Least Absolute Deviations (L1-norm) line fit - degree 1 - MATLAB Cody - MATLAB Central

Problem 45851. Least Absolute Deviations (L1-norm) line fit - degree 1

Matlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system. <https://www.mathworks.com/help/matlab/ref/polyfit.html>
An often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model https://en.wikipedia.org/wiki/Least_absolute_deviations
- - -
You are given two vectors X and Y (coordinates of observations on a plane). Return a row vector P = [a, b] with the coefficients of the best-fit line, in the L1-norm sense. I.e., find a and b that minimize sum( abs( Y - a*X - b ) ) .
(compare your results with polyfit on the test suite!)
Solve

Solution Stats

44.0% Correct | 56.0% Incorrect
Last Solution submitted on May 12, 2024

Problem Comments

Solution Comments

Show comments
PIVlab surpasses 100K all-time File Exchange downloads
During the past twelve months, PIVlab, a MATLAB Community Toolbox for particle...
Mike Croucher in General
4
8
View Post

Problem Recent Solvers6

Suggested Problems

More from this Author10

Problem Tags

fit optimization regression

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!