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September 12, 2000, 05:45 
How to get a formula from data.

#1 
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hello, everyone.
Now I have a lot of data from simulation to be dealt with. The only thing I want to do is to summarize a formula with those data. For example, y=f(x1,x2,x3). CAN anyone tell me a thread about how to do to get a formula from a series of data. Thank you. 

September 12, 2000, 06:53 
Re: How to get a formula from data.

#2 
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Well, what you should do is interpolate your data in your computational domain, but there are a lot of ways for doing this. The simpler thing to do is defining a polinomial such as
a0 + a1x +a2x^2 + .... = y where a0,... are the unknowns and x is your variable (you can easily extend this to multiple variable), and assign your data to this curve obtain the numerical coefficients a. The accuracy of course depends from the maximum exponent of the polinomial you choose. This is obviously not the best method but you can find a lot of bibliography on this argument (data interpolation). Just one more thing ... remember that the relation you'll find will be valid (with a certain error of course) only within your computational domain. 

September 12, 2000, 18:43 
Re: How to get a formula from data.

#3 
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Plot the data in a spreadsheet like excel. Now using excel graph plotting join the points with a line through the data. It might be linear, nonlinear, exponential, power law, semilog etc, etc.
Depending on what type of curve you choose, excel will automatically display the formula of the stline or nonlinear curve which you see on the plot. Hope it helps. 

September 13, 2000, 00:28 
Re: How to get a formula from data.

#4 
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Thank you indeed. But i still don`t know how to extend one variable to multiple variables. And would you please tell me what bibliography should I refer to. I`am sorry for wasting your time.


September 13, 2000, 03:49 
Re: How to get a formula from data.

#5 
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Application like Excel and so on do exactly what I said, but of course they are useful for statistical data (spreadsheet were firstly made for economical study) but not at all for mathematical. I mean, does Excel give you the error of your (its...) approximation ? Of course NOT ! This means that for simple and rough study Excel it's good, but if you need some relevant data to compare with others you have to proceed with an interpolation scheme (usually more complex than what Excel can do).
The extension to multiple variable means you have to build a complete polinomial, like this (two variable x1,x2) a0+a1(x1)+a2(x2)+a3(x1)^2+a4(x2)^2+a5(x1)(x2)+... =y Bibliography. I may advise you a lot of books but none is in english (Italian, Russian ...), you'll find more explanation on every book of numerical methods. You may even search over the net ... As a first step try www.efunda.com/math/num_interpolation/num_interpolation.cfm Bye. 

September 13, 2000, 04:37 
I really appreciate.

#6 
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September 13, 2000, 07:33 
Re: How to get a formula from data.

#7 
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The best book I've found on this topic is by far:
INTRODUCTION TO LINEAR REGRESSION ANALYSIS Douglas C Montgomery & Elizabeth A Peck AFFILIATION: Arizona State University; CocaCola Company SOURCE: (New York City, New York, USA; John Wiley, 1992, Wiley series in probability and mathematical statistics  applied probability and statistics, 2nd ed., 540pp.)  most of their stuff can be implemented quite easily in MATLAB. 

September 13, 2000, 09:57 
Re: I really appreciate.

#8 
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Beside all the aforementioned suggestions, I meight recommend you to read about the subject in one of the "deisgn of experiment" book. Also, if you have an access to one of the statistical packages (for example: SPSS or MINITAB) I was using the later for something like what you are looking for. Good luck


September 13, 2000, 21:43 
HELP!!!

#9 
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Dear CFD user,
I am totally new to CFD and would very much appreciate if you could possibly give me an idea of any books that are at a beginner level. Also any books that cover CFD for sprays. Thanks 

September 14, 2000, 03:25 
Re: HELP!!!

#10 
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I meight suggest the book"Numerical Heat Transfer and Fluid Flow" by Patankar.


September 14, 2000, 05:09 
Re: Interpolation

#11 
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Hi You see I'm working at the same problem First of all you should know what for do you need this formula!!! If only for graphical demonstration  for example You don't need it at all ) As for me I prefer to work with splines they are just easier to use! For example using polinoms you can have problems with finding coefficients!!! You have to solve the linear system and so on May be Matlab will be enough for your purposes I don't know So if you are interested you can mail me for soon I'll have some source code and sure have some more ideas.
Yours Lex.Privalov 

September 17, 2000, 00:28 
Re: How to get a formula from data.

#12 
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perhaps the best thing would be for you to acquire som software package that does this right off the top of my head i can't think of one but you can check in ASME's "mechanical engineer" there's a software advertised each month in here that does this kind of thing. also you mathematician statistician friends can recommend one to you or any techniques to do it yourself.


September 25, 2000, 13:30 
Re: Interpolation

#13 
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besides, polynomial fitting can lead to oscilations, so it is better to use splines!


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