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

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Ihor
Ihor 2022-12-10
编辑： Torsten 2022-12-11
How can I find the coeficients alpha, beta for the X coordinates of the simple linear regression, using "\" operator?

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Torsten
Torsten 2022-12-10
Ran in:
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
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Torsten
Torsten 2022-12-11
编辑：Torsten 2022-12-11
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.

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