Mathematical explanation for Linear Regression working

Suppose we are given a dataset

Given is a Work vs Experience dataset of a company and the task is to predict the salary of a employee based on his / her work experience.
This article aims to explain how in reality Linear regression mathematically works when we use a pre-defined function to perform prediction task.
Let us explore how the stuff works when Linear Regression algorithm gets trained.
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Iteration 1 – In the start, θ0 and θ1 values are randomly choosen. Let us suppose, θ0 = 0 and θ1 = 0.

  • Predicted values after iteration 1 with Linear regression hypothesis.
  • Cost Function – Error
  • Gradient Descent – Updating θ0 value
    Here, j = 0

  • Gradient Descent – Updating θ1 value
    Here, j = 1