While simple linear regression can help us understand the relationship between a single predictor and a response, using more than one predictor often proves to be beneficial in predicting responses. Multiple linear regression assigns different slope coefficients to each predictor to build a more comprehensive model than its simple counterpart.

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Based on the number of independent variables used, there are two types of linear regression:
- Simple Linear Regression
- Multiple Linear Regression

Types of linear regression

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Simple Linear Regression predicts a model for the relationship between a predictor matrix (independent variable) $X$ and the response (dependent variable) $Y$.
$$Y=\beta _1 X+\beta _0+\epsilon$$
The coefficients $\beta _1$ and $\beta _0$ are called slope and intercept, respectively. The estimated values for these coefficients are shown as $\hat{\beta _1}$ and $\hat{\beta _0}$.
$$\hat{Y}=\hat{\beta _1} X+\hat{\beta _0}$$

Simple Linear Regression

Multiple Linear Regression is a linear regression that uses **two or more independent variables** to predict the outcome of a response variable. It is more effective and practical to predict or estimate dependent variables by the optimal combination of multiple independent variables than only one independent variable. 
$$y_i = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + ... + \beta_p x_{ip} + \epsilon$$

Multiple Linear Regression

Simple Linear Regression vs. Multiple Linear Regression

https://towardsdatascience.com/regularization-in-machine-learning-76441ddcf99a#:~:text=This%20is%20a%20form%20of,linear%20regression%20looks%20like%20this

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