Exploratory Steps With Synthetic Data

Lesson: Introduction to R Programming and Data Science

Overview

In this lesson, we will introduce you to R programming by loading a synthetic dataset, performing basic correlations, and visualizing the data with several plots. After each code block, we’ll explain how the code works step by step.

Prerequisites

Before we begin, make sure that you have R installed. You can download R from CRAN and use RStudio as an IDE to write and execute R code.

Step 1: Loading a Synthetic Dataset

First, we’ll create a synthetic dataset that simulates a simple survey of people’s ages, heights, weights, and annual income. We will store this data in a data frame, which is a fundamental data structure in R.

# Load the necessary library
library(tibble)

# Create a synthetic dataset
set.seed(123)  # Set a seed for reproducibility

data <- tibble(
  # Random ages between 20 and 60
  Age = sample(20:60, 100, replace = TRUE),  
  # Heights with a mean of 170 cm and SD of 10
  Height = rnorm(100, mean = 170, sd = 10),  
  # Weights with a mean of 70 kg and SD of 15
  Weight = rnorm(100, mean = 70, sd = 15),   
  # Income with a mean of 50,000 and SD of 15,000
  Income = rnorm(100, mean = 50000, sd = 15000)
)

# View the first few rows of the data
head(data)

Explanation:

• library(tibble): This loads the tibble package, which provides a modern version of data frames that are more user-friendly.
• set.seed(123): Ensures that the random numbers generated are the same every time you run the code. This makes your results reproducible.
• tibble(): Creates a tibble (data frame) with columns for Age, Height, Weight, and Income.
• rnorm(): Generates random numbers from a normal distribution. We use this for Height, Weight, and Income.
• head(data): Displays the first six rows of the dataset so we can inspect it.

Step 2: Calculating Basic Correlations

Now, let’s calculate the correlation between different columns (variables) in the dataset. Correlation tells us the strength and direction of the relationship between two variables.

# Calculate correlations between numeric columns
correlation_matrix <- cor(
    data[, c(
        "Age",
        "Height",
        "Weight",
        "Income")])

# View the correlation matrix
print(correlation_matrix)

Explanation:

• cor(): This function computes the correlation matrix for the selected columns in the dataset. It ranges from -1 to 1, where:
  • 1 indicates a perfect positive correlation.
  • -1 indicates a perfect negative correlation.
  • 0 indicates no correlation.
• data[, c("Age", "Height", "Weight", "Income")]: This selects only the numeric columns from the dataset for the correlation computation.
• print(correlation_matrix): Displays the resulting correlation matrix.

Step 3: Creating Plots to Visualize the Data

Visualization is key in data science to explore relationships between variables. We will now generate a few plots.

1. Scatter Plot: Age vs. Income

# Load the ggplot2 library for data visualization
library(ggplot2)

# Create a scatter plot of Age vs. Income
ggplot(data, aes(
    x = Age,
    y = Income)) +
  geom_point() +
  labs(
    title = "Scatter Plot of Age vs. Income",
    x = "Age",
    y = "Income")

Explanation:

• library(ggplot2): Loads the ggplot2 package, which is a popular library for creating visualizations.
• ggplot(data, aes(x = Age, y = Income)): Initializes the plot with the data and sets the x and y axes to Age and Income, respectively.
• geom_point(): Adds points to the plot, creating a scatter plot.
• labs(): Adds a title and labels to the axes.

2. Histogram: Distribution of Height

# Create a histogram of Height
ggplot(data, aes(x = Height)) +
  geom_histogram(
    binwidth = 2,
    fill = "blue",
    color = "black",
    alpha = 0.7) +
  labs(
    title = "Histogram of Height",
    x = "Height (cm)",
    y = "Frequency")

Explanation:

• geom_histogram(): Creates a histogram, which shows the frequency distribution of the Height variable. We define the bin width as 2.
• fill and color: Customize the color of the bars and their borders.
• alpha: Adjusts the transparency of the bars.

3. Boxplot: Weight Distribution by Age Group

# Create a boxplot of Weight by Age Group
data$AgeGroup <- 
    ifelse(
        data$Age < 30, 
        "Under 30", 
    ifelse(
        data$Age <= 40, 
        "30-40", 
        "Over 40"))
ggplot(
    data,
    aes(
        x = AgeGroup,
        y = Weight,
        fill = AgeGroup)
        ) +
  geom_boxplot() +
  labs(
    title = "Boxplot of Weight by Age Group",
    x = "Age Group",
    y = "Weight (kg)") +
  theme_minimal()

Explanation:

• ifelse(): Creates a new variable, AgeGroup, which categorizes the participants into three age groups: “Under 30”, “30-40”, and “Over 40”.
• geom_boxplot(): Creates a boxplot, which shows the distribution of Weight for each Age Group.
• theme_minimal(): Applies a clean minimal theme to the plot.

Step 4: Summarizing the Results

We have completed a few basic tasks:

1. We loaded a synthetic dataset and explored its structure.
2. We calculated correlations between the numeric variables to understand their relationships.
3. We created visualizations using ggplot2 to explore the data further.

The following key observations could be made:

• If the correlation between variables like Age and Income is strong, the scatter plot would show a clear trend.
• The histogram of Height helps us understand the distribution of people’s heights in the dataset.
• The boxplot allows us to see how Weight varies across different age groups.

Conclusion

In this lesson, you learned how to:

• Load and explore a synthetic dataset.
• Perform basic correlation analysis to understand relationships between variables.
• Visualize data using scatter plots, histograms, and boxplots in R.