Flow rate

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Originally Posted by angelica2007

So would the best fit line be the one that crosses the most points?

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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

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?

Quote:

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Originally Posted by angelica2007

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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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

So

Quote:

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Originally Posted by angelica2007

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?

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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

en

Quote:

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Originally Posted by angelica2007

This is what my graph looks like:
http://img236.imageshack.us/img236/4264/quarticdy5.png
Is it sufficient enough although, there are a couple outliers?

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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