Lecture 3: Introduction to R

Lecture 3: Introduction to R#

Note

R is an open-source programming language and software environment specifically designed for statistical computing, data analysis, and data visualization. Originally developed by statisticians Ross Ihaka and Robert Gentleman in the early 1990s, R has since grown into a powerful tool used by scientists, researchers, and analysts across a range of disciplines. Its strength lies in its extensive ecosystem of packages, active community support, and seamless integration with advanced statistical methods, making it ideal for tasks such as hypothesis testing, regression modeling, data mining, and creating high-quality visualizations.

Installing R and RStudio on Windows#

Follow these steps:

Step 1: Install R#

  1. Visit https://cran.r-project.org

  2. Click on “Download R for Windows” > “base” > Download the installer

  3. Run the .exe file and follow installation instructions

Step 2: Install RStudio#

  1. Visit https://posit.co/download/rstudio-desktop/

  2. Download the RStudio Desktop version for Windows

  3. Run the installer and follow instructions

Once installed, open RStudio to begin writing R code!

Hello World!#

# Hello World in R
print("Hello World!")

[1] "Hello World!"

Data Types in R#

R supports the following basic data types:

  • Character

  • Numeric

  • Integer

  • Logical

  • Complex

Here are some examples:

# Character
x <- "CE5540"
message("Type of x is: ", typeof(x))

# Numeric
r <- 3.14
message("Type of y is: ", typeof(r))

# Integer
v <- 42L
message("Type of v is: ", typeof(v))

# Logical
f <- TRUE
message("Type of f is: ", typeof(f))

# Complex
z <- 2 + 3i
message("Type of z is: ", typeof(z))

Type of x is: character

Type of y is: double

Type of v is: integer

Type of f is: logical

Type of z is: complex

Data Structures in R#

R supports the following data structures:

  • Vectors

  • Matrices

  • Lists

  • Data Frames

Here are some examples:

# Vectors
v1 <- c("Apple", "Banana", "Mango")
v2 <- c(9, 1, 5, 4, 6, 7, 0, 3, 8)
v3 <- c(1:5)
message("# Vectors")
print(v1)
print(v2)
print(v3)
message("Accessing a value in a vector: v1[1] = ", v1[1], ". Notice that R follows 1-based indexing!")

# Matrices
m1 <- matrix(c(9, 1, 5, 4, 6, 7, 0, 3, 8), nrow = 3, byrow = TRUE)
m2 <- matrix(c(9, 1, 5, 4, 6, 7, 0, 3, 8), nrow = 3, byrow = FALSE)
message("\n# Matrices")
print(m1)
print(m2)
message("Accessing a value in a matrix: m1[1][3] = ", m1[1,3])

# Lists
l <- list(name="John", age=25L, scores=c(90, 85, 88))
message("\n# List")
print(l)
message("Accessing a value in a list: l$name = ", l$name)

# Data Frames
df <- data.frame(Name=c("Alice", "Bob"), Age=c(23L, 25L))
message("\n# Data Frames")
print(df)
message("Accessing a value in a data frame: df$Age[1] = ", df$Age[1])

# Vectors

[1] "Apple"  "Banana" "Mango" 
[1] 9 1 5 4 6 7 0 3 8
[1] 1 2 3 4 5

Accessing a value in a vector: v1[1] = Apple. Notice that R follows 1-based indexing!


# Matrices

     [,1] [,2] [,3]
[1,]    9    1    5
[2,]    4    6    7
[3,]    0    3    8
     [,1] [,2] [,3]
[1,]    9    4    0
[2,]    1    6    3
[3,]    5    7    8

Accessing a value in a matrix: m1[1][3] = 5


# List

$name
[1] "John"

$age
[1] 25

$scores
[1] 90 85 88

Accessing a value in a list: l$name = John


# Data Frames

   Name Age
1 Alice  23
2   Bob  25

Accessing a value in a data frame: df$Age[1] = 23

Control Flow#

Here is how you would write control flow statements in R

x <- 10

if (x > 0) {
  message("x is a positive number")
} else if (x < 0) {
  message("x is a negative number")
} else {
  message("x is zero!")
}

x is a positive number

Writing Loops in R#

R supports both for and while loops.

# For loop
message("# For Loop")
for (i in 1:5) {
  message("Iteration:", i)
}

# While loop
message("\n\n# While Loop")
i <- 1
while (i <= 5) {
  message("Count:", i)
  i <- i + 1
}

# For Loop

Iteration:1

Iteration:2

Iteration:3

Iteration:4

Iteration:5



# While Loop

Count:1

Count:2

Count:3

Count:4

Count:5

Writing Functions in R#

Functions are blocks of code that can be reused. Here’s how to define and call one.

# Factorial Function (Iterative Form)
factorial_iterative <- function(n) {
  result <- 1
  for (i in 2:n) {
    result <- result * i
  }
  return(result)
}

# Example usage
factorial_iterative(5)
120
# Factorial Function (Recursive Form)
factorial_recursive <- function(n) {
  if (n == 0 || n == 1) {
    return(1)
  } else {
    return(n * factorial_recursive(n - 1))
  }
}

# Example usage
factorial_recursive(5)
120

Summarising Data in R#

In this segment of the lecture, we will develop measures of location, dispersion, and shape discussed in the previous lecture through 2024 ITUS sample individual dataset.

# 2024 ITUS Individual Data (original)
url  <- "https://raw.githubusercontent.com/anmpahwa/CE5540/refs/heads/main/resources/ITUS_IND_OG.csv"
data <- read.csv(url) # Loading Data
message("2024 ITUS sample individual data is retreived as ", typeof(data), " as follows: ")
str(data)             # Data Structure

2024 ITUS sample individual data is retreived as list as follows: 

'data.frame':	533719 obs. of  23 variables:
 $ survey_year      : int  2024 2024 2024 2024 2024 2024 2024 2024 2024 2024 ...
 $ fsu_serial_no    : int  30010 30010 30010 30010 30010 30010 30010 30010 30010 30010 ...
 $ sector           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ nss_region       : int  241 241 241 241 241 241 241 241 241 241 ...
 $ district         : int  17 17 17 17 17 17 17 17 17 17 ...
 $ stratum          : int  13 13 13 13 13 13 13 13 13 13 ...
 $ sub_stratum      : int  11 11 11 11 11 11 11 11 11 11 ...
 $ sub_round        : int  2 2 2 2 2 2 2 2 2 2 ...
 $ fod_sub_region   : int  2420 2420 2420 2420 2420 2420 2420 2420 2420 2420 ...
 $ nsc              : int  4 4 4 4 4 4 4 4 4 4 ...
 $ household_id     : int  1 2 2 2 2 3 3 3 3 3 ...
 $ individual_id    : int  1 1 2 3 4 1 2 3 4 5 ...
 $ response_code    : int  1 1 1 1 99999 1 1 1 1 1 ...
 $ day_of_week      : int  2 3 3 3 99999 7 7 7 7 7 ...
 $ type_of_day      : int  1 1 1 1 99999 1 1 1 1 1 ...
 $ relation_to_head : int  1 1 2 4 6 1 2 5 5 5 ...
 $ gender           : int  1 1 2 2 1 1 2 1 1 2 ...
 $ age              : int  45 54 52 29 3 48 44 23 13 18 ...
 $ marital_status   : int  1 2 2 2 1 2 2 1 1 1 ...
 $ education_level  : int  10 6 4 10 1 5 2 5 4 4 ...
 $ employment_status: int  10 94 92 31 99999 51 92 11 91 92 ...
 $ industry         : int  85 99999 99999 86 99999 1 99999 1 99999 99999 ...
 $ weight           : num  208857 208857 208857 208857 208857 ...

library(dplyr)

# Filtering out into a smaller dataset
data <- data %>% filter(data$nss_region==241, data$employment_status==81)
View(data)
A data.frame: 78 × 23
survey_yearfsu_serial_nosectornss_regiondistrictstratumsub_stratumsub_roundfod_sub_regionnsc⋯day_of_weektype_of_dayrelation_to_headgenderagemarital_statuseducation_levelemployment_statusindustryweight
<int><int><int><int><int><int><int><int><int><int>⋯<int><int><int><int><int><int><int><int><int><dbl>
2024300101241171311224204⋯1151221108199999208857
2024300131241261310124234⋯4151181 58199999207000
2024300131241261310124234⋯7161181 58199999207000
2024300131241261310124234⋯7151191 48199999207000
2024300141241291311424204⋯7151351 28199999196571
2024300191241241311324244⋯2161181 48199999233429
20243004012412513 3124234⋯6161281 18199999214629
20243004012412513 3124234⋯4151201 58199999214629
20243004712412113 4424204⋯6112783 18199999269500
20243004812412513 3224234⋯1151221 48199999177739
20243007012412013 8324204⋯6151181 58199999225129
20243007012412013 8324204⋯3161181 58199999225129
20243009012412113 6224204⋯2151251 58199999267650
20243009212412113 5224204⋯3151221 58199999152221
2024308201241231313324244⋯6151191 68199999211693
2024308201241231313324244⋯7151281108199999211693
2024308211241181314224204⋯2161181 48199999173107
2024308231241251312124234⋯4131352 58199999261914
2024308231241251312124234⋯1131522 58199999261914
2024308231241251312124234⋯2151351 48199999261914
2024308231241251312124234⋯2132384 58199999261914
2024308291241261314124234⋯5151201 48199999236268
2024308341241181316324204⋯5111552 58199999193541
2024308371241231317324244⋯7151231118199999235750
2024308381241231316224244⋯4151401 58199999283938
2024308391241231316124244⋯5151281 68199999304798
2024308391241231316124244⋯7151321 38199999304798
2024308621241251317224234⋯4131332 48199999276000
2024308621241251317224234⋯7261171 58199999276000
2024308631241251317424234⋯1151211 48199999267950
⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋱⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
20246648322412113124204⋯5161171 58199999 322071
20246648322412113124204⋯4152 81 28199999 322071
20246648722412321424244⋯4181481 88199999 194448
20246648722412321424244⋯4161161 28199999 194448
20246648722412321424244⋯5131442 68199999 194448
20246648722412321424244⋯1111542108199999 194448
20246649022411942424204⋯5131352118199999 185784
20246649122411943324204⋯1161241 48199999 156975
20246649122411943324204⋯5151291118199999 156975
20246649322411941324204⋯2161292 58199999 208214
20246649822411942224204⋯2151291 58199999 211621
20246692022412556424234⋯61512511081999991005964
20246692022412556424234⋯6151191 481999991005964
20246692022412556424234⋯61522311081999991005964
20246692722412557424234⋯4151231 78199999 201875
20246692722412557424234⋯4151221 78199999 201875
20246692822412556324234⋯5111422 58199999 282161
20246692922412556124234⋯1161181 58199999 274800
20246693022412558324234⋯6151231 48199999 403196
20246693022412558324234⋯6151221108199999 403196
20246693022412558324234⋯6151201 58199999 403196
20246693322412557324234⋯1111301 28199999 166813
20246693322412557324234⋯7251151 48199999 166813
20246693322412557324234⋯3151211 38199999 166813
20246693422412559224234⋯4151301108199999 179852
20246693422412559224234⋯3111522 48199999 179852
20246693422412559224234⋯3151211108199999 179852
20246693522412558424234⋯2152251108199999 322557
20246693522412558424234⋯5151191 48199999 322557
20246693922412559424234⋯4151241108199999 253698
 
# Creating frequency table
v  <- sort(unique(data$age))
f  <- numeric(length(v))
for (r in 1:nrow(data)) {
  z <- data$age[r]
  i <- which(v == z)
  f[i] <- f[i] + 1
}
df <- data.frame(x=v, f=f)
View(df)
A data.frame: 30 × 2
xf
<int><dbl>
81
152
162
173
188
195
203
213
228
236
242
254
263
284
293
302
321
331
355
361
381
401
411
421
441
481
522
541
551
781
 
# Measures of Location
df <- data.frame(x=v, f=f/sum(f)) 

## Mean
### Manually Computed Mean
v1 <- sum(df$x * df$f)
### Auto Computed Mean
v2 <- mean(data$age)
message("Manually Computed Mean = ", round(v1, digits=3), " and Auto Computed Mean = ", round(v2, digits=3))

## Median
### Manually Computed Median
qtl <- function (x, f, p) {
  v <- NA
  F <- cumsum(f)
  n <- length(x)
  for (i in 2:n) {
      if (F[i] == p) {
        v <- (x[i] + x[i+1]) / 2
        return(v)
      }
      if (F[i-1] < p & F[i] > p) {
        v <- x[i]
        return(v)
      }
  }
}
v1 <- qtl(df$x, df$f, 0.5)
### Auto Computed Median
v2 <- median(data$age)
message("Manually Computed Median = ", round(v1, digits=3), " and Auto Computed Median = ", round(v2, digits=3))

## Mode
v <- df$x[which.max(df$f)]
message("Mode = ", v)

Manually Computed Mean = 26.949 and Auto Computed Mean = 26.949

Manually Computed Median = 23 and Auto Computed Median = 23

Mode = 18

# Measures of Dispersion

## Range
v = max(df$x) - min(df$x)
message("Range = ", v)

## Inter-Quartile Range
### Manually Computed Inter-Quartile Range
v1 <- qtl(df$x, df$f, 0.75) - qtl(df$x, df$f, 0.25)
### Auto Computed Inter-Quartile Range
v2 <- IQR(data$age)
message("Manually Computed Inter-Quartile Range = ", round(v1, digits=3), " and Auto Computed Inter-Quartile Range = ", round(v2, digits=3))

## Standard Deviation
### Manually Computed Standard Deviation
v1 <- sqrt(sum(df$f * (df$x - sum(df$x * df$f))^2))
### Auto Computed Standard Deviation
v2 <- sd(data$age)
message("Manually Computed Standard Deviation = ", round(v1, digits=3), " and Auto Computed Standard Deviation = ", round(v2, digits=3))

Range = 70

Manually Computed Inter-Quartile Range = 11 and Auto Computed Inter-Quartile Range = 11

Manually Computed Standard Deviation = 11.35 and Auto Computed Standard Deviation = 11.423

# Measures of Shape
library(moments)

## Skewness
### Manually Computed Skewness
v1 <- (sum(df$f * (df$x - sum(df$x * df$f))^3)) / (sqrt(sum(df$f * (df$x - sum(df$x * df$f))^2)))^3
### Auto Computed Skewness
v2 <- skewness(data$age)
message("Manually Computed Skewness = ", round(v1, digits=3), " | Auto Computed Skewness = ", round(v2, digits=3))

## Kurtosis
### Manually Computed Kurtosis
v1 <- (sum(df$f * (df$x - sum(df$x * df$f))^4) / sum(df$f)) / (sqrt(sum(df$f * (df$x - sum(df$x * df$f))^2)))^4
### Auto Computed Kurtosis
v2 <- kurtosis(data$age)
message("Manually Computed Kurtosis = ", round(v1, digits=3), " | Auto Computed Kurtosis = ", round(v2, digits=3))

Manually Computed Skewness = 1.816 | Auto Computed Skewness = 1.816

Manually Computed Kurtosis = 7.337 | Auto Computed Kurtosis = 7.337
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