Fitting a Line using Least Squares

Interactive links:
1DOF: https://cryptic-spinach.github.io/1DoF/
2DOF: https://cryptic-spinach.github.io/2DoF/
2DOF mobile: https://cryptic-spinach.github.io/lea...

Collaboration links:
I worked with Chase Reynolds for the #SoME2 contest. Check out his website and Twitter here.
https://chasereynolds.me/

The Least Squares method is widely used to fit curves to data. This is called Least Squares regression. This video shows how to solve the ordinary least squares minimization problem for 1 unknown and 2 unknowns. In practice though, it can be used to fit many different types of nonlinear functions too! As long as the minimization can be expressed like this:
min || [A]X - b ||

Then the solution is
X = inv([A]^T[A])[A]^T b

Chapters:
0:00 Intro
0:40 Problem Definition
1:32 Def 1: Vertical Distance: min || r || (1 norm)
2:15 Def 2: Perpendicular distance
2:38 Def 3: Least Squares min || r || (2 norm)
3:28 Calculate Error
5:06 Convex Parabola (1D)
6:06 Proof (1D)
8:51 2D Intro
9:27 Calculate Error in Matrix form
11:52 Convex Parabaloid (2D)
12:45 Proof (2D)
15:58 MATLAB code & summary
16:47 Outro

Music:
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

Other Music:
Nuclear Lynx - Discovery
--
Patreon:   / virtuallypassed  
Instagram:   / virtuallypassed