[1] 12Introduction to R and RStudio
Raphael Morsomme
Welcome
Meet the instructor
- Ph.D. candidate in statistics at Duke University
- Research focus: stochastic epidemic models and breast cancer overdiagnosis
- Fan of Formula 1 and model building
- UCM alum of 2018
Objectives of the workshop
- to introduce you to
RandRStudio - to give you the tools to conduct the data analysis portion of your research project in
R
Expectations
- What background is assumed for the workshop? Everyone is welcome.
-
Will we be doing coding? Yes. We will use
R. -
What if I have never coded? I do not expect participants to have any experience with
Ror any other programming language. -
Will we learn the mathematical theory of statistics? No. We will only learn to visualize and implement simple statistical models in
R.
Outline
- data analysis
-
RandRStudio - manipulating numbers, vectors and dataframes
- visualization
- modeling
- visualizing models
Data analysis
What is data analysis?
“Data analysis is a process of inspecting, cleansing, transforming, and modelling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. (…) In today’s business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively.”
Source: Wikipedia
Examples of data analyses in practice
R and RStudio
Why R
- free and open-source,
- large community of users (stackoverflow)
- used in almost every industry
- go-to programming language for statisticians, and
- great tools for visualization
Getting started
Getting started with RStudio
Manipulating numbers
Using R as a calculator
Type the following in the Console (lower left corner in RStudio)
and press (ctrl/command + enter) to run the line of code.
Instead of typing, you can also simply copy and paste the code in the console.
Calculating more complex expressions
The sky is the limit.
Assigning values
Suppose you want to use the number
for different purposes, e.g. multiply it, divide it, raise it to different powers, etc.
We can simply store this number by assign it to some object with the command =.
The object x is the number I wanted to save.
Reconstructing x
Let us use what we just learned to reconstruct x from the numerator, denominator and exponent.
The environment
Check the environment in the upper right corner. It contains the objects that you have created.
you should see the objects denom, expon, numer, x and x_reconstructed.
Note that x and x_reconstructed have the same value!
Simple operations
Here is a list of R commands for common mathematical operations
On the previous slide, note that the last line of code is equivalent to the following two lines
Manipulating vectors
Vectors
A vector of length \(k\) is simply a sequence of \(k\) numbers.
In R, we create vectors with the c command
Assigning a vector
I can of course assign a vector to an object
Overwriting objects
Note that this piece of code replaced the previous object x present in the environment. The previous value of x is now lost.
Operations on vectors
Here is a list of R commands for common operations on vectors
Manipulating dataframes
Dataframes
A dataframe is simply a collection of vectors of same length.
Vectors: columns
Dataframes: rectangles
Libraries
Packages are user-created collections of new functions for R.
Packages need to be
- installed on your machine once
- loaded every session.
The mpg dataframe
For simplicity, I assign the dataframe mpg to the object d
I print its first few rows for inspection with the command head.
# A tibble: 6 x 11
manufacturer model displ year cyl trans drv cty hwy fl class
<chr> <chr> <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <chr>
1 audi a4 1.8 1999 4 auto(l5) f 18 29 p compa~
2 audi a4 1.8 1999 4 manual(m5) f 21 29 p compa~
3 audi a4 2 2008 4 manual(m6) f 20 31 p compa~
4 audi a4 2 2008 4 auto(av) f 21 30 p compa~
5 audi a4 2.8 1999 6 auto(l5) f 16 26 p compa~
6 audi a4 2.8 1999 6 manual(m5) f 18 26 p compa~Dimensions of mpg
The commands nrow and ncol respectively provide the number of rows (observations) and columns (variables) of a dataframe.
Accessing variables
I use the command $ to access a variable
[1] 1.8 1.8 2.0 2.0 2.8 2.8 3.1 1.8 1.8 2.0 2.0 2.8 2.8 3.1 3.1 2.8 3.1 4.2
[19] 5.3 5.3 5.3 5.7 6.0 5.7 5.7 6.2 6.2 7.0 5.3 5.3 5.7 6.5 2.4 2.4 3.1 3.5
[37] 3.6 2.4 3.0 3.3 3.3 3.3 3.3 3.3 3.8 3.8 3.8 4.0 3.7 3.7 3.9 3.9 4.7 4.7
[55] 4.7 5.2 5.2 3.9 4.7 4.7 4.7 5.2 5.7 5.9 4.7 4.7 4.7 4.7 4.7 4.7 5.2 5.2
[73] 5.7 5.9 4.6 5.4 5.4 4.0 4.0 4.0 4.0 4.6 5.0 4.2 4.2 4.6 4.6 4.6 5.4 5.4
[91] 3.8 3.8 4.0 4.0 4.6 4.6 4.6 4.6 5.4 1.6 1.6 1.6 1.6 1.6 1.8 1.8 1.8 2.0
[109] 2.4 2.4 2.4 2.4 2.5 2.5 3.3 2.0 2.0 2.0 2.0 2.7 2.7 2.7 3.0 3.7 4.0 4.7
[127] 4.7 4.7 5.7 6.1 4.0 4.2 4.4 4.6 5.4 5.4 5.4 4.0 4.0 4.6 5.0 2.4 2.4 2.5
[145] 2.5 3.5 3.5 3.0 3.0 3.5 3.3 3.3 4.0 5.6 3.1 3.8 3.8 3.8 5.3 2.5 2.5 2.5
[163] 2.5 2.5 2.5 2.2 2.2 2.5 2.5 2.5 2.5 2.5 2.5 2.7 2.7 3.4 3.4 4.0 4.7 2.2
[181] 2.2 2.4 2.4 3.0 3.0 3.5 2.2 2.2 2.4 2.4 3.0 3.0 3.3 1.8 1.8 1.8 1.8 1.8
[199] 4.7 5.7 2.7 2.7 2.7 3.4 3.4 4.0 4.0 2.0 2.0 2.0 2.0 2.8 1.9 2.0 2.0 2.0
[217] 2.0 2.5 2.5 2.8 2.8 1.9 1.9 2.0 2.0 2.5 2.5 1.8 1.8 2.0 2.0 2.8 2.8 3.6This is simply a vector. I can assign it to a object and manipulate it.
Break
Visualization
Visualization
“The simple graph has brought more information to the data analyst’s mind than any other device.” — John Tukey
“The greatest value of a picture is when it forces us to notice what we never expected to see.” — John Tukey
Types of variables
Roughly speaking, there are two types of variables
- numerical (height, age, number of siblings, etc)
- categorical (eye color, level of education, place of birth, etc)
Histograms
A histogram summarizes the distribution of a continuous variable. Simply use the command hist.
Title, axis label and number of bins
We can improve the figure by adding a title, improving the x-axis label and changing the number of breaks
Help files
The help file of a R function describes
- what a function does,
- what arguments are available (e.g.
xlab,main,breaks) - a few examples (often)
Boxplots
Boxplots are a more compact way than histograms to summarizes the distribution of a continuous variable. To make a boxplot, simply use the command boxplot.
Figure editing
Again, we can add a title and a y-axis label to improve the figure.
Scatterplot
Scatterplot are used to visualize the relationship between two continuous variables
Figure editing
Tables
To summarize a categorical variable, we can use a table
Table for numerical variable?
What happens if we make a table for a numerical variable?
12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 41
5 2 10 7 31 10 13 11 2 7 7 13 15 32 14 7 22 4 7 4 2 1 2 2 1 1
44
2 This is not helpful! A histogram would be much better.
R is only a tool
R is only a tool. It will let you use it to do stupid things!
Two-way tables
To look at the relation between two categorical variables, we can use a two-way table
Modeling (requires statistics)
t-test
Is the fuel consumption in the city and on the highway the same?
Welch Two Sample t-test
data: d$cty and d$hwy
t = -13.755, df = 421.79, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-7.521683 -5.640710
sample estimates:
mean of x mean of y
16.85897 23.44017 Scientific notation
e-16 is equivalent to the scientific notation \(10^{-16}\).
Paired t-test
Actually, we should use a paired t-test in this case.
Simple linear regression
Call:
lm(formula = hwy ~ cty, data = d)
Residuals:
Min 1Q Median 3Q Max
-5.3408 -1.2790 0.0214 1.0338 4.0461
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.89204 0.46895 1.902 0.0584 .
cty 1.33746 0.02697 49.585 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.752 on 232 degrees of freedom
Multiple R-squared: 0.9138, Adjusted R-squared: 0.9134
F-statistic: 2459 on 1 and 232 DF, p-value: < 2.2e-16Multiple linear regression
Call:
lm(formula = hwy ~ cty + displ, data = d)
Residuals:
Min 1Q Median 3Q Max
-5.3124 -1.2423 0.0053 1.0296 4.1243
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.15145 1.21271 0.949 0.343
cty 1.32914 0.04490 29.602 <2e-16 ***
displ -0.03432 0.14791 -0.232 0.817
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.756 on 231 degrees of freedom
Multiple R-squared: 0.9138, Adjusted R-squared: 0.913
F-statistic: 1224 on 2 and 231 DF, p-value: < 2.2e-16Interactions
Call:
lm(formula = hwy ~ cty + displ + cty:displ, data = d)
Residuals:
Min 1Q Median 3Q Max
-4.2546 -1.0888 0.1424 0.8978 4.1637
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.32675 1.48875 3.578 0.000422 ***
cty 1.03665 0.07795 13.299 < 2e-16 ***
displ -1.69320 0.39471 -4.290 2.64e-05 ***
cty:displ 0.12029 0.02670 4.505 1.06e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.687 on 230 degrees of freedom
Multiple R-squared: 0.9208, Adjusted R-squared: 0.9198
F-statistic: 891.2 on 3 and 230 DF, p-value: < 2.2e-16Or simply
Call:
lm(formula = hwy ~ cty * displ, data = d)
Residuals:
Min 1Q Median 3Q Max
-4.2546 -1.0888 0.1424 0.8978 4.1637
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.32675 1.48875 3.578 0.000422 ***
cty 1.03665 0.07795 13.299 < 2e-16 ***
displ -1.69320 0.39471 -4.290 2.64e-05 ***
cty:displ 0.12029 0.02670 4.505 1.06e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.687 on 230 degrees of freedom
Multiple R-squared: 0.9208, Adjusted R-squared: 0.9198
F-statistic: 891.2 on 3 and 230 DF, p-value: < 2.2e-16ANOVA
Pairwise t-tests
pairwise.t.test(
x = d$hwy, # response variable
g = d$class, # grouping variable
p.adjust.method = "bonferroni" # Bonferroni correction to control type-I error rate.
)
Pairwise comparisons using t tests with pooled SD
data: d$hwy and d$class
2seater compact midsize minivan pickup subcompact
compact 0.59562 - - - - -
midsize 1.00000 1.00000 - - - -
minivan 1.00000 7.1e-06 0.00052 - - -
pickup 3.9e-05 < 2e-16 < 2e-16 0.00011 - -
subcompact 0.82210 1.00000 1.00000 2.9e-05 < 2e-16 -
suv 0.00064 < 2e-16 < 2e-16 0.00335 1.00000 < 2e-16
P value adjustment method: bonferroni Visualizing models
Visualizing simple regression
Visualizing ANOVA
Going further
Two excellent books
Introduction to Modern Statistics, available on Openintro
R for Data Science, available on R4DS
Both books are freely available online.
Raphael Morsomme
Introduction to R and RStudio Raphael Morsomme
Comments
What follows a “#” is a comment
The part
2 ^ 10is run byRand the part# exponentis ignored byR.Comments are useful for communicating with collaborators.