MATLAB: How to vectorize this loop

MATLABregressionvectorization

I have a time series of X and Y variables and I want to run a linear regression on it based on a specific time window length. This ends up giving me a time series of regression coefficients. My current implmentation using a loop to picking out data and running a regression on it. How can I vectorize this piece of code?
window_length = 10;
regression_coeff = [];
for i =1:length(X) - window_length 
   regression_coeff = [regression_coeff; regress(Y(i:i+window_length ),X(i:i+window_length )];
end

Best Answer

You are calling regress with two vectors. That is the same as a projection using the dot product. So then your code could be written like this:
window_length = 10;
W =ones(window_length+1,1);
regression_coeff = conv(X.*Y,W,'valid')./conv(X.^2,W,'valid');
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