# How does R fit a linear model?

*2021-04-16*

# Chapter 1 Intro & Motivation

This book is the product of my goal to answer the question ‘How does R fit a linear model using the `lm`

function?’ A seemingly simple question based on one of the most humble formulas in all of statistics led me down a rabbit hole of math and programming I never expected.

The goal of writing this is for my own etification, but also to provide a thorough walkthrough so that R-users at all levels of math and programming can have a better grasp on one of the most ubiquitous tools in a statisticians toolbelt.

The book wil be structured largely following my own journey:

- What is a linear model and what is the least squares problem?
- What are the various methods for solving the least squares problem
- How could I write my own
`lm`

function? - How does R fit a linear model with the
`lm`

function

Along the way I include various appendices the dive a bit deeper into some relevant backgroun information. Surprisingly, this humble function will take us on a jounrye through some pretty sophisticated math as well as not one, but two additional programming languages (`C`

and `fortran`

).