Help with linear regression function

Hello, community.

Can someone help me with the following assignment.

Given a set of approximate x and y coordinates of points in a plane, determine the best fitting line in the least square sense. Using the standard formula of a line ax + b = y, compute a and b. That is, write a function that takes two row verctors of the same length called x and y as input arguments (containing x and y coordinates of points) and returns two scalars, a and b specifying the line, as output arguments.

I can't use polyfit

Thank you in advance!

Answer 1

[Image Analyst]

Homework hint: Use the backslash operator. See the FAQ:

https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data.3F

They do it there.

[Jesus Alejandro Rodriguez Morales]

Thank you, it's done

[parsa soleimani]

if you have the answer now can you send it please?

Answer 2

[Erandi T. Sandarenu]

This was done without using backslash operator. But it works!

function [a b] = lin_reg(x,y)
  X = mean(x);
  Y = mean(y);
  a = sum((x-X).*(y-Y))./sum((x-X).^2);
  b = Y - a*X;
end

Answer 3

[Erandi T. Sandarenu]

This was done by using the backslash operator.

function [a b] = lin_reg(x,y)
 matrix = [x; ones(1,length(x))]';
 x = matrix \ y';
 a = x(1);
 b = x(2);
end

[Mohaddeseh Mohammadi]

Hello, Could you please explain the method you used? I can not understand what is matrix = [x; ones(1,length(x))]'; for.

[Image Analyst]

It's easy just to try something and see. Make x a row vector of 4 elements and see what it gives:

x = [1,2,3,4]

x = 1×4

1 2 3 4

matrix = [x; ones(1,length(x))]'

matrix = 4×2

1 1 2 1 3 1 4 1

So it takes a row vector and puts a row of ones below it

m = [x; ones(1,length(x))] % Append row of 1s below our x row vector.

m = 2×4

1 2 3 4 1 1 1 1

matrix = m'    % Transpose it.

matrix = 4×2

1 1 2 1 3 1 4 1

and then transposes it, with the apostrophe operator, to make the 1s be in the right column instead of the bottom row.