Interview Prep
Career
GenAI
Prompt Engg
ChatGPT
LLM
Langchain
RAG
AI Agents
Machine Learning
Deep Learning
GenAI Tools
LLMOps
Python
NLP
SQL
AIML Projects

Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

A Quick Guide to Bivariate Analysis in Python

ASHWINI
ASHWINI Last Updated : 27 Nov, 2023
7 min read

Introduction

In all kinds of data science projects across domains, EDA (exploratory data analytics) is the first go-to analysis, without which the analysis is incomplete or almost impossible to do. One of the key objectives in many multi-variate analyses is to understand relationships between variables which helps answer questions for critical objectives. Examples:

  • How do sales vary with time of day or day of the week?
  • How does the amount of house loan amount issued vary with an individual’s income?
  • We observe high fraud in claims for a particular motor part in auto insurance?
  • How does mileage vary with the weight of the truckload?
  • What keywords are used in positive customer reviews on Facebook vs keywords in negative customer reviews?

To answer these questions, one must grasp how changes in one variable or feature correspond with another. Variables can encompass numerical, categorical, or text data. It’s vital to comprehend which methods and visuals effectively elucidate the relationships or concurrence between variables.

This article was published as a part of the Data Science Blogathon.

Table of contents

What is Bivariate Analysis?


Bivariate analysis is a systematic statistical technique applied to a pair of variables (features/attributes) to establish the empirical relationship between them. In other words, it aims to identify any concurrent relations, typically beyond simple correlation analysis.

In supervised learning, this method aids in determining essential predictors. When conducting bivariate analysis with one variable as the dependent variable (Y) and others as independent variables (X1, X2, etc.), all Y, X pairs are plotted. Essentially, it serves as a method for feature selection and prioritization.

E.g. How does the sale of air conditioners look with the average daily temperature during summers – here, we could plot the daily deals with the daily average temperature to observe patterns, trends, or empirical relations, if any.

Correlation vs Causality

It is a widespread fallacy to assume that if one variable is observed to vary with a change in values of another empirically, then either of them is “causing” the other to change or leading the other variable to change. In bivariate analysis, it might be observed that one variable (especially the Xs) is causing Y to change. Still, in actuality, it might just be an indicator and not the actual driver.

The example below would help grasp this concept and avoid the fallacy during bivariate analysis.

Let us quickly look at the illustration below:

Bivariate Analysis in Python

Though it would be seen that both sunburn and ice cream sales are correlated, ice-creams do not cause sunburn (maybe they do the opposite)!

Bivariate Analysis for Each Variable Type

There are essentially two types of variables in data – Categorical and continuous (numerical). So, in the case of bivariate analysis, there could be four combinations of analysis that could be done that is listed in the summary table below:

Bivariate Analysis in Python
Source: Designed by the author

To develop a further hands-on understanding, the following is an example of bivariate analysis for each combination listed above in Python:

Categorical vs Categorical Variables

This is used in case both the variables being analyzed are categorical. In the case of classification, models say, for example, we are classifying a credit card fraud or not as Y variables and then checking if the customer is at his hometown or away or outside the country. Another example can be age vs gender and then counting the number of customers who fall in that category. It is important to note that the visualization/summary shows the count or some mathematical or logical aggregation of a 3rd variable/metric like revenue or cost and the like in all such analyses. It can be done using Crosstabs (heatmaps) or Pivots in Python. Let us look at examples below:

Crosstabs

It is used to count between categories, or get summaries between two categories. Pandas library has this functionality.

Source: Designed by the author

Import pandas as pd
Import seaborn as sns
# need to summarize on x and y categorical variables
pd.crosstab(    dd.categ_x, dd.categ_y, margins=True,     values=dd.cust, aggfunc=pd.Series.count)
# 3 any other aggregation function can be used based on column type
# to create a heatmap by enclosing the above in sns.heatmap
sns.heatmap(pd.crosstab(   dd.categ_x, dd.categ_y, margins=True,     values=dd.cust, aggfunc=pd.Series.count),
            cmap="YlGnBu", annot=True, cbar=False)

Pivots

Another useful functionality that can be applied to Pandas dataframes to get Excel like Pivot tables. This can work for 2+ categorical variables when placed in the proper hierarchy.

Pandas Pivot Table
Source: Pbpython

Python code: Assuming the above dataset, just this one line of code can produce the desired bivariate views.

Pd.pivot_table(df,index =[“Manager”,”Status”],columns=[“Product”],aggfunc=[np.sum]

Categorical vs continuous (numerical) variables

It is an example of plotting the variance of a numerical variable in a class. Like how age varies in each segment or how do income and expenses of a household vary by loan re-payment status.

Categorical plot for aggregates of continuous variables: Used to get total or counts of a numerical variable eg revenue for each month. PS: This can be used for counts of another categorical variable too instead of the numerical.

Plots used are: bar plot and count plot
sns.barplot(x='sex',y='total_bill',data=t)
sns.countplot(x='sex',data=t)

Plots for distribution of continuous (numerical) variables: Use to see the range and statistics of a numerical variable across categories

Plots used are – box plot, violin plot, swarm plot

sns.boxplot(x='day',y='total_bill',data=t,palette='rainbow')
sns.violinplot(x="day", y="total_bill", data=t,palette='rainbow')
sns.stripplot(x="day", y="total_bill", data=t)
sns.swarmplot(x="day", y="total_bill", data=t)
Box Plot, Strip Plot, Swarm Plot and Violin Plot
Source: Designed by the author for this writing

 

Continuous vs continuous

This is the most common use case of bivariate analysis and is used for showing the empirical relationship between two numerical (continuous) variables. This is usually more applicable in regression cases.

The following plots make sense in this case: scatterplot, regplot.

Code below:

Import seaborn as sns
 Sns.regplot(x=‘a’,y=‘b’,data=df)
Plt.ylim(0,)

Bivariate Analysis at Scale

In case we have large datasets with 30-70+ features (variables), there might not be sufficient time to run each pair of variables through bivariate analysis one by one. We could use the pairplot or pair grid from the seaborn library in such cases. It makes a grid where each cell is a bivariate graph, and Pairgrid also allows customizations. Code snippets and sample outputs below (assuming seaborn is imported and the iris dataset).

Pairplot

g = sns.pairplot(iris, diag_kind="kde", markers="+",
                 plot_kws=dict(s=50, edgecolor="b", linewidth=1),
                 diag_kws=dict(shade=True))
Bivariate Analysis
Source: Designed by the author for this writing

Pairgrid

g = sns.PairGrid(iris)

g = g.map_upper(sns.scatterplot)

g = g.map_lower(sns.kdeplot, colors="C0")

g = g.map_diag(sns.kdeplot, lw=2)
Pairgrid

Why not just run a correlation matrix here?

The correlation matrix only provides a single numerical value without providing any information about the distribution which provides an in-depth picture of empirical relationships between variables in the bivariate analysis.

Practical Tips

Please note this only works for numerical variables (to do it for categorical we need to first convert to numerical forms with techniques like one-hot encoding).

For very large datasets, group independent variables into groups of 10/15/20 and then run bivariate for each with respect to the dependent variable.

EDA with one line of code!

The pandas profiling library – a shorthand & quick way for EDA and bivariate analysis – more on this here. It does most of the univariate, bivariate and other EDA analyses.

Conclusion

Bivariate analysis is crucial in exploratory data analysis (EDA), especially during model design, as the end-users desire to know what impacts the predictions and in what way. This can be extended to multi-variate cases, but the human mind is designed to comprehend the 2-D or 3-D world easily. Where there are two variables, it is easier to interpret, gain intuition and take action. Thus, the bivariate analysis goes a long way in defining how a particular variable is empirically related to another and what can we expect if one happens to be in a specific range or have a particular value.

Reiterating that this (correlation) should not be confused with causation (experimentation is better to use in that case). 

Hope you liked my article on Bivariate Analysis in Python.

Frequently Asked Questions

Q1. What is bivariate in Python?

A. Bivariate in Python refers to the analysis involving two variables. It uses statistical methods and visualizations to explore the relationship and interactions between these two variables in a dataset.

Q2. What is bivariate analysis with an example?

A. Bivariate analysis studies the relationship between two variables. For example, analyzing the correlation between a person’s study hours and exam scores to understand if study time impacts performance.

Q3. How to do multivariate analysis in Python?

A. Multivariate analysis in Python involves studying relationships among multiple variables. Techniques like regression analysis or machine learning algorithms can be employed to simultaneously analyze the impact of several variables on an outcome.

Q4. How do you test for bivariate analysis?

A. Bivariate analysis can be tested using correlation coefficients or regression analysis. These tests help quantify the strength and nature of the relationship between two variables in a dataset.

The media shown in this article is not owned by Analytics Vidhya and are used at the Author’s discretion. 

ASHWINI
ASHWINI

Analytics & Data Science Leader | Applies analytics in Retail, Communications & Media domain across marketing, Omni channel sales, operations and people management functions| Helps convert Business Strategy to Data Strategy

Free Courses

Generative AI 4.7

Generative AI - A Way of Life

Explore Generative AI for beginners: create text and images, use top AI tools, learn practical skills, and ethics.
Large Language Models 4.5

Getting Started with Large Language Models

Master Large Language Models (LLMs) with this course, offering clear guidance in NLP and model training made simple.
Prompt Engineering 4.6

Building LLM Applications using Prompt Engineering

This free course guides you on building LLM apps, mastering prompt engineering, and developing chatbots with enterprise data.
LlamaIndex 4.8

Improving Real World RAG Systems: Key Challenges & Practical Solutions

Explore practical solutions, advanced retrieval strategies, and agentic RAG systems to improve context, relevance, and accuracy in AI-driven applications.
RAG systems using LlamaIndex 4.7

Microsoft Excel: Formulas & Functions

Master MS Excel for data analysis with key formulas, functions, and LookUp tools in this comprehensive course.

Recommended Articles

Responses From Readers

Clear

Write for us

Write, captivate, and earn accolades and rewards for your work
  • Reach a Global Audience
  • Get Expert Feedback
  • Build Your Brand & Audience
  • Cash In on Your Knowledge
  • Join a Thriving Community
  • Level Up Your Data Science Game
imag

We use cookies essential for this site to function well. Please click to help us improve its usefulness with additional cookies. Learn about our use of cookies in our Privacy Policy & Cookies Policy.

Show details