

10. What can R do? – Generating reports 2
An example of Sweave code:
documentclass[a4paper]{article}
title{A table generated by xtable}
begin{document}
maketitle
<<LM>>=
library(MASS)
library(xtable)
data(cats)
mylm = lm(Hwt ~ Bwt,data=cats)
@
<<echo=FALSE,results=tex>>=
print(xtable(mylm,caption=
"Linear regreesin results"))
@
end{document}

11. What can R do? – Web tools

12. Basic statistic analysis: linear regression
§ Linear model is the most fundamental topic for data
scientist.
§ Before you perform any fancy machine learning
methods, your go-to-method will be the linear model.

13. Linear correlation
Y
X
Y
X
Y
Y
X
X
Linear relationships Curvilinear relationships
n Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

14. Linear regression
§ In correlation, the two variables are treated as equals.
§ In regression, one variable is considered independent
(predictor) variable X and the other the dependent
(outcome, response) variable Y.

15. Regression equation
yi= α + β*xi + random errori
Follows a normal distributionFixed values
Regression equation:
What is ‘linear”?
The mean of the response variable is a linear combination of the
parameters (regression coefficients) and the predictor variables.

16. Assumptions for a linear regression:
§ The relationship between X and Y is linear.
§ Y is distributed normally at each value of X.
§ The variance of Y at every value of X is the
same (homogeneity of variances).
§ The observations are independent.

17. Least squares estimation (LSE)
§ Estimating the intercept and slope: least
squares estimation

18. Significance test
Distribution of slope ~ Tn-2(β,s.e.( ))βˆ
H0: β1 = 0 (no linear relationship)
H1: β1 ≠ 0 (linear relationship does exist)
)ˆ.(.
0ˆ
β
β
es
−Tn-2=

19. Residual analysis for linearity
Not Linear Linear
ü
x
residuals
x
Y
x
Y
x
residuals
n Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

20. Residual analysis for homoscedasticity
Non-constant variance
ü Constant variance
x x
Y
x x
Y
residuals
residuals
n Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

21. Residual analysis for independence
Not Independent
Independent
X
X
residuals
residuals
X
residuals
ü
n Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

22. Multivariate regression pitfalls - overfitting
§ In multivariate linear modeling, you can get significant
but meaningless results if you use too many
predictors in the model (no predictive ability for new
samples).
§ But how about big data? For example, for next
generation sequencing data, there are thousands of
genes but few samples.
§ When the number of features p is as large as, or
larger than, the number of observations n , least
squares cannot be performed. (Large p, small n
problem).

23. Linear regression for big data
§ Shrinkage Methods
• LASSO (Least Absolute Shrinkage and Selection
Operator)
§ Dimension Reduction Methods
• Principal Components Regression

24. Questions?

25. R programming: preliminaries
§ Install: http://www.r-project.org/
§ Manual: https://cran.r-project.org/manuals.html
§ Start and quit: R; q();
§ R and statistics
• Around 25 built-in statistical packages
• Much more available at:
• http://CRAN.R-project.org
• http://www.bioconductor.org
§ Getting help
• help(‘plot’)
• ?plot
§ Useful website: http://stackoverflow.com/

26. R and Rstudio
Rstudio (http://www.rstudio.com/)

27. R programming: variables and assignment
§ Variable: alphanumeric symbols, plus “.” and “_” are
allowed.
§ Variables are case sensitive, so “A” are “a” are two
different variables.
§ Assignment: <-
• A<-3; a<-4; X.1<-9;
• During the development of s at bell labs, a key
corresponding to ‘_” was printed as a by
time-shared terminal execuport.
§ In 2001, the “=“ assignment was introduced for compatibility with
other languages.

28. Arithmetic operators
§ Addition: +
§ Subtraction: -
§ Division: /
§ Multiplication: *
§ Exponentiation: ^
§ Using R as a calculator:
28

29. Function calls
§ Syntax: functionName(arg1, arg2)
§ Arguments can be specified by position or by name, while
name overrides position.
§ > log(x=16,base=2)
§ [1] 4
§ > log(16,2)
§ [1] 4
§ > log(2,16)
§ [1] 0.25
§ > log(base=2,x=16)
§ [1] 4

30. Data type
§ Three major data types: numeric, character, and
logical.
• # numeric variables
• X<-3.1
• # character variables
• X<-"Male"
• # Logical variables
• X<-TRUE; Y<-FALSE

31. Data structure: vector, matrix and array
§ Vector: an ordered collection of data.
• x<-c(3.1,4.2,5.6); y<-c("F","M","F”); z<-c(T,F,T,F,T)
• c(…) is a fonction to concatenate its arguments end
to end.
§ Matrix: two-dimensional generalizations of vectors
§ Array: multi-dimensional generalizations of vectors

32. Data structure: data frame
§ Data frames are matrix-like structures.
§ The columns in data frame can be of different data types.
§ Generate a new data frame
§ Covert a matrix to a data frame

33. Indexing and selecting
§ Indexing: appending an index
vector in square brackets to
the name of a vector, matrix or
data frame.
§ The index vector can be a
numeric vector or a character
vector.

34. Deleting
Deleting: using negative subscripts

35. Loops
Syntax:
for(variable in sequence) {
statements
}

36. Loops
Avoid ‘for’ looping and use “apply” instead if possible.

37. The “apply” family of functions
37

38. The “apply” family of functions
38
??apply

39. Conditional execution
Comparison Operators
equal: ==
not equal: !=
greater: >
less than: <
greater or equal: >=
less than or equal:<=
Logical Operators
and: &
or: |
not: !

40. Conditional execution
Syntax:
if (condition) {
statement
} else {
alternative
}

41. User-defined functions
Syntax to define a function:
myfunction <- function(arg1, arg2, ...) {
function_body
}
Syntax to call a function:
myfunction(arg1=..., arg2=...)

42. Package installation
§ Install packages from CRAN network
• install.packages(“MASS”)
§ Install packages from Bioconductor
• source("http://bioconductor.org/biocLite.R")
• biocLite("biomaRt")

43. Reading and writing
?read.table
?write.table

44. Basic Statistical Analysis
Descriptive statistics

45. Visualization: Parallel boxplots

46. T-test
46
?t.test

47. A t-test (and ANOVA) is a linear regression
47

48. Basic statistics: Linear regression
§ library(MASS)
§ data(cats)
§ ?cat

49. Data summary

50. Data visualization
plot(Hwt ~ Bwt, data=cats)
The tilde (~) operator is used to specify that Hwt is described by
Bwt.

51. Linear model
§ Express the relationship as formula: Hwt ~ Bwt
• It reads: Hwt predicted by Bwt, or Hwt as a function of
Bwt.
• Variable on the left side: dependent variable. Variable on
the right side: independent variable.
§ Hwt is not totally predicted by Bwt, we add random factors
into the linear model: Hwt ~ Bwt + ε. This model divided
Hwt related factors into two parts: factors that we can
control (systematic part) and random errors (random or
probabilistic part of the model).
§ Implement in R:
• Mylm <- lm(Hwt ~ Bwt, data=cats)
• summary(mylm)

52. Linear regression results

53. Linear regression results
§ It looks complicated. Let’s check it. The first part is the review of
linear model.
§ The second part is the residuals.

54. Residuals
§ Ideally, the residuals are independent, identically distributed (iid) random
variables.

55. Residuals

56. Outliers
§ Sample 144 looks like an outliers/influence point. How to test it?
§ plot(mylm,which=4)
§ Remove outliers and re-conduct the analysis

57. Results: coefficient table
The p-value for Bwt is same as the p-value for the
model since there is only one independent variable.
plot(Hwt ~ Bwt,data=cats)
abline(mylm)

58. Results: R-squared and p-value
§ The last part:
§ R-squared: a measure of variance explained. In this case,
64.66% our data is explained by the model.
§ Adjusted R-squared: adjusts for the number of
independent variables in a model relative to the number of
data points.
§ F-statistic is used to test if one or more of the non-constant
coefficients in the regression equation are non-zero or not.
§ Finally, we got the p-value. But what is p-value?

59. P-value
Statistic hypothesis
H0 : All non-constant coefficients in the regression model are zero.
Ha : At least one of the non-constant coefficients in the regression model
is non-zero
Under the null hypothesis, the data is unlikely when the p-value is small.

60. Report the results
• Linear regression analysis was conducted and the results
indicated that body weight significantly predicted heart weight (β
= 4.03, p<0.01). Body weight also explained a significant
proportion of variance in heart weight, R2=0.65, F(1,142)=259.8,
p<0.01.

61. Questions?