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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

An Introductory Note on Linear Regression

Karpuram
Karpuram Last Updated : 08 Feb, 2022
5 min read

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

Introduction

In this article, I will explain linear Regression, one of the machine learning algorithms. After reading this, we will get some basic knowledge about linear Regression, its uses, its types, and so on. Let us start with the table of contents.

Table of contents

What is Linear Regression

Uses of Linear Regression

Selection Criteria

When will Linear Regression be used?

Types of Linear Regression

Understanding Linear Regression

How to find the effectiveness of the model?

R Square method

Regression analysis is a form of predictive modeling technique that investigates the relationship between X and Y, where x is the independent variable Y is the dependent variable.

Types of Regression – There are two types of Regression. One is linear Regression used with continuous variables,  and the other is logistic Regression used with categorical variables.

Linear Regression

Regression analysis is graphing a line on a set of data points that most closely fits the overall shape of the data.

In other words, Regression shows the changes in a dependent variable on the y-axis to the changes in the explanatory variable on the x-axis.

Uses of Regression

  1. We determine the strength of predictors, for example, the relation between sales and marketing spending or the connection between age and income.
  2. It is forecasting an effect and is used to predict the impact or impact of changes. This is used to understand how much the dependent variable changes with the evolution of the independent variable. For example, how much sales are increased with extra 1000 rupees spent on marketing?
  3. Trend forecasting. This can be used to get the point estimates.

Selection Criteria

  1. Classification and regression capabilities: Predicts the continuous variable (For example-Temperature of a place)
  2. Data quality: Each missing point removes one data point that could optimize the Regression.
  3. Computational complexity: Linear Regression is not always computationally expensive than the decision tree or the clustering algorithm.
  4. Comprehensible and Transparent: Linear Regression is easily understandable, and a simple mathematical notation can represent transparency.

Where will Linear Regression be used?

  1. Evaluating trends and sales estimates
  2. Analyzing the impact of price changes
  3. Estimation of risk in financial services and insurance domain

Types of Linear Regression

Linear Regression is of two types. One is positive Linear Regression, and the other is negative Linear Regression.

Positive Linear Regression– If the value of the dependent variable increases with the increase of the independent variable, then the slope of the graph is positive; such Regression is said to be Positive Linear Regression.

Linear Regression

                                                                        Source: Author

y=mx+c, where m is the slope of the line. In Positive Linear Regression, the value of m is positive.

Negative Linear Regression- If the value of the dependent variable decreases with the increase in the value of the independent variable, then such Regression is said to be negative linear Regression.

Negative Linear Regression

                                                                          Source: Author

In Negative Linear Regression, the value of m is Negative.

Understanding Linear Regression

First of all, we need to have some data set to design the model.

Let us say the data is as below

x y
1 3
2 4
3 2
4 4
5 5

 

The values given are actual values.

Based on the above matters, the graph that most closely fits is as below

y=mx+c, where m is the slope of the line and c is Y-intercept.

From now on x(mean) is referred as x(m) and y(mean) as y(m).

m as per least square method=∑(x-x(m))(y-y(m))/∑(x-x(m))2

As per above data table, x(m)=3, y(m)=3.6.

x y x-x(m) y-y(m) (x-x(m))2 (y-y(m))2
1 3 -2 -0.6 4 1.2
2 4 -1 0.4 1 -0.4
3 2 0 -1.6 0 0
4 4 1 0.4 1 0.4
5 5 2 1.4 4 2.8

As per the equation of m, its value is m=4/10=0.4,c=2.4, so that the line equation would be y=0.4x+2.4.

x-x(m) is the distance of all the points x through the line y=3.

y-y(m) is the distance of all the points y through the line x=3.6.

Now we will calculate the predicted values of y based on the equation y=mx+c, where m=0.4 and c=2.4.

For x=1,y=0.4*1+2.4=2.8

For x=2,y=0.4*2+2.4=3.2

For x=3,y=0.4*3+2.4=3.6

For x=4,y=0.4*4+2.4=4.0

For x=5,y=0.4*5+2.4=4.4

Now we have actual values and predicted values of y; we need to calculate the distance between them and then reduce them, which means we need to reduce the error, and finally, the line with the minor error would be the line of Regression best fit line.

Finding the best fit line:

For different values of m, we need to calculate the line equation, where y=mx+c as the value of m changes, the equation changes. After every iteration, the predicted value changes according to the line’s equation. It needs to compare with the actual value and the importance of m for which the minimum difference gives the best fit line.

Let’s check the goodness of fit:

To test how good our model is performing, we have a method called the R Square method

R square method

This method is based on a value called the R-Squared value. It measures how close the data is to the regression line—and also known as the coefficient of determination.

R Square method | Linear Regression

                                                              Source: Author

To check our model’s good, we need to compare the distance between the actual value and mean versus the distance between the predicted value and mean; here comes the R formula.

R2=∑(yp-y(m))2/∑(y-y(m))2

If the value of R2 is nearer to 1, then the model is more effective

If the value of R2 is far away from 1, then the model is least effective

x y y-y(m) (y-y(m))2 yp (yp-y(m))2
1 3 -0.6 0.36 2.8 -0.8
2 4 0.4 0.16 3.2 -0.4
3 2 -1.6 2.56 3.6 0
4 4 0.4 0.16 4.0 0.4
5 5 1.4 1.96 4.4 0.8

R2=1.6/5.2=0.3

This means that the data points are far away from the regression line.

If the value of R is 1, then the actual data points would be on the regression line.

Conclusion

We have covered all the topics related to Linear Regression. And we also found the effectiveness of the model using the R square method. For example, R-value might come close to 1 if the data is regarding a company’s sales. R-value might be too low if the information is from a doctor in psychology since different persons have different characters. So the conclusion is if the R-value is closer to one, the more accurate is the predicted value.

Thanks for reading this article. Learn more here.

Connect with me on https://www.instagram.com/?hl=en.

Image Source: Author.

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

Karpuram
Karpuram

Hello Everyone,
This is Srivani. I had completed my B.Tech in the computer science department. I am interested in Data Science and programming. Thanks for reading my articles and hope you get knowledge from them.

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