Problem 43553. Linear Least Squares (L2 fitting problem )

Created by Luca Fenzi

Solve Later

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

Last solution submitted on Mar 18, 2019

Last 200 Solutions

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1 Comment

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

Problem 43553. Linear Least Squares (L2 fitting problem )

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Problem 43553. Linear Least Squares (L2 fitting problem )

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Last 200 Solutions

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