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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

What is Regression Analysis?

Yana Khare
Yana Khare Last Updated : 17 Jun, 2024
5 min read

Introduction

A fundamental component of statistical technique, regression analysis is essential for examining and measuring connections between variables. Its uses are numerous and diverse, from forecasting financial trends to evaluating medical results. This in-depth manual explores the essence of regression analysis, explaining its various kinds, applications, and underlying concepts.

Overview

  • Discover the various regression techniques, their uses, and the underlying mathematics.
  • Acquire knowledge of fundamental ideas, including the regression equation, coefficient evaluation, and fit metrics quality.
  • Examine the fundamental presumptions of regression analysis and their significance for trustworthy outcomes.
  • Recognize the many ways that regression analysis may be used in various contexts.
  • Analyze the benefits and drawbacks of regression analysis, considering its diagnostic capabilities, quantification of correlations, ability to account for confounding factors, predictive strength, and limits.
Regression Models | What is Regression Analysis?

Table of contents

What is Regression Analysis?

Regression analysis is a reliable statistical method for ascertaining the relationship between a dependent variable and one or more independent variables. It clarifies how changes in the independent components impact the dependent variable, making it a basic idea in finance, economics, and the social sciences.

Types of Regression

  • Simple Linear Regression: As simple linear regression shows, a line that passes through the displayed data points represents the association between one predictor variable and one responder variable. The objective is to determine sales using, for example, the amount of money spent on advertising or to approximate the level of the dependent variable numerically such that it corresponds to the level of the independent variable.
  • Multiple Linear Regression: Multiple linear regression incorporates two or more independent variables to predict a single dependent variable, extending the capabilities of basic linear regression. This method estimates property values based on size, location, and age and reflects the cumulative influence of several factors on the dependent variable.
  • Logistic Regression: Logistic regression is used when the dependent variable is categorical or binary (e.g., true or false, yes/no). Instead of fitting a straight line to forecast the likelihood of a specific result, it utilizes a logistic function (sigmoid curve). For example, it can predict if a consumer will make a purchase (yes or no).
  • Polynomial Regression: Polynomial regression uses an nth-degree polynomial to express the relationship between the independent and dependent variables. By changing the predictors, it can now fit more intricate, nonlinear connections.

Also Read: 7 Regression Techniques You Should Know!

The Regression Equation

The fundamental idea is to fit a mathematical equation to observed data. In simple linear regression, the equation is:

The Regression Equation

Coefficients Interpretation

The coefficients represent the intercept and slope. They show that the amount of y varies when x increases by one unit. Every independent variable in multiple regression has a coefficient representing its influence on the dependent variable.

Measuring Goodness of Fit

  • R-squared (R²): The percentage of the dependent variable’s volatility can be predicted based on the independent variables. Higher R² values suggest a better match.
  • Adjusted R-squared: This approach provides a more accurate estimate in multiple regression settings by adjusting R² for the number of predictors in the model.
  • P-values: Evaluate the coefficients’ significance. Low P-values, usually less than 0.05, indicate that the association is statistically significant.

Assumptions in Regression

  • Linearity: The relationship between dependent and independent variables should be linear.
  • Independence: Observations should be independent of each other.
  • Homoscedasticity: The variance of errors should be consistent across all levels of the independent variables.
  • Normality: One should normally distribute the errors.

Applications of Regression Analysis

  • Business and Economics: Regression analysis helps businesses forecast sales, adapt prices, and search for market indicators. It is also used to understand
  • Finance: They enable evaluation of the threats facing a certain investment and portfolio management by demonstrating dependency between asset prices and other variables, such as interest rates or profits.
  • Healthcare: It employs information on patients’ clinical and demographic data to identify factors associated with ill health. It also evaluates the effectiveness of therapeutic interventions and predicts patient outcomes.
  • Marketing: Regression analysis is a method marketers use to predict sales, evaluate advertising campaigns, and analyze consumer behavior.
  • Social Sciences: Sociologists and psychologists use regression analysis to comprehend the relationship between variables and results, such as education and income patterns.

Advantages of Regression Analysis

  • Predictive Power: This research’s data
  • Quantification of Relationships: It offers a precise mathematical framework for calculating the direction and intensity of correlations between different variables. This aids in comprehending how modifications to one variable impact those to another.
  • Control for Confounding Variables: Multiple regression can include several independent variables, which aids in determining one variable’s influence while accounting for others. This is especially helpful in challenging real-world situations.
  • Diagnostic Tools:  Regression analysis helps with model validation and improvement by offering diagnostic tools (such as R-squared, p-values, and residual plots) to evaluate the model’s fit and the importance of predictors.
  • Versatility: Regression analysis works with various data kinds and scenarios, including continuous, categorical, and binary outcomes. Moreover, it applies to multiple professions, including economics, engineering, and social sciences.
  • Ease of Implementation: Thanks to modern statistical software and tools, regression analysis is now easier to apply, even for those without extensive statistical knowledge. Process simplification is achieved using automated tools in Python, R, and other platforms.
  • Hypothesis Testing: Regression analysis aids in testing theories about the correlations between variables. It offers a structure for determining whether specific predictors significantly impact the dependent variable.

Disadvantages of Regression Analysis

  • Assumption Dependencies: Several presumptions, including linearity, independence, homoscedasticity, and error normalcy, underpin regression models. Breaking these presumptions may lead to erroneous or deceptive results.
  • Multicollinearity: Many independent variables may affect outcomes, making it difficult to determine the influence of specific predictors.
  • Overfitting: When trained on training data, a model overfits the training data and performs much worse predicting new data. This happens when the model collects noise in addition to the signal.
  • Sensitivity to Outliers: Outliers can significantly alter the model’s coefficients and outcomes in regression analysis.
  • Limited by Linear Relationships: The assumption of a linear connection between variables in simple linear regression may not hold in all cases. Researchers need advanced methods like polynomial regression or machine learning models for more complicated interactions.
  • Interpretability Issues:  It can be challenging to determine how each predictor affects the results of a model with many predictors, particularly in multiple regression. This difficulty increases if there are interactions between the variables.
  • Sample Size Requirements: Regression analysis requires a substantial sample size to yield accurate estimations. Tiny sample sizes may result in unstable estimates and inadequate generalization.

Conclusion

As a fundamental tool for data analysis, regression analysis continues to provide insights and predictive power for a wide range of applications. However, reliability depends on paying close attention to assumptions, model selection, and validation, even if it offers valuable tools for forecasting and relationship comprehension.

Frequently Asked Questions

Q1. What is a regression analysis in simple terms?

A. Regression analysis is a statistical method used to understand the relationship between one dependent variable and one or more independent variables.

Q2. What does a regression analysis tell you?

A. It tells you how changes in the independent variables are associated with changes in the dependent variable, helping to predict or explain the dependent variable.

Q3. What is the main purpose of regression analysis?

A. The main purpose is to model the relationship between variables, allowing for predictions, insights into causal relationships, and understanding the strength of these relationships.

Q4. What is an example of a regression analysis?

A. An example is predicting a person’s salary (dependent variable) based on their years of experience and education level (independent variables).

Yana Khare
Yana Khare

A 23-year-old, pursuing her Master's in English, an avid reader, and a melophile. My all-time favorite quote is by Albus Dumbledore - "Happiness can be found even in the darkest of times if one remembers to turn on the light."

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