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

University of Michigan - Ann Arbor

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

Simple linear regression predicts a model for the relationship between a single predictor (independent variable) $$X$$ and a response (dependent variable) $$Y$$. $$Y = \beta_1 X + \beta_0 + \epsilon$$ The coefficients $$\beta_1$$ and $$\beta_0$$ are called the 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

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.

Learn Before

Related