Recent times have seen a surge in the interest surrounding Artificial Intelligence (AI). It's being embraced by individuals across diverse fields who seek to simplify their work. Economists, physicians, meteorologists, and HR recruiters are just a few who benefit from the power of AI. The driving force behind this widespread adoption is the Machine Learning algorithms, and today we’ll explore one of the fundamental algorithms - Linear Regression.

## Understanding Regression

Broadly classified under machine learning models, regression is pivotal in determining relationships between variables. Classification models ascertain which category an observation belongs to, whereas regression-based models predict a numeric value. Perfect for real-world applications, regression machine learning is used when handling problems with continuous numbers.

## Introduction to Linear Regression

Linear Regression in AI, a type of supervised machine learning, is characterized by constant and continuous performance. Unlike classifying values into categories, it’s designed to estimate values within a continuous range, such as predicting price or revenue. It can be categorized mainly into Simple Regression and Multiple Regression.

### Simple Linear Regression (SLR)

Simple Linear Regression focuses on elucidating the relationship between a dependent variable and a single independent variable. It aims to exhibit a linear or sloped connection, which gives it the name, Simple Linear Regression. While the dependent variable is always continuous, the independent variable can either be continuous or categorical.

The core objectives of SLR are:

- Modeling relationships between two variables like the income-expenditure ratio or the experience-salary ratio.
- Making predictions based on known data, such as forecasting weather based on temperature or revenue projections based on annual expenditure.

### Multiple Linear Regression (MLR)

Similar in nature to SLR, Multiple Linear Regression uses an independent variable to predict the response variable. However, when the response variable is affected by more than one predictor variable, MLR becomes essential. It builds upon SLR by predicting the response variable using multiple influencing variables.

## Fundamental Assumptions of Linear Regression

Several key assumptions guide the Linear Regression model:

- A linear correlation between the target and independent variables.
- Minimal or no multicollinearity among the predictors.
- Homoscedasticity, which ensures a consistent error term across all independent variables.
- Error terms should follow a normal distribution.
- Error terms should not display autocorrelation; otherwise, the model's accuracy can be compromised.