About the regression of origin polynomial
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Hello everyone! I am currently using Orign to fit a set of polynomials to a set of data. How do I determine the highest order term? Polynomial in nonlinear curve fitting, it fits the default (I think it is the default) n=9. However, if you choose n=4, 6, R^2 is better, close to 1. So I don’t understand how to choose n in polynomial fitting. I hope if you have done it, please give me some advice. Thank you.
It depends on how many sets of data you have made. I suggest you take a look at the principle of fitting.
I want to learn numerical analysis recently. Can you recommend some good books? Thanks in advance.
"Practical Chemical Computer Simulation—Application of MATLAB in Chemical Engineering" written by Huang Huajiang is very good
Well, thank you. Matlab uses the least squares method for numerical regression, right? What about origin? What kind of regression is used?
Origin should use Gaussian.
Theoretically speaking, the degree of the polynomial should be determined by the model you fit, and this model has been established before the data comes out. Of course, if it is just for processing data, such as calculating interpolation and integrating, this number does not matter much, but within the allowable range of fitting accuracy, it is better to have a lower number. For books on numerical analysis, I recommend reading a textbook for engineering masters, "Fundamentals of Scientific and Engineering Computation", which is quite good, and then combine it with matlab to learn it - it is very easy to get started with this software, but it is too luxurious to install M just to fit point data, haha.
Now I personally try to fit polynomials step by step. When the curves of Nth power and N+1 power are not much different, I choose Nth power.
Low-order ones can be observed, and high-order ones usually only take three to five times. Higher ones are generally not used. If you use them, you should also consider whether there is a problem with the model:)
In other words, you can try them one by one from low to high (for example, starting from 2) and see which one is better for the degree of agreement? Is that what you mean? Now for my data, 2, 3, and 4 all fit better. In the end, I can just choose 2? I can understand it that way. Thank you.