R and R studio

• R is a programming language for data analysis and statistical computing
• R studio is an environment for the R language that provides user-friendly interface

Installation

Even if you use RStudio, you’ll still need to download R to your computer. RStudio helps you use the version of R that lives on your computer, but it doesn’t come with a version of R on its own.

• download and install R at https://cran.r-project.org
• download and install R studio at https://rstudio.com/products/rstudio/download/#download

Install and load packages

Currently, the CRAN package repository features 20646 available packages.

• In RStudio’s console, install a package named packageName with the command install.packages("packageName"). This command only needs to be run once for each package.
• Or, click the install button under Rstudio’s Packages tab, select install from repository, and enter the packageName.
• Load the package with library(packageName) at the start of each new R session when you plan to use the package. You can load packages in Rstudio’s Console, an R script file, or an R markdown file.

R Markdown

This is an R Markdown document. It is a file format in R that lets you mix text, figures, R code, and the code’s results in one document, which can be HTML, PDF, or MS Word. When you click the Knit button a document will be generated.

For more details on using R Markdown see the NYTcovid files on Canvas, as well as http://rmarkdown.rstudio.com.

Tufte handout style

• Install by running install.packages("tufte") in the Rstudio Console.
• To make a new R Markdown document using Tufte style: Go to File > New File > R Markdown > From template > Tufte Handout.
• Below, we list a few commonly used features. For more examples, see the Rstudio Tufte Handout template.

The Tufte handout style is a style that Edward Tufte uses in his books and handouts. Tufte’s style is known for its extensive use of sidenotes, tight integration of graphics with text, and well-set typography.

Any use of a footnote will automatically be converted to a sidenote.11 This is a sidenote that was entered using a footnote.

To place ancillary information in the margin without the sidenote mark (the superscript number), you can use the margin_note() function. ⊕This is a margin note. Notice that there is no number preceding the note.

Or, you can write a chunk starting with ```{marginfigure} instead of R code chunks ```{r}. See an example on the right about the first fundamental theorem of calculus. ⊕We know from the first fundamental theorem of calculus that for \(x\) in \([a, b]\): \[\frac{d}{dx}\left( \int_{a}^{x} f(u)\,du\right)=f(x).\]

By default, figures are placed in the main column.

When you want a margin figure, all you need to do is the chunk option fig.margin = TRUE.

simple margin picture.

a <- c(1:10)
plot(a)

When you want a full-width figrue, set fig.fullwidth = TRUE.

a <- c(1:10)
plot(a)

simple full-width picture.

This style provides first and second-level headings (that is, # and ##), demonstrated in the next section. You may get unexpected output if you try to use ### and smaller headings.

References can be displayed as margin notes for HTML output. For example, we can cite R here (⊕R Core Team 2025R Core Team. 2025. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.).

⊕In R, both = and <- can be used for assigning a value to variables. ⊕R uses 1-indexing, meaning that the indexing of elements in vectors and matrices starts at 1, not 0 as in some other programming languages.

Vectors

vector_a <- c(1:10)
cat("vector_a:", vector_a,'\n') 

## vector_a: 1 2 3 4 5 6 7 8 9 10

#cat stands for "concatenate and print"
vector_b <- seq(1, 10, by=2)  
# Create a vector with a sequence of numbers
cat("vector_b:", vector_b,'\n')

## vector_b: 1 3 5 7 9

vector_c <- rep(2, length(vector_b))  
# Replicate 2, matching the length of vector_c
cat("vector_c:", vector_c,'\n')

## vector_c: 2 2 2 2 2

vector_d <- vector_b + vector_c 
# Element-wise addition of vectors
cat("vector_d:", vector_d,'\n')

## vector_d: 3 5 7 9 11

Matrices

matrix_a <- matrix(1:9, nrow=3, byrow=TRUE)  
# A 3x3 matrix with values 1 to 9
print(matrix_a)

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
## [3,]    7    8    9

matrix_b <- diag(3) 
# Create a 3x3 identity matrix
print(matrix_b)

##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1

# Element-wise multiplication of matrices
element_wise_product <- matrix_a * matrix_b
print(element_wise_product)

##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    5    0
## [3,]    0    0    9

# Matrix multiplication
product_matrix <- matrix_a %*% matrix_b
print(product_matrix)

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
## [3,]    7    8    9

# Applying a function to rows of a matrix
row_means <- apply(matrix_a, 1, mean)  
# Calculate mean of each row
print(row_means)

## [1] 2 5 8

# Eigenvalues and eigenvectors of a matrix
eigen_values_vectors <- eigen(matrix_a)
print(eigen_values_vectors$values)

## [1]  1.611684e+01 -1.116844e+00 -1.303678e-15

# Accessing eigenvectors
eigenvectors <- eigen_values_vectors$vectors
# Indexing an eigenvector, e.g., the first eigenvector
first_eigenvector <- eigenvectors[, 1]
# Print the first eigenvector
print(first_eigenvector)

## [1] -0.2319707 -0.5253221 -0.8186735