I understand the concept of least squares but I'm not able to wrap my head around weighted least squares (the matrix form).
We convert Ax=bAx=b to WAx=WbWAx=Wb. What exactly happens when we multiply the equation with W? Is the column space of A modified based on the changed equations? Also how do I find this matrix W, assuming I have the given data (The probability of each observation according to a textbook example "Linear Algebra and it's Applications" by Gilbert Strang, page 174, question 42).
Suppose you guess your professor's age, making errors e=−2,−1,5 with probabilities 1/2,1/4,1/4. If the professor guesses too (or tries to remember), making errors −1,0,1 with probabilities 1/8,6/8,1/8, what weights w1 and w2 give the reliability of your guess and the professor's guess?
