How can I find the coeficients alpha, beta of the simple linear regression, using "\" operator

How can I find the coeficients alpha, beta for the X coordinates of the simple linear regression, using "\" operator?

Answer 1

[Torsten]

x = (0:0.1:1).';
y = 3*x + 4 + 0.01*randn(numel(x),1);
A = [x,ones(size(x))];
b = y;
coeffs = A\b;
coeffs(1)

ans = 3.0072

coeffs(2)

ans = 3.9919

[Ihor]

Thank you! What does it mean?:

A = [x,ones(size(x))];

I know that will be a matrix, but what does it do?

[Torsten]

You want to solve

x(1)*a + 1*b = y(1)
x(2)*a + 1*b = y(2)
...
x(end)*a + 1*b = y(end)

for a and b.

If you write this in matrix form M*[a;b] = v, you get the above M and v (I named them A and b), and you solve for [a;b] as

ab = M\v.