Finding polynomials from a set of coordinates

[Csaba Tizedes]

(03-12-2017 11:31 PM)Dieter Wrote:  

(03-12-2017 08:27 PM)Csaba Tizedes Wrote:  1.) Why do not teach him how he can decide which polynomial degree is sufficient to fit?

Sure – why not? Go ahead! ;-)

OK, let's see:

0.) I'm an engineer, my solution shows clearly how an engineer is thinking about this kind of problems
1.) This data has a minimal- and a maximal value
2.) If I want to select a polynom, at least 3rd order must to use - because the 3rd order has a min. and max. extremum
3.) We have 6 data points, therefore we can use max. 5th order of polynom
4.) Fit 1st, 2nd, 3rd, 4th and 5th order polynom and check where the correlation coefficient is changes dramatically - see the picture below

   

5.) It's looks the 1st and 2nd is worst and 3rd order and above is better solution, the question is that what magnitude of error in each points is acceptable
6.) If no any special requirement, the 3rd is the simplest to use


Csaba