About Polynomial Curve Fitting?

Question

I am using Polynomial Curve Fitting to analyse data,
but it only work for two N-by-1 vectors of data values, x and y,
how about if I got more than two vectors?

It seems difficult to google relative topic about this.

Answer 1

if you have more than 2 vectors of data, you won't have a polynomial to fit. polynomials graph as curved lines in a 2-dimensional space (like the xy plane). if you have 2 input variables (data vectors) and 1 result vector, your graph will be a surface in a 3-dimensional space. basically, 1 dimension for each variable. try searching on "phase space" and see what you find. and try "multivariable analysis" too.

Answer 2

You're right, this is unique. Usually, people try to approximate complex functions x-->y with a polynomial. If you are trying to predict y with two variables x and z, the best approach would be to predetermine the polynomial coefficients you want to use and use a multiple linear regression to do the fitting.



For example, the usual polynomial fit is



y = a + bX + cX^2 ... and so on



You can add z terms to the equation, and even cross terms between x and z:



For example



y = a + bX + cX^2 + dZ + eZ^2 + f XZ



Hope this helps!

Answer 3

Unless you know that your data is accurately represented by a polynomial, it is better to use cubic splines to represent or interpolate measured data. Polynomials can - and do! - introduce relatively large systematic errors during the curve-fitting process.



Unless you are familiar with the techniques involved, I would recommend you use commercial software suited to your purpose. It would cover multivariate analysis as well. Unfortunately I've been retired for some years now, and have lost contact with my colleagues who were experts in the field and could have recommended a supplier.

Answer 4

The horizontal tangent at (a million/2, a million/2) shows that the vertex is right here. for this reason, we've y = a*(x - a million/2)^2 + a million/2. Plug interior the ingredient (0, a million): a million = a*(-a million/2)^2 + a million/2 a million/2 = (a million/4)a a = 2 y = 2(x - a million/2)^2 + a million/2