Linear Regression Algorithm —Under The Hood Math For Non

Linear Regression Algorithm —Under The Hood Math For Non

It is one of the oldest algorithms in the field of mathematics and statistics borrowed in machine learning. Linear regression is one of the most popular algorithms used in different fields well before the advent of computers. Today with the powerful computers, we can solve multi-dimensional linear regression which was not possible earlier. In single or multidimensional linear regression, the basic mathematical concept is quite the same.

Linear regression is one of the most popular algorithms used in different fields well before the advent of computers. Today with the powerful computers, we can solve multi-dimensional linear regression which was not possible earlier. In single or multidimensional linear regression, the basic mathematical concept is quite the same.

Today with machine learning libraries, like Scikit-learn, it is possible to use the linear regression in modelling without understanding the mathematical concept behind it. In my opinion, it is quite essential for a data scientist and machine learning professional to understand the mathematical concept and logic behind an algorithm before using it.

Most of us may not have studied advanced mathematics and statistics, and we get scared by seeing the mathematical notation and jargon behind the algorithms. In this article, I will explain the math and logic behind linear regressions with simplified python code and easy math to build your understanding


Overview

We will start with a simple linear equation with one variable and without any intercept/bias. First, we will learn the step by step approach taken by packages like Scikit-learn to solve linear regression. During this walkthrough, we will understand the important concept of Gradient Descent. Further, we will see an example with a simple linear equation with one variable and an intercept/bias.

Step 1: We will use the python package NumPy for working with a sample dataset and Matplotlib to plot various graphs for visualisation.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

_Step 2: _Let us consider a simple scenario where a single input /independent variable controls the outcome/dependent variable value. In the code below, we have declared two NumPy arrays to hold the values of the independent and dependent variables.

Independent_Variable=np.array([1,2,3,12,15,17,20,21,5,7,9,10,3,12,15,17,20,7])
Dependent_Variable=np.array([7,14,21,84,105,116.1,139,144.15,32.6,50.1,65.4,75.4,20.8,83.4,103.15,110.9,136.6,48.7])

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