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Least Squares

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Given this data:

    hours / value
    -----------
    2 | 1.6
    4 | 1.5
    6 | 1.45
    8 | 1.42
    10 | 1.38
    12 | 1.36

    fit a curve of the form Y ≈ [itex]ae^{-bx}[/itex]

    What value can you predict after 15 hours?

    3. The attempt at a solution

    So i can rewrite the equation as Y ≈ log(a)-bx by taking the logarithm of the original equation.

    How do i go about doing a least squares approximation of this? Our lecture notes have no examples that actually show how we are supposed to compute these coefficients.
     
  2. jcsd
  3. Apr 2, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your equation rewrite is wrong:

    If y = a e^(-bx) then you must take logarithms of BOTH sides to obtain:

    LN(y) = LN(a) - b*x

    You can use least squares for linear equations to fit the data.
     
  4. Apr 2, 2013 #3
    Are there any suggested readings for actually figuring out how to compute a least squares approximation? I've read a handful of different notes and i'm still stumped. It would be nice if there was just a nice step by step methodology to this.
     
  5. Apr 2, 2013 #4

    Ray Vickson

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    Google is your friend. There are hundreds of explanatory articles, ranging from very elementary to very advanced.
     
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