How to Investigate Relationships Between Multiple Variables Using EDA

Exploratory Data Analysis (EDA) is a crucial step in understanding and analyzing the relationships between multiple variables in a dataset. It helps uncover patterns, trends, correlations, and outliers, offering valuable insights for model development or further analysis. Here’s a comprehensive guide on how to investigate relationships between multiple variables using EDA.

1. Start with Descriptive Statistics

Before delving into more complex visualizations, begin with basic descriptive statistics to get an overview of your dataset. This includes:

• Mean, Median, and Mode: These measures of central tendency give a sense of the “average” value for your variables.

• Standard Deviation and Variance: These tell you how much the data deviates from the mean, indicating the spread of values.

• Range and Interquartile Range (IQR): These give you a sense of the extremes (min and max) and the spread of the middle 50% of the data, respectively.

• Skewness and Kurtosis: These measures help you understand the shape of the data distribution, such as whether it is symmetric, or has heavy tails.

For numerical variables, these statistics give you a quick insight into the overall trends and the potential relationships to explore.

2. Univariate Analysis

Univariate analysis involves examining each variable individually to understand its distribution and structure. For multiple variables, this step gives you initial insights into how each variable behaves before looking at their interrelationships.

• For Numerical Variables: Use histograms or box plots to visualize the distribution. Histograms are useful for showing the frequency of data points within certain ranges, while box plots highlight the median, quartiles, and potential outliers.

• For Categorical Variables: Bar plots or pie charts can be used to visualize the frequency distribution of categories in a variable.

By understanding the distribution of individual variables, you set the stage for investigating how these variables interact with each other.

3. Pairwise Relationships

Once you have a sense of individual variables, you can start looking at pairwise relationships between them. This is where you start exploring how one variable correlates or interacts with others.

Scatter Plots

A scatter plot is one of the simplest and most informative tools for visualizing the relationship between two continuous variables. It helps identify:

• Linear Relationships: A straight line pattern suggests a linear relationship.

• Non-Linear Relationships: A curved pattern suggests a non-linear relationship.

• Outliers: Outliers will appear as isolated points away from the general trend.

Correlation Coefficients

The correlation coefficient, such as Pearson’s correlation for linear relationships, measures the strength and direction of the relationship between two continuous variables. Correlation values range from -1 to 1:

• Positive correlation: As one variable increases, the other increases.

• Negative correlation: As one variable increases, the other decreases.

• Zero correlation: No discernible linear relationship.

It’s crucial to remember that correlation does not imply causation. Further analysis and tests may be needed to validate any observed relationships.

Pairwise Plots

Pairwise plots (also known as pair plots or scatterplot matrices) visualize the relationships between multiple variables simultaneously. These plots display scatter plots for each pair of variables in a grid, helping to visualize interactions across several variables at once.

4. Multivariate Analysis

When you have more than two variables, multivariate analysis helps explore the interrelationships between them.

Heatmaps

A heatmap of the correlation matrix is a great way to visualize the relationships between multiple variables. It provides a color-coded matrix that shows the pairwise correlation coefficients between variables. Positive correlations are typically shown in warmer colors (e.g., red), and negative correlations are shown in cooler colors (e.g., blue).

Pairwise Regression Lines

If you have a large number of variables, fitting regression lines between each pair can help visualize the relationships. For example, in a 3D scatter plot, you can fit planes or lines to explore how variables interact in multiple dimensions.

5. Categorical vs. Numerical Variables

Sometimes, it’s important to explore the relationship between categorical and numerical variables.

Box Plots

Box plots can be used to compare the distribution of a numerical variable across different categories of a categorical variable. The box plot will show you the median, quartiles, and potential outliers for each category, allowing you to visually compare the central tendency and spread of the numerical variable across the categories.

Violin Plots

Violin plots combine aspects of both box plots and density plots. They show the distribution of the numerical variable and also give insights into the frequency and density of values for each category.

Bar Plots

Bar plots can also show the mean or median of a numerical variable for each category, though they are less informative than box plots or violin plots when it comes to distribution details.

6. Time Series Analysis (If Applicable)

If your data is time-dependent, such as data collected over multiple periods, you can use time series analysis to explore the relationships between variables over time.

Line Plots

A simple line plot can be used to visualize trends over time for one or more variables. Overlaying multiple variables on the same plot can help you identify relationships between them over time.

Autocorrelation

Autocorrelation measures how a variable correlates with its past values. This is useful when dealing with time series data to understand the temporal dependencies between variables.

7. Dimensionality Reduction

If you have many variables and want to explore relationships in lower dimensions, dimensionality reduction techniques like PCA (Principal Component Analysis) or t-SNE (t-Distributed Stochastic Neighbor Embedding) can be useful.

PCA

PCA transforms a large set of variables into a smaller set of uncorrelated components. The resulting components are ordered by the amount of variance they explain in the data. This can help visualize the relationships between variables in a lower-dimensional space.

t-SNE

t-SNE is another dimensionality reduction technique that’s particularly useful for visualizing high-dimensional data in 2D or 3D. It focuses on preserving the local structure of the data, making it useful for understanding clusters or groups of variables.

8. Handling Missing Data and Outliers

Before interpreting relationships, you must account for any missing values or outliers that could skew your analysis.

• Imputation: Fill in missing values using imputation techniques, such as replacing with the mean, median, or mode, or using more complex methods like k-NN imputation.

• Outlier Detection: Use statistical techniques like the Z-score or IQR to identify and manage outliers. You can remove or transform outliers depending on the context of the data.

9. Feature Engineering

While EDA primarily focuses on exploration, it often leads to insights that inform feature engineering. For example, you might discover new relationships between variables that suggest useful transformations (such as creating interaction terms or aggregating categories).

Conclusion

Exploratory Data Analysis is an essential part of understanding relationships in your data. By using a combination of statistical techniques, visualizations, and summary metrics, you can uncover hidden patterns, correlations, and trends. Whether you’re working with two variables or hundreds, the goal of EDA is to provide insights that guide further analysis and modeling, ultimately helping you make data-driven decisions.