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.**

.**Iteration 1** – In the start, θ_{0} and θ_{1} values are randomly choosen. Let us suppose, θ_{0} = 0 and θ_{1} = 0.

**Predicted values after iteration 1 with Linear regression hypothesis.****Cost Function – Error****Gradient Descent – Updating θ**_{0}value

Here, j = 0**Gradient Descent – Updating θ**_{1}value

Here, j = 1

**Predicted values after iteration 1 with Linear regression hypothesis.**Now, similar to iteration no. 1 performed above we will again calculate Cost function and update θ

_{j}values using Gradient Descent.

We will keep on iterating until Cost function doesn’t reduce further. At that point, model achieves best θ values. Using these θ values in the model hypothesis will give the best prediction results.

**Iteration 2** – θ_{0} = 0.005 and θ_{1} = 0.02657