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
