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Homework Help: Finding coefficients from equation

  1. Oct 15, 2008 #1
    Hello,
    I am stuck on a math problem for one of my engineering courses which seems fairly straight forward, but I have had little success with. The problem reads as follows:
    The following data has the form y=ax^b. Estimate the coefficients a+b.
    Given data:
    Y X
    1: (0.0014) (0.5)
    2: (0.0251) (2)
    3: (0.153) (5)
    4: (0.6371) (10)

    What I was trying to do was plug in the first set of values and solve the equation for one coefficient in terms of the other. Then I would take the second set of data and plug my answer in, giving me like terms. If someone could explain to me the process of solving this equation I would really appreciate it
    Thanks
     
  2. jcsd
  3. Oct 15, 2008 #2

    EnumaElish

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    Homework Helper

    Log y = Log a + b Log x

    Use least squares to estimate Log a and b.
     
  4. Oct 16, 2008 #3

    HallsofIvy

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    The problem does not ask you to FIND the coefficients, it asks you to ESTIMATE them. Putting x and y equal to each pair of given numbers into y= axb gives you an equation for a and b. You should only need two equations but you have four and probably can't find a single a and b that will satisfy all four.

    From the "extreme" pairs, 0.0014= a (0.5)b and .6731= a 10b. Dividing the second by the first eliminates a: .6731/.0014= 0.5b/10b which is the same as 480= (1/20)b= 20-b. As EnumaElish said, you will need to use logarithms to solve that.

    (Thanks to TheoMcCloskey for noting my error. I had started to use the first two points and didn't complete change when I decided to use first and last.)
     
    Last edited by a moderator: Oct 16, 2008
  5. Oct 16, 2008 #4
    Hall's - I think you better review your response - it needs some corrections.
     
  6. Oct 16, 2008 #5
    Thank you for the help. I was able to determine the answer both algebraically and on my calculator
     
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