Category: Examples

Simulation studies are crucial for understanding the behavior of statistical methods. Here’s an example of simulating the Central Limit Theorem.

Step 1: Set Parameters

rCopy code# Set parameters
n <- 30  # Sample size
num_simulations <- 1000  # Number of simulations

# Set seed for reproducibility
set.seed(123)

Step 2: Simulate Sample Means

rCopy code# Simulate sample means from an exponential distribution
sample_means <- replicate(num_simulations, mean(rexp(n, rate = 1)))

# View the first few sample means
head(sample_means)

Step 3: Plot the Distribution of Sample Means

rCopy code# Plot the distribution of sample means
hist(sample_means, breaks = 30, main = "Distribution of Sample Means",
 xlab = "Sample Mean", col = "lightblue", probability = TRUE)
lines(density(sample_means), col = "red")

Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. In R, you can use functions like lapply, sapply, and map from the purrr package.

Step 1: Install and Load purrr

rCopy codeinstall.packages("purrr")
library(purrr)

Step 2: Create a Sample List

rCopy code# Create a list of numeric vectors
num_list <- list(a = 1:5, b = 6:10, c = 11:15)

Step 3: Use lapply and sapply

rCopy code# Apply a function to each element using lapply
squared_list <- lapply(num_list, function(x) x^2)
print(squared_list)

# Use sapply to simplify the output to a matrix
squared_matrix <- sapply(num_list, function(x) x^2)
print(squared_matrix)

Step 4: Use map from purrr

rCopy code# Use map to apply a function and return a list
squared_map <- map(num_list, ~ .x^2)
print(squared_map)

R can connect to databases to perform data analysis on large datasets. Here’s how to connect to a MySQL database.

Step 1: Install and Load Required Packages

rCopy codeinstall.packages("DBI")
install.packages("RMySQL")
library(DBI)
library(RMySQL)

Step 2: Connect to the Database

rCopy code# Connect to the MySQL database
con <- dbConnect(RMySQL::MySQL(), 
             dbname = "your_database_name",
             host = "your_host",
             user = "your_username",
             password = "your_password")

Step 3: Query Data

rCopy code# Query data from a table
data_db <- dbGetQuery(con, "SELECT * FROM your_table_name LIMIT 100")

# View the queried data
head(data_db)

Step 4: Disconnect from the Database

rCopy code# Disconnect from the database
dbDisconnect(con)

Geospatial data analysis is crucial for visualizing and analyzing spatial relationships. We’ll use the sf package for handling spatial data.

Step 1: Install and Load sf

rCopy codeinstall.packages("sf")
install.packages("ggplot2")  # Make sure ggplot2 is installed
library(sf)
library(ggplot2)

Step 2: Load Geographic Data

For this example, you can use built-in datasets or download shapefiles. Here, we’ll use a simple example with the nc dataset from the sf package.

rCopy code# Load the North Carolina shapefile (included in the sf package)
nc <- st_read(system.file("shape/nc.shp", package = "sf"))

# Plot the geographic data
ggplot(data = nc) +
  geom_sf() +
  labs(title = "North Carolina Counties",
   x = "Longitude", y = "Latitude") +
  theme_minimal()

Step 3: Analyze and Visualize Attributes

rCopy code# Calculate the area of each county and add it as a new column
nc$area <- st_area(nc)

# Plot with area as fill
ggplot(data = nc) +
  geom_sf(aes(fill = area)) +
  labs(title = "Area of North Carolina Counties",
   fill = "Area (sq meters)") +
  theme_minimal()

Mixed-effects models are useful when dealing with data that have both fixed and random effects. We’ll use the lme4 package for this.

Step 1: Install and Load lme4

rCopy codeinstall.packages("lme4")
library(lme4)

Step 2: Create a Sample Dataset

rCopy code# Create a sample dataset with random effects
set.seed(222)
data_mixed <- data.frame(
  id = rep(1:10, each = 10),
  x = rnorm(100),
  y = rnorm(100)
)

# Introduce a random effect
data_mixed$y <- data_mixed$y + rep(rnorm(10, mean = 5, sd = 1), each = 10)

Step 3: Fit a Mixed-Effects Model

rCopy code# Fit a mixed-effects model
model_mixed <- lmer(y ~ x + (1 | id), data = data_mixed)

# Display the model summary
summary(model_mixed)

Network analysis is essential for understanding relationships in data. We’ll use the igraph package.

Step 1: Install and Load igraph

rCopy codeinstall.packages("igraph")
library(igraph)

Step 2: Create a Sample Graph

rCopy code# Create a sample graph
edges <- data.frame(
  from = c("A", "A", "B", "C", "C", "D", "E"),
  to = c("B", "C", "D", "D", "E", "E", "A")
)

# Create a graph object
graph <- graph_from_data_frame(edges, directed = TRUE)

# Plot the graph
plot(graph, vertex.color = "lightblue", vertex.size = 30, edge.arrow.size = 0.5,
 main = "Sample Directed Graph")

Step 3: Analyze the Graph

rCopy code# Calculate degree centrality
degree_centrality <- degree(graph)
print(degree_centrality)

# Identify the largest connected component
largest_component <- components(graph)$membership
print(largest_component)

Text analysis is vital for extracting insights from unstructured data. Here, we’ll analyze a simple text corpus.

Step 1: Install and Load Required Packages

rCopy codeinstall.packages("tm")
install.packages("wordcloud")
library(tm)
library(wordcloud)

Step 2: Create a Sample Text Corpus

rCopy code# Create a sample text corpus
texts <- c("R is great for data analysis.",
       "Data science is an exciting field.",
       "R and Python are popular programming languages.",
       "Data visualization is key to understanding data.")
# Create a Corpus
corpus <- Corpus(VectorSource(texts))

# Preprocess the text (convert to lower case, remove punctuation)
corpus <- tm_map(corpus, content_transformer(tolower))
corpus <- tm_map(corpus, removePunctuation)
corpus <- tm_map(corpus, removeWords, stopwords("en"))

Step 3: Create a Term-Document Matrix

rCopy code# Create a term-document matrix
tdm <- TermDocumentMatrix(corpus)
tdm_matrix <- as.matrix(tdm)
word_freqs <- sort(rowSums(tdm_matrix), decreasing = TRUE)
word_freqs_df <- data.frame(word = names(word_freqs), freq = word_freqs)

Step 4: Generate a Word Cloud

rCopy code# Create a word cloud
set.seed(1234)
wordcloud(words = word_freqs_df$word, freq = word_freqs_df$freq, min.freq = 1,
      max.words = 100, random.order = FALSE, rot.per = 0.35,
      colors = brewer.pal(8, "Dark2"))</code></code></pre>