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math_proof
method of least squares fit, y=Bx to the following n=6 points (3,4),(1,2),(5,4),(6,8),(3,6),(4,5) and it has to go through the origin can someone help me get started?
Did you answer the question last night? \(\sum{xy} = B\cdot\sum{x^{2}}\) Have you seen it? Can you create it?
you have to minimize the B right?
how did you already get the summation etc without minimazing and taking derivatives?
No, you are minimizing the error. You must select the B that accomplishes this task.
You are asking good questions. This suggests that you have seen the development of Normal Equations.
\(I(B) = \left(y - Bx\right)^{2}\) Find \(\dfrac{dI}{dB}\).
I don't get how did you get the summation equation that you posted, i know how to solve it from there, but how did you figured it out so fast
It doesn't matter, in this case. I just wanted to check to see that you had it right and were moving on.
the question is if there is other way to coming up with the equation to the problem you came up with, instead of going through the minimalization formula then partial derivative =0
Well, there are some Matrix methods, but I'm guessing we don't want to talk about those, today. You have it just fine, excepting that this is a one-parameter derivation so it's just a Derivative, not a Partial Derivative. -2x(y-Bx) = 0 leads to what?
2Bx^2=+2xy B=2xy/2x^2 B=xy/x^2
More importantly, \(xy = Bx^{2}\). Resist the temptation to solve for B. If you've more than one parameter, you WILL become confused. Reach for the standard Normal Equation form.
i am not really familiar with Normal Equation yet
Pretty much just: 1) Everything without a parameter on one side, and 2) Everything with a parameter on the other side - in ascending Order of the terms.
Solving for y = a + bx comes out: y = a + bx yx = ax + bx^2 For example.