# Which function should I use for generating the weighted least squares fit linear line for a given data?

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Vihaan Misra on 4 Oct 2020
Commented: Sindar on 5 Oct 2020
I have a set of data which I generate using the following code:
x = linspace(-10, 10, 20);
slope = 1.5;
intercept = -1;
noiseAmplitude = 15;
y = slope .* x + intercept + noiseAmplitude * rand(1, length(x));
I want to generate a weighted linear least squares fit regression line for the above data points. I don't have the weights matrix so I can go with using the formula w(i) = 1/variance(i)^2 or any other default formula that a MATLAB function may use for generating the weights matrix. I don't know how to generate this matrix and make sure its diagonal and then fit a regression line in the data, is there a function in MATLAB which can help me achieve this?

Sindar on 4 Oct 2020
Edited: Sindar on 5 Oct 2020
fitlm accepts weights as a vector, but doesn't come with any pre-designed ones
mdl = fitlm(x,y,'Weights',weight);
Ypred = predict(mdl,x);
plot(x,y,'k*',x,Ypred,'r')
determining variance values for your points is a separate question (my answer would be "huh? I don't think that's a sensible quantity," but if you ask clearly, others may have an answer)

Sindar on 5 Oct 2020
(if the variance is defined from your underlying distribution, it looks like it should be constant since your noise doesn't depend on x)
Vihaan Misra on 5 Oct 2020
Thanks a lot!! I have been trying to generate the weights matrix but can't seem to do so, I am very new to MATLAB so any input will be really helpful
Sindar on 5 Oct 2020
I'd check out the Matlab online trainings (I believe most are currently free), starting with the Onramp (always free).