cost function을 그래프로 어떻게 그려야 할지 모르겠습니다.

3개의 data (1,1), (2,3), (2,2)를 이용해 직선 y=ax+b의 parameter estimation을 하는 문제입니다.

이의 cost fuction을 3차원에 plot을 해야하는데요

a, b의 구간은 둘 다 [0,5]라고 합니다.

estimate한 직선을 y=1.5x-0.5라고 구했는데

여기서 cost function을 구하라는게 무슨말인지 모르겠습니다.

Answer 1

[Pavan Sahith]

Hello,

I understand you want to estimate the parameters of a linear equation y= ax + b using three data points (1,1), (2,3), and (2,2). You want to plot the cost function in 3d space.

Commonly used cost functions for linear regression problems include mean squared error (MSE).

Please refer to this example code to plot an example cost function for some sample data:

% Data points 
data = [1, 1; 2, 3; 2, 2]; 

% Function to compute the cost (MSE) 
cost_function = @(a, b) mean((data(:, 2) - (a * data(:, 1) + b)).^2); 

% Grid of 'a' and ‘b’ values 
a_values = linspace(0, 5, 100);   
b_values = linspace(0, 5, 100);   
% Create a meshgrid for 3D plotting 
[a_grid, b_grid] = meshgrid(a_values, b_values); 
cost_grid = zeros(size(a_grid)); 

for i = 1:numel(a_grid) 
    cost_grid(i) = cost_function(a_grid(i), b_grid(i)); 
end 
figure; 
surf(a_grid, b_grid, cost_grid); 
xlabel('a'); 
ylabel('b'); 
zlabel('Cost'); 
title('Cost Function Plot'); 

% you can also find best a and best b  
[min_cost, min_index] = min(cost_grid(:)); 
best_a = a_grid(min_index); 
best_b = b_grid(min_index);

Please refer to the MathWorks documentation links to know more about

‘meshgrid’ -https://in.mathworks.com/help/matlab/ref/meshgrid.html

and ‘surf’- https://in.mathworks.com/help/matlab/ref/surf.html