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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
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

Creating Linear Model, It’s Equation and Visualization for Analysis

Kelechi
Kelechi Last Updated : 25 Oct, 2024
4 min read

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

Introduction

Have you ever been tasked with visualizing the relationship between each feature and the target in a Linear regression model to analyze the line of best fit? Well, soon or later you’ll have to. This article explains this in easy to understand steps. Let’s go!

Linear Regression:

Simple Linear Model

Fig. 1.0: The Basic Linear Regression model Visualization

 

The Linear model (Linear Regression) was probably the first model you learned and created, using the model to predict the Target’s continuous values. You sure must have been happy that you’ve completed a model. You were probably also taught the theories behind its functionality– The Empirical Risks Minimization, The Mean Squared Loss, The Gradient descent, The Learning Rate among others.

Well, this is great and all of a sudden I was called to explain a model I created to the manager, all those terms were like jargons to him, and when he asked for the model visualization (as in fig 1.0) that is the model fit hyperplane(the red line) and the data points(the blue dots). I froze to my toes not knowing how to create that in python code.

Well, That’s what the first part of this article is about Creating the Basic Linear Model Visualization in your Jupyter notebook in Python.

Let’s begin using this random data:

Xy
12
23
311
413
528
632
750
859
985

 

Method 1: Manual Formulation

Importing our library and creating the Dataframe: 

# string_to_hex.py
str  =  "245FC"
# pass the str to the int () function to perform type casting and  to convert it into base16
basehexINT  =  int ( str ,  16 )
print ( "val" , basehexINT )
print ("val" , type (basehexINT))
hex_value  =  hex (basehexINT)
print (hex_value)
# checking the type of the value
print (type (hex_value))

now at this stage, there are two ways to perform this visualization:

1.) Using  Mathematical knowledge

2.) Using the Linear_regression Attribute for scikit learns Linear_model.

  • Let’s get started with the Math😥😥.

just follow through it’s not that difficult, First we define the equation for a linear relationship between y(dependent variables/target) and X(independent variable/features) as :

         y = mX + c

where y = Target

            X = features

           a = slope

           b = y-intercept constant

To create the model’s equation we have to get the value of m and c , we can get this from the Y and X with the equations below:

Linear model formula

The slope, a is interpreted as the product between the summation of the difference between each individual x value and its mean and the summation of the difference between each individual y point and its mean then divided by the summation of the square of each individual x and its mean.

The intercept is simply the mean of y  minus the product of the slope and mean of x

That is a lot to take in. probably read it over and over  till you get it, try reading with the picture

👆👆 that was the only challenge; if you’ve understood it congratulations let’s move on.

Now writing this in python code is ‘eazy-pizzy’  using the numpy library, check it out👇👇.

Linear Model - Sum and Mean

 

now we have our  a and b we just insert it to the equation—->  y = 9.95 -1218.56x

To blow your mind now, did you know that this is the model’s equation. and we just created a model without using scikit learn. we will confirm it now using the second method which is the scikit learn Linear Regression package

 

Method 2: Using scikit-learn’s Linear regression

 We’ll be importing Linear regression from scikit learn, fit the data on the model then confirming the slope and the intercept. The steps are in the image below.

so you can see that there is almost no difference, now let us visualize this as in fig 1.

Linear model - prediction graph

 

Graph

 

The red line is our line of best fit that will be used for the prediction and the blue point are our initial data. With this, I had something to report back to the manager. I particularly did this for each feature with the target to add more insight.

Now we have achieved our goal of creating a model and showing its plotted graph

This technique may be time-consuming when it comes to data with larger sizes and should only be used when visualizing your line of best fit with a particular feature for analysis purposes. It is not really necessary during modeling unless requested, Errors and calculation may suck up your time and computation resources especially if you’re working with 3D and higher data. But the insight gotten is worth it.

I hope you enjoyed the article if yes that great, you can also tell me how to improve in any way. I still have a lot to share especially on regressions(Linear, Logistics, and Polynomial ).

Thank You for reading through.

blogathon
Kelechi
Kelechi

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How a Math equation is used in building a Linear Regression model?
How a Math equation is used in building a Linear Regression model?
Build Your First Linear Regression Machine Learning Model
Build Your First Linear Regression Machine Learning Model

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