Manual Weighted Least Squares Estimation

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!

Answer 1

[Ajit Kasturi]

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; 

For more information, refer the following link:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

[Chris Herdelin]

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]

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

'.^'.