# Manual Weighted Least Squares Estimation

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Chris Herdelin on 17 Jun 2020
Commented: Chris Herdelin on 19 Jun 2020
I have estimated WLS manually by dividing each of the coefficients by income^0.5. My question is, when I do that, does it automatically divde the constant by income^0.5? If not, how would I add 1/income^0.5 for the constant? Would I just create a variable for 1/income^2 and then add it to the matrix where I have all of my coefficents? Any help you could give would be greatly appreciated!

Ajit Kasturi on 18 Jun 2020
Assuming that you are asking whether division of each element of the matrix works, Yes it does. You can divide/add the constant (in your case it is 1/income^2) element-wise to a matrix as shown below.
Income = 2;
x= [1 2 3; 2 3 4; 4 5 6];
c= income^2;
Y=x/c;
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Chris Herdelin on 18 Jun 2020
Thanks so much! Ok. That makes sense. Then how do I include the constatn when performing the regression mdl = fitlm(X,Y)? Doesn't the regression automatically calculate the constant? How do I incorporate the constant 1/income^2 into the regression equation? Thanks again!
Chris Herdelin on 19 Jun 2020
Income = 2;
x= [1 2 3; 2 3 4; 4 5 6];
c= income^2;
Y=x/c;
Error using ^ (line 51)
Incorrect dimensions for raising a matrix to a power.
Check that the matrix is square and the power is a
scalar. To perform elementwise matrix powers, use
'.^'.

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