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Math Help - 3rd order polynomial

  1. #1
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    3rd order polynomial

    When I plot the following data set for x,y

    0,280.32
    60,437.03
    120,441.10
    180,434.34

    I get a curve, that best fits to a 3rd order polynomial which is this equation

    y=0.0001x^3 - 0.0409x^2 + 4.6716x + 280.32


    However, when I re-enter in my x values on my calculator And do the Maths for the equation I do not get the resulting y values which I originally started with, I get out

    0,280.32 which is correct
    60,434.97 which is a little bit off
    120,424.752 far off
    180,379.248 which is very far off

    I did the above in my calulator and online so both are wrong

    why are my last 3 y-values different? And how can I get around this? Basically, I want to calculate all the y values for every x value I enter.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: 3rd order polynomial

    When I plug the values of x into the equation you wrote I get:

    (0,280.32)
    (60, 437.011)
    (120, 441.032)
    (180, 434.193)

    which is a lot closer than your calculation woudl indicate. I don't know why your calculator is giving you answers that are so far off - but I'm guessing that yuo may have used 4.6713 instead of 4.6717 for the third coefficient.

    Also, consider how you have rounded off the coefficients, especially the second one which is good to only three signficant digits (0.0409). Given this rounding the result can be expected to be accurate to only three significant digits as well. If you want more accuracy you need to provide more digits. Try:

    y = 0.0001x^3 - 0.0408958x^2 + 4.671667x + 280.32
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  3. #3
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    Re: 3rd order polynomial

    Can you post your calculation? Exactly the numbers you used

    Yes I tried that too but it made hardly any difference, I mean the rounding shouldn't make that much difference should it?

    Here's a worked example

    0.0001(120^3) -0.0409(120^2)+4.6716(120)+280.32

    =172.8-588.96+560.59+280.32

    =424.73 when the y value is actually 441.10!!

    I'm thinking can there be more than 1 x solution for each y vaue?
    Last edited by aziqbal; March 4th 2013 at 12:49 PM.
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: 3rd order polynomial

    The accuracy of the first coedfficient is very important. You have 0,0001, but a more accurate number is 0.0010942. This is an increase of almost 10%, and when you multiply it by a large number like 120^3 it makes a big difference. Here's the math:

    Your version:
    0.0001(120^3) -0.0409(120^2)+4.6716(120)+280.32 = 172.8-588.96+560.59+280.32 = 424.73

    My version, using 5 significant digits for the coefficients:
    0.00010942(120^3)- 0.040896(120^2)+4.6717(120)+280.32 = 189.08 - 588.90 + 560.6 +280.32 = 441.10
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  5. #5
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    Re: 3rd order polynomial

    Quote Originally Posted by ebaines View Post
    The accuracy of the first coedfficient is very important. You have 0,0001, but a more accurate number is 0.0010942. This is an increase of almost 10%, and when you multiply it by a large number like 120^3 it makes a big difference. Here's the math:

    Your version:
    0.0001(120^3) -0.0409(120^2)+4.6716(120)+280.32 = 172.8-588.96+560.59+280.32 = 424.73

    My version, using 5 significant digits for the coefficients:
    0.00010942(120^3)- 0.040896(120^2)+4.6717(120)+280.32 = 189.08 - 588.90 + 560.6 +280.32 = 441.10
    OMG your so correct thanks for that it works now!!!
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