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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
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

All you need to know about your first Machine Learning model – Linear Regression

Deepanshi
Deepanshi Last Updated : 20 Jul, 2023
7 min read

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

Introduction

If you are reading this article, I am assuming that you are already into the Data Science world and have an idea about Machine Learning. If not, then no problem. I will start with the basic terminologies which one needs to know before understanding the main topic of discussion i.e. Linear Regression.

This article will cover everything you need to know about Linear Regression, the first Machine Learning algorithm of Data Science.

Table of contents

Introduction to Machine Learning

Machine learning is a branch of Artificial Intelligence (AI) focused on building applications that learn from data and improve their accuracy over time without being programmed to do so. 

Types of Machine Learning:

Supervised Machine Learning: It is an ML technique where models are trained on labeled data i.e output variable is provided in these types of problems. Here, the models find the mapping function to map input variables with the output variable or the labels.
Regression and Classification problems are a part of Supervised Machine Learning.

Unsupervised Machine Learning: It is the technique where models are not provided with the labeled data and they have to find the patterns and structure in the data to know about the data.
Clustering and Association algorithms are a part of Unsupervised ML.

Understanding Linear Regression

In the most simple words, Linear Regression is the supervised Machine Learning model in which the model finds the best fit linear line between the independent and dependent variable i.e it finds the linear relationship between the dependent and independent variable.

Linear Regression is of two types: Simple and Multiple. Simple Linear Regression is where only one independent variable is present and the model has to find the linear relationship of it with the dependent variable

Whereas, In Multiple Linear Regression there are more than one independent variables for the model to find the relationship.

Equation of Simple Linear Regression, where bo is the intercept, b1 is coefficient or slope, x is the independent variable and y is the dependent variable.

linear regression 1

Equation of Multiple Linear Regression, where bo is the intercept, b1,b2,b3,b4…,bn are coefficients or slopes of the independent variables x1,x2,x3,x4…,xn and y is the dependent variable.

linear regression 2

A Linear Regression model’s main aim is to find the best fit linear line and the optimal values of intercept and coefficients such that the error is minimized.
Error is the difference between the actual value and Predicted value and the goal is to reduce this difference.

Let’s understand this with the help of a diagram.

linear regression 3

Image Source: Statistical tools for high-throughput data analysis

In the above diagram,

  • x is our dependent variable which is plotted on the x-axis and y is the dependent variable which is plotted on the y-axis.
  • Black dots are the data points i.e the actual values.
  • bo is the intercept which is 10 and b1 is the slope of the x variable.
  • The blue line is the best fit line predicted by the model i.e the predicted values lie on the blue line.

The vertical distance between the data point and the regression line is known as error or residual. Each data point has one residual and the sum of all the differences is known as the Sum of Residuals/Errors. 

Mathematical Approach:

Residual/Error = Actual values – Predicted Values

Sum of Residuals/Errors = Sum(Actual- Predicted Values)

Square of Sum of Residuals/Errors = (Sum(Actual- Predicted Values))2

i.e

linear regression

For an in-depth understanding of the Maths behind Linear Regression, please refer to the attached video explanation.

Assumptions of Linear Regression

The basic assumptions of Linear Regression are as follows:

1. Linearity: It states that the dependent variable Y should be linearly related to independent variables. This assumption can be checked by plotting a scatter plot between both variables.

Assumptions of Linear Regression 1

2. Normality: The X and Y variables should be normally distributed. Histograms, KDE plots, Q-Q plots can be used to check the Normality assumption. 

Please refer to my attached blog for a detailed explanation on checking the normality and transforming the variables violating the assumption.

Assumptions of Linear Regression 2

Source: https://heljves.com/gallery/vol_1_issue_1_2019_8.pdf

3. Homoscedasticity: The variance of the error terms should be constant i.e the spread of residuals should be constant for all values of X. This assumption can be checked by plotting a residual plot. If the assumption is violated then the points will form a funnel shape otherwise they will be constant.

Assumptions of Linear Regression 2

Source: OriginLab

4. Independence/No Multicollinearity: The variables should be independent of each other i.e no correlation should be there between the independent variables. To check the assumption, we can use a correlation matrix or VIF score. If the VIF score is greater than 5 then the variables are highly correlated.

In the below image, a high correlation is present between x5 and x6 variables.

correlation Assumptions of Linear Regression

                                                         Source: towards data science

5. The error terms should be normally distributed. Q-Q plots and Histograms can be used to check the distribution of error terms.

error term

                                Source: http://rstudio-pubs-static.s3.amazonaws.com

6. No Autocorrelation: The error terms should be independent of each other. Autocorrelation can be tested using the Durbin Watson test. The null hypothesis assumes that there is no autocorrelation. The value of the test lies between 0 to 4. If the value of the test is 2 then there is no autocorrelation.

Autocorrelation

                                                                Source: itfeature.com

How to deal with the Violation of any of the Assumption

The Violation of the assumptions leads to a decrease in the accuracy of the model therefore the predictions are not accurate and error is also high.
For example, if the Independence assumption is violated then the relationship between the independent and dependent variable can not be determined precisely.

There are various methods are techniques available to deal with the violation of the assumptions. Let’s discuss some of them below.

Violation of Normality assumption of variables or error terms

To treat this problem, we can transform the variables to the normal distribution using various transformation functions such as log transformation, Reciprocal, or Box-Cox Transformation.
All the functions are discussed in this article of mine: How to transform into Normal Distribution

Violation of MultiCollineraity Assumption 

It can be dealt with by:

  • Doing nothing (if there is no major difference in the accuracy)
  • Removing some of the highly correlated independent variables.
  • Deriving a new feature by linearly combining the independent variables, such as adding them together or performing some mathematical operation.
  • Performing an analysis designed for highly correlated variables, such as principal components analysis.

Evaluation Metrics for Regression Analysis

To understand the performance of the Regression model performing model evaluation is necessary. Some of the Evaluation metrics used for Regression analysis are:

1. R squared or Coefficient of Determination: The most commonly used metric for model evaluation in regression analysis is R squared. It can be defined as a Ratio of variation to the Total Variation. The value of R squared lies between 0 to 1, the value closer to 1 the better the model.

R squared

Source: medium.datadriveninvestor.com

where SSRES is the Residual Sum of squares and SSTOT is the Total Sum of squares

2. Adjusted R squared: It is the improvement to R squared. The problem/drawback with R2 is that as the features increase, the value of R2 also increases which gives the illusion of a good model. So the Adjusted R2 solves the drawback of R2. It only considers the features which are important for the model and shows the real improvement of the model.
Adjusted R2 is always lower than R2.

Ra

Source: stats.stackexchange.com

3. Mean Squared Error (MSE): Another Common metric for evaluation is Mean squared error which is the mean of the squared difference of actual vs predicted values.

Mean Squared Error

Source: cppsecrets.com

4. Root Mean Squared Error (RMSE): It is the root of MSE i.e Root of the mean difference of Actual and Predicted values. RMSE penalizes the large errors whereas MSE doesn’t.

Root Mean Squared Error

Source: community.qlik.com

Frequently Asked Questions

Q1. What is linear regression explain with an example?

A. Imagine you want to know how the price of a house is determined. Linear regression is like drawing a straight line through historical data on house prices and factors like size, location, and age. This line helps you make predictions; for instance, if you have a house with specific features, the model can estimate how much it might cost based on the past data.

Q2. What are the types of linear regression?

A. There are several types of linear regression:
1. Simple Linear Regression: Involves one dependent variable and one independent variable.
2. Multiple Linear Regression: Includes multiple independent variables to predict the dependent variable.
3. Polynomial Regression: Fits a curve instead of a straight line to the data by adding powers of the independent variable.

End Notes 

We have covered most of the concepts of the Regression model in this blog. If you wish to explore more about the mathematics behind the model, please refer to the links attached to the blog.

Please feel free to connect with me on LinkedIn and share your valuable inputs. Kindly refer to my other articles here.

About the Author :

I am Deepanshi Dhingra currently working as a Data Science Researcher, and possess knowledge of Analytics, Exploratory Data Analysis, Machine Learning, and Deep Learning.

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

blogathonlinear regression
Deepanshi
Deepanshi

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Responses From Readers

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Omkar Jadhav
Omkar Jadhav

Thank you Mam for such a great explanation.

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Sanskriti
Sanskriti

This article really explains all the concepts very clearly.

123

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Different Types of Regression Models
Different Types of Regression Models
Linear Regression with Python Implementation
Linear Regression with Python Implementation

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