Problem 43553. Linear Least Squares (L2 fitting problem )

Created by Luca Fenzi

Difficulty:Rate

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Given a set of real measurements

     (x(i), y(i))

find a line sol(1)x + sol(2) (more specifically furnish the vector with sol=[sol(1),sol(2)])such that it fits the data (it minimises the 2 norm)

Example: Input:

% INPUT
x=linspace(0,1,50);
y=4*x-1+ randn(50,1); % perturbed observations
% SOLUTION:
sol=[4,-1]

HINT : This problem can be expressed as a convex optimisation problem:

min_{sol} sum(sol(1)*x+sol(2)-y)^2

Suggestion: use the following code to test your function:

plot(x,y,'.') % plot the data
hold on
plot(x,sol(1)*x+sol(2))
legend('measurements', 'L2 fit')

Solve

Solution Stats

56 Solutions
15 Solvers

Last Solution submitted on Mar 21, 2023

Last 200 Solutions

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1 Comment

David Verrelli on 5 Jul 2018

Hello, Luca Fenzi. This looks like an interesting problem. However, it can still be improved a bit. (1) It is recommended that at least four test cases be provided, though more are often necessary to prevent hard-coded workarounds. (2) The Test Suite does not rigorously check the individual elements of the output vector, only their sum; that leaves it open to passing completely incorrect submissions as demonstrated in Solution 1575892. (3) In the Problem Statement, it is highly unlikely that the output would be exactly [4, -1]; the presence of random perturbations means that the output might be [4.3, -1.2] or [3.9, -0.8], say. Although there is a suitable allowance in the Test Suite for 'random' variation in the outputs, it would still be advisable to amend the Problem Statement. —DIV

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Problem 43553. Linear Least Squares (L2 fitting problem )

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Problem 43553. Linear Least Squares (L2 fitting problem )

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