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Math Help - Flow rate

  1. #16
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    Quote Originally Posted by angelica2007 View Post
    So would the best fit line be the one that crosses the most points?
    The choice of best fit criteria is really dependent on what you want to
    do, but if y(t_1) ... y(t_n) are what the model predicts at times t_1, .. t_n,
    and o(t_1), .. , o(t_n) are the observed values, then the model which
    minimises:

    SSR = (o(t_1)-y(t_1))^2 + (o(t_2)-y(t_2))^2 + ... + (o(t_n)-y(t_n))^2

    would be considered the best (subject to a number of considerations about
    how much noise there is in the measurement process, and how many
    parameters you have to estimate in the model from the data).

    You should be aware that you can put a polynomial of degree (n-1)
    through any n data points of this type. So perfection is possible but
    is overkill, and will result in a poor model.

    RonL
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  2. #17
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    I appreciate you help so much! You have helped me out alot. To estimate the flow rate of the data would take the average of the values for the flow?
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  3. #18
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    Quote Originally Posted by angelica2007 View Post
    I appreciate you help so much! You have helped me out alot. To estimate the flow rate of the data would take the average of the values for the flow?
    You either differentiate you prefered model, or you compute the
    difference quotients from the data, as I described and plotted in
    my second post in this thread.

    RonL
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  4. #19
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    So
    Last edited by angelica2007; March 1st 2007 at 12:06 PM.
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  5. #20
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    Quote Originally Posted by angelica2007 View Post
    So my best-fit curve is y=.00005x^4 - .01318x^3 + .80781x^2 + 6.202162x + 346.64309 and for my rate of change i got .00021x^3 - .03956x^2 + 1.61562 + 6.20216. Does that look reasonable?
    Can't comment on how good the quartic is a fit to the data, but the rate
    of change looks OK except where you seem to have lost the x in the next to
    last term.

    RonL
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  6. #21
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    en
    Last edited by angelica2007; March 1st 2007 at 12:05 PM.
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  7. #22
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    Quote Originally Posted by angelica2007 View Post
    This is what my graph looks like:

    Is it sufficient enough although, there are a couple outliers?
    What do you think? It depends on what you want to do with the model.

    Is it a good model of the variability of the data, only partialy. There
    should not be long runs of points either above or below the curve with
    a good model.

    RonL
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