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math_proof Group Title

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?

  • one year ago
  • one year ago

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  1. tkhunny Group Title
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    Did you answer the question last night? \(\sum{xy} = B\cdot\sum{x^{2}}\) Have you seen it? Can you create it?

    • one year ago
  2. math_proof Group Title
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    you have to minimize the B right?

    • one year ago
  3. math_proof Group Title
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    how did you already get the summation etc without minimazing and taking derivatives?

    • one year ago
  4. tkhunny Group Title
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    No, you are minimizing the error. You must select the B that accomplishes this task.

    • one year ago
  5. tkhunny Group Title
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    You are asking good questions. This suggests that you have seen the development of Normal Equations.

    • one year ago
  6. tkhunny Group Title
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    \(I(B) = \left(y - Bx\right)^{2}\) Find \(\dfrac{dI}{dB}\).

    • one year ago
  7. math_proof Group Title
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    2x(y-Bx)?

    • one year ago
  8. math_proof Group Title
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    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

    • one year ago
  9. tkhunny Group Title
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    Negative x?

    • one year ago
  10. tkhunny Group Title
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    It doesn't matter, in this case. I just wanted to check to see that you had it right and were moving on.

    • one year ago
  11. math_proof Group Title
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    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

    • one year ago
  12. tkhunny Group Title
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    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?

    • one year ago
  13. math_proof Group Title
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    -2xy-2bx^2 =0

    • one year ago
  14. math_proof Group Title
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    -2xy+Bx^2=0 sorry

    • one year ago
  15. math_proof Group Title
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    2Bx^2=+2xy B=2xy/2x^2 B=xy/x^2

    • one year ago
  16. math_proof Group Title
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    ii see it now

    • one year ago
  17. tkhunny Group Title
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    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.

    • one year ago
  18. math_proof Group Title
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    i am not really familiar with Normal Equation yet

    • one year ago
  19. tkhunny Group Title
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    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.

    • one year ago
  20. tkhunny Group Title
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    Solving for y = a + bx comes out: y = a + bx yx = ax + bx^2 For example.

    • one year ago
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