Hi, I’m PARVEJ HOSSAIN
a GIS Enthusiast. Cartographer. Geospatial Data Analyst.

Learn R – Part 4

1. Basic Statistical Functions

R provides built-in functions for statistical analysis:

summary(): Summary statistics (min, max, quartiles, mean).

sum(): Total of values.

range(): Minimum and maximum.

var(): Variance.

sd(): Standard deviation.

Demo Data

# Basic dataset  
data_basic <- c(2, 4, 6, 8, 10)  
# Advanced dataset (mtcars)  
data(mtcars)  

mpg <- mtcars$mpg  

Practice

# BASIC TASKS  
# HW1: Calculate the sum of data_basic  
# HW2: Find the range (min and max) of data_basic  
# HW3: Compute the variance of data_basic  

# ADVANCED TASKS  
# HW4: Calculate the standard deviation of mtcars$mpg  

# HW5: Generate a summary of mtcars$hp (horsepower)  

Solution

# BASIC SOLUTIONS  
sum_basic <- sum(data_basic)  
range_basic <- range(data_basic)  
var_basic <- var(data_basic)  

# ADVANCED SOLUTIONS  
sd_mpg <- sd(mpg)  
summary_hp <- summary(mtcars$hp)  

2. Mean, Median, Mode

Mean : Average (mean()).

Median : Middle value (median()).

Mode : Most frequent value (no built-in function—custom code required).

Demo Data

# Basic dataset  
data_numbers <- c(1, 2, 2, 3, 4, 5, 5, 5)  
# Advanced dataset (iris)  
data(iris)  
sepal_length <- iris$Sepal.Length 

Practice

# BASIC TASKS  
# HW1: Calculate the mean of data_numbers  
# HW2: Find the median of data_numbers  
# HW3: Write a function to compute the mode  

# ADVANCED TASKS  
# HW4: Compute the mean of iris$Sepal.Length  

# HW5: Find the median of iris$Petal.Length grouped by Species  

Solution

# BASIC SOLUTIONS  
mean_val <- mean(data_numbers)  
median_val <- median(data_numbers)  
mode_func <- function(x) {  
  ux <- unique(x)  
  ux[which.max(tabulate(match(x, ux)))]  
}  
mode_val <- mode_func(data_numbers)  

# ADVANCED SOLUTIONS  
mean_sepal <- mean(sepal_length)  
median_petal <- aggregate(Petal.Length ~ Species, iris, median)  

3. Max, Min, and Percentiles

max()/min(): Extreme values.

quantile(): Percentiles (e.g., 25th, 50th).

IQR(): Interquartile range.

Demo Data

# Basic dataset  
data_scores <- c(45, 67, 89, 34, 56, 78, 90, 23)  
# Advanced dataset (airquality)  
data(airquality)  

temp <- airquality$Temp  

Practice

# BASIC TASKS  
# HW1: Find the max and min of data_scores  
# HW2: Calculate the 75th percentile of data_scores  
# HW3: Compute the IQR of data_scores  

# ADVANCED TASKS  
# HW4: Find the 90th percentile of airquality$Temp  

# HW5: Identify outliers in airquality$Ozone using IQR  

Solution

# BASIC SOLUTIONS  
max_score <- max(data_scores)  
min_score <- min(data_scores)  
percentile_75 <- quantile(data_scores, 0.75)  
iqr_score <- IQR(data_scores)  

# ADVANCED SOLUTIONS  
percentile_90 <- quantile(temp, 0.90)  
# Outlier detection (IQR method)  
q1 <- quantile(airquality$Ozone, 0.25)  
q3 <- quantile(airquality$Ozone, 0.75)  
iqr <- IQR(airquality$Ozone)  
outliers <- airquality$Ozone[airquality$Ozone < (q1 - 1.5*iqr) | airquality$Ozone > (q3 + 1.5*iqr)]  

4. Hypothesis Testing (T-Test/ANOVA)

Perform t-tests (t.test()), ANOVA (aov()), and chi-square tests (chisq.test()) to compare groups.

Demo Data

# Create sample data  
group_a <- c(20, 22, 19, 18, 24)  

group_b <- c(25, 24, 22, 23, 20)  

Practice

# HW1: Perform an independent t-test between group_a and group_b  

# HW2: Run a one-way ANOVA on `mtcars` to compare `mpg` across cylinder groups  

Solution

# HW1  
t.test(group_a, group_b)  
# HW2  
cyl_groups <- split(mtcars$mpg, mtcars$cyl)  
anova_result <- aov(mpg ~ factor(cyl), data=mtcars)  
summary(anova_result)  

5. Regression Analysis (Linear Regression)

Fit linear (lm()) and logistic regression models. Use summary() to interpret coefficients and p-values.

Demo Data

# Use `mtcars` for linear regression  

Practice

# HW1: Fit a linear model predicting `mpg` from `wt` and `hp`  

# HW2: Check the R-squared value of the model  

Solution

# HW1  
model <- lm(mpg ~ wt + hp, data=mtcars)  
# HW2  
summary(model)$r.squared  

6. Data Transformation

Recode variables with dplyr::mutate() and case_when(). Create new variables using arithmetic/logical operations.

Demo Data

# Create sample data  
df <- data.frame(  
  age = c(18, 25, 30, 35, 40),  
  income = c(50000, 60000, 75000, 90000, 120000) 
 
)  

Practice

# HW1: Recode `age` into categories: "<25", "25-35", ">35"  

# HW2: Create a new variable `income_group` (Low: <70k, High: >=70k)  

Solution

# HW1  
library(dplyr)  
df <- df %>%  
  mutate(age_group = case_when(  
    age < 25 ~ "<25",  
    age >= 25 & age <= 35 ~ "25-35",  
    age > 35 ~ ">35"  
  ))  
# HW2  
df <- df %>%  
  mutate(income_group = ifelse(income >= 70000, "High", "Low"))  

7. Exporting Results

Export tables and plots using write.csv(), stargazer, or flextable.

Practice

# HW1: Save `mtcars` summary to a CSV  

# HW2: Export a ggplot to PNG  

Solution

# HW1  
write.csv(summary(mtcars), "mtcars_summary.csv")  
# HW2  
ggsave("plot.png", plot=last_plot())  

8. Additional Statistical Concepts

Skewness : Measure of asymmetry (moments package).

Kurtosis : Tailedness of the distribution (moments package).

Covariance : cov().

Correlation : cor().

Demo Data

# Advanced dataset (cars)  
data(cars)  
speed <- cars$speed  

dist <- cars$dist  

Practice

# HW1: Calculate covariance between speed and distance  
# HW2: Compute correlation between speed and distance  

# HW3: Install the `moments` package and calculate skewness of speed  

Solution

# HW1  
covariance <- cov(speed, dist)  
# HW2  
correlation <- cor(speed, dist)  
# HW3  
library(moments)  
skewness_speed <- skewness(speed)  

9. Handling Missing Values

Use na.rm = TRUE to ignore NA values in calculations.

Demo Data

data_missing <- c(1, 2, NA, 4, 5)  

Practice

# HW1: Calculate the mean of data_missing (ignore NA)  

# HW2: Check if data_missing contains any NA values  

Solution

mean_missing <- mean(data_missing, na.rm = TRUE)  
has_na <- anyNA(data_missing)  

Learn R – Part 3

1. Plot (Data Visualization)

Plots visualize trends and relationships. Use plot() for basic graphs, lines()/points() for overlays, and par() for layouts. Customize with main, xlab, ylab, col, lwd, pch, and bg.

Demo Data (Basic)

# Simple dataset for beginners  
x <- 1:10  

y <- c(2, 4, 6, 8, 7, 5, 3, 1, 9, 10)  

Demo Data (Advanced)

# Complex dataset: mtcars (built-in)  
data(mtcars)  
mpg <- mtcars$mpg  # Miles per gallon  
hp <- mtcars$hp    # Horsepower  

wt <- mtcars$wt    # Weight  

Practice

# BASIC TASKS  
# HW1: Plot x vs. y as points  
# HW2: Add a blue line to the plot  
# HW3: Create a plot with red triangles (pch=17)  

# ADVANCED TASKS  
# HW4: Plot mpg vs. hp from mtcars, add a smooth line  
# HW5: Create a multi-plot layout (2x2 grid) 

# HW6: Customize mpg vs. wt plot: title, axis labels, green points, gray background  

Solution

# BASIC SOLUTIONS  
plot(x, y)  
plot(x, y, type="l", col="blue")  
plot(x, y, pch=17, col="red")  

# ADVANCED SOLUTIONS  
plot(mpg ~ hp, data=mtcars, main="MPG vs Horsepower", col="purple")  
lines(lowess(hp, mpg), col="orange")  

par(mfrow=c(2,2))  
plot(mpg ~ hp, data=mtcars)  
plot(mpg ~ wt, data=mtcars)  
hist(mpg, col="lightblue")  
boxplot(mpg, col="yellow")  

plot(mpg ~ wt, data=mtcars,  
     main="Weight vs MPG",  
     xlab="Weight (1000 lbs)",  
     ylab="Miles Per Gallon",  
     pch=21, bg="green",  
     panel.first=grid())  

2. Pie Chart

Pie charts show proportions. Use pie(), legend(), and ifelse() for conditional formatting.

Demo Data (Basic)

# Simple sales data  
sales <- c(25, 35, 40)  

labels <- c("Apparel", "Electronics", "Groceries")  

Demo Data (Advanced)

# Complex dataset: Titanic survival rates  
survivors <- c(203, 118, 178, 528)  

groups <- c("1st Class", "2nd Class", "3rd Class", "Crew")  

Practice

# BASIC TASKS  
# HW1: Create a pie chart for sales data  
# HW2: Add a title and explode the "Groceries" slice  

# ADVANCED TASKS  
# HW3: Plot Titanic survival rates with gradient colors  
# HW4: Add a legend and percentage labels  

# HW5: Create a 3D pie chart (use plotrix package)  

Solution

# BASIC SOLUTIONS  
pie(sales, labels=labels)  
pie(sales, labels=labels, main="Sales Distribution", explode=0.1)  

# ADVANCED SOLUTIONS  
# Install the plotrix package (only needed once)
install.packages("plotrix")

# Load the package
library(plotrix)

library(plotrix)  
pie3D(survivors, labels=groups, main="Titanic Survival Rates",  
      col=heat.colors(4), explode=0.05)  

pie(survivors, labels=paste(groups, " (", round(survivors/sum(survivors)*100, 1), "%)", sep=""),  
    col=rainbow(4))  
legend("right", groups, fill=rainbow(4))  

3. Bar Chart

Bar charts compare categories. Use barplot(), beside=TRUE for grouped bars, and col for gradients.

Demo Data (Basic)

# Monthly sales  
months <- c("Jan", "Feb", "Mar")  

sales <- c(200, 450, 300)  

Demo Data (Advanced)

# Complex dataset: Olympic medal counts  
countries <- c("USA", "China", "Russia", "UK")  
gold <- c(39, 38, 20, 22)  
silver <- c(41, 32, 28, 21)  

bronze <- c(33, 18, 23, 22)  

Practice

# BASIC TASKS  
# HW1: Create a vertical bar chart for monthly sales  
# HW2: Add grid lines and rotate labels  

# ADVANCED TASKS  
# HW3: Create stacked bars for Olympic medals  
# HW4: Create grouped bars with legends  

# HW5: Add error bars using arrows()  

Solution

# BASIC SOLUTIONS  
barplot(sales, names.arg=months, main="Monthly Sales", xlab="Month", ylab="Revenue")  
barplot(sales, names.arg=months, las=2, cex.names=0.8, col="lightgreen")  
abline(h=seq(0, 500, by=100), lty=2)  

# ADVANCED SOLUTIONS  
medals <- rbind(gold, silver, bronze)  
barplot(medals, names.arg=countries, col=c("gold", "silver", "darkorange"),  
        legend=rownames(medals), main="Olympic Medals", beside=TRUE)  

# Error bars  
barplot(gold, names.arg=countries, ylim=c(0, 50), col="gold")  
arrows(x0=1:4, y0=gold-2, y1=gold+2, code=3, angle=90, length=0.1)  

Learn R – Part 2

1. Vectors

Vectors are 1D data structures holding elements of the same type .

Sort : sort() (ascending) or rev(sort()) (descending).

Create : Use c(), seq(from, to, by), or rep(value, times).

Access : Use [index] (positive/negative), logical vectors, or names.

Length : length(vector).

# HW1: Create a vector of even numbers 2, 4, 6 using `seq()`  
# HW2: Access the 3rd element of `c(10, 20, 30, 40)`  
# HW3: Sort `c(5, 1, 3)` in descending order  
# HW4: Check the length of `c("a", "b", "c")`  

# HW5: Create a vector with 3 copies of "R" using `rep()`  

# HW1  
vec_seq <- seq(2, 6, by=2)  # Output: 2, 4, 6  
# HW2  
print(c(10, 20, 30, 40)[3])  # Output: 30  
# HW3  
sorted <- rev(sort(c(5, 1, 3)))  # Output: 5, 3, 1  
# HW4  
print(length(c("a", "b", "c")))  # Output: 3  
# HW5  
vec_rep <- rep("R", 3)  # Output: "R", "R", "R"  

2. Lists

Lists store mixed or nested data .

Add/Remove : list[[new_index]] <- value or list[index] <- NULL.

Create : list().

Access : [index] (returns sublist), [[index]] (returns element), or $name.

Modify : Assign new values via [[ ]] or append().

# HW1: Create a list with "apple", 25, and a sub-list `c(1, 2)`  
# HW2: Access the sub-list `c(1, 2)` from HW1  
# HW3: Change "apple" to "banana" in the list  
# HW4: Add `TRUE` to the end of the list  

# HW5: Remove the 2nd element (25)  

# HW1  
my_list <- list("apple", 25, list(1, 2))  
# HW2  
print(my_list[[3]])  # Output: 1, 2  
# HW3  
my_list[[1]] <- "banana"  
# HW4  
my_list <- append(my_list, TRUE)  
# HW5  
my_list[2] <- NULL  

3. Matrices

Matrices are 2D, same-type data structures.

Generate Values : seq(), rep().

Create : matrix(data, nrow, ncol).

Access : [row, col], [,] for entire rows/columns.

Add Rows/Columns : rbind(), cbind().

# HW1: Create a 3x2 matrix with 1-6 using `matrix()`  
# HW2: Extract the 2nd row  
# HW3: Extract the 1st column  
# HW4: Add a row `7, 8` to the matrix  

# HW5: Create a matrix with 1, 2 repeated 3 times using `rep()`  

# HW1  
mat <- matrix(1:6, nrow=3)  
# HW2  
print(mat[2, ])  # Output: 2, 5  
# HW3  
print(mat[, 1])  # Output: 1, 2, 3  
# HW4  
mat <- rbind(mat, c(7, 8))  
# HW5  
mat_rep <- matrix(rep(1:2, 3), nrow=3)  

4. Arrays

Arrays extend matrices to multi-dimensional data .

Dimensions : dim() to check or set dimensions.

Create : array(data, dim=c(rows, cols, ...)).

Access : [i, j, k] for specific elements.

# HW1: Create a 2x2x2 array with values 1-8  
# HW2: Access the 3rd element of the 1st layer  
# HW3: Extract the 2nd layer (all rows/columns)  
# HW4: Check the total length of the array  

# HW5: Convert a vector `1:12` into a 3x4 array  

# HW1  
arr <- array(1:8, dim=c(2, 2, 2))  
# HW2  
print(arr[3])  # Output: 3  
# HW3  
print(arr[, , 2])  
# HW4  
print(length(arr))  # Output: 8  
# HW5  
arr_3d <- array(1:12, dim=c(3, 4))  

5. Data Frames

Data frames store tabular data (mixed types allowed).

Modify : Add/remove columns via $ or [ ].

Create : data.frame().

Access : $column, [, "column"], or subset().

# HW1: Create a data frame with Name (Alice, Bob), Age (25, 30)  
# HW2: Access the "Name" column using `$`  
# HW3: Add a column "Salary" with 5000, 6000  
# HW4: Remove the "Age" column  

# HW5: Check the number of rows  

# HW1  
df <- data.frame(Name=c("Alice", "Bob"), Age=c(25, 30))  
# HW2  
print(df$Name)  # Output: Alice, Bob  
# HW3  
df$Salary <- c(5000, 6000)  
# HW4  
df$Age <- NULL  
# HW5  
print(nrow(df))  # Output: 2  

6. Factors

Factors store categorical data with predefined levels.

Ordered Factors : ordered=TRUE for ranking.

Create : factor().

Modify Levels : levels(), factor(..., levels=).

# HW1: Create a factor with "Low", "Medium", "High"  
# HW2: Check the levels of the factor  
# HW3: Add "Very High" as a new level  
# HW4: Remove "Medium" from the factor  

# HW5: Convert the factor to an ordered factor  

# HW1  
f <- factor(c("Low", "Medium", "High"))  
# HW2  
print(levels(f))  # Output: "High", "Low", "Medium"  
# HW3  
f <- factor(f, levels=c("Low", "Medium", "High", "Very High"))  
# HW4  
f <- f[f != "Medium"]  
# HW5  
f_ordered <- factor(f, ordered=TRUE)