How do I can build a MATLAB code to fit the following equation using least square sense ?

here is my equation : y=a+bx;

x=[1 2 3 4 5 6];

y=[3.5 0.5 -1.5 -3 -4.5 -7 ];

I've try this code

clc;
clear all;
close all;

%we need to do a line fitting to the following equation (y=a+bx) 
X=[1; 2; 3; 4; 5; 6]; %
Y=[3.5; 0.5; -1.5; -3; -4.5; -7];
N=length(X);
AB=(X'.*X)*(X'.*Y); %coefficient matrix [a,b]
plot(X,Y,'o') 
hold;
plot(AB(1:3,:),AB(4:6,:),'r-');

is that right? and what is the values of a,b

Answer 1

[Hiro Yoshino]

The X dependes on how you want to fit your line to the data.

e.g., then X will be a series of stacked vertically upto the end of the data number.

[Mohammad Adeeb]

how is that going to br reflected on my code?

[Mohammad Adeeb]

is it like this

clc;
clear all;
close all;
%This program is to solve proplem in HW"8"
%we need to do a line fitting to the following equation (y=a+bx) 
x=[1; 2; 3; 4; 5; 6]; %
y=[3.5; 0.5; -1.5; -3; -4.5; -7];
N=length(x);
X=[ones(N,1),x];%write x in this format to prepare for fitting process
Y=y;
AB=(X'.*X)*(X'.*Y); %coefficient matrix [a,b]
plot(X,Y,'o') 
hold;
plot(AB(1)+AB(2),'r-');

[Mohammad Adeeb]

if yes an error will happen

''Matrix dimensions must agree.

Error in HW8_least_square_Method (line 11)

phi=(X'.*X)\(X'.*Y); %coefficient matrix [a,b]''

[Hiro Yoshino]

AB = X\y;
y_hat = X*AB;
plot(x,y,'b-',x,y_hat,'r-');

Please try to see how it fits to your thought.

[Mohammad Adeeb]

i don't think this is right

[Hiro Yoshino]

This is what I got. It looks all OK.

[Hiro Yoshino]

x=[1; 2; 3; 4; 5; 6]; %
y=[3.5; 0.5; -1.5; -3; -4.5; -7];
N=length(x);
X=[ones(N,1),x];
b = X\y;
y_hat = X*b;
plot(x,y,'bo', x,y_hat,'r-');

This is good enough.

[Mohammad Adeeb]

Ok Thank u so much

[Mohammad Adeeb]

How can i get the values of a,b ?

[Hiro Yoshino]

b = X\y

is the corresponding estimated coefficient vector.

[Mohammad Adeeb]

Thank u ❤