Linear regression vs. Generalized linear models (GLM): What’s the difference?

This post shows difference between 1) linear regression and 2) generalized linear models

Linear Regression Definition

Linear Regression is a modelling approach that assumes a linear relationship between an output (a.k.a. “dependent variables”) and one or more inputs (a.k.a. “independent variables”).

Example of a simple linear regression with only 1 input variable X1

Here are a few examples of linear regression models in life :

1. Weight(as Y) as a function of a person’s Height (as X)
2. Report Happiness (as Y) as a function of Income (as X)
3. Sales Revenue (as Y) as a function of Marketing Budget (as X)

Assumptions for Linear Regression

• Linear relationship between inputs(s) and output
• Output variable is continuous and unbounded
• Residuals are normally distributed (or follows student-t distribution, if you want to allow for greater variance). Residuals are also called “errors” as they measure how well the regression line fits the data.