MATLAB: Is left divison faster than polyfit(x, y, 1)

ldividelinear regressionpolyfit

In linear regression, results from two approach are the same.
>> x = 1:10;
>> y = x * 2 + randn(1, 10);
>> b = [ones(1, 10); x]' \ y'
b =
    -0.7021
    2.2412
>> p = polyfit(x, y, 1);
p =
    2.2412    -0.721
I can see the implementation of `polyfit` by typing `edit polyfit`. However, I can't see the built-in function `ldivide`

Best Answer

There is some overhead in polyfit due to the error handling. Checking the inputs is a really good idea, but if you are absolutely sure that the inputs are correct, this can save some time:
function p = fPolyFit(x, y, n)
x = x(:);
V = ones(length(x), n + 1);   % Vandermonde matrix
for j = n:-1:1
   V(:, j) = V(:, j + 1) .* x;
end
[Q, R] = qr(V, 0);            % Solve least squares problem
p      = transpose(R \ (transpose(Q) * y(:)));
And if you have to solve this with the same x and different y, storing the Vandermonde matrix can accelerate the code again.
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