What is the best solution for fitting points to a curve? (nonlinear data)?

Answer 1

Ther is Lagrange interpolation polynomial, which hits all data points exactly (provided it is a function) but I would go with the previous answer......

Answer 2

The simplest way would be using a non-linear least squares method, but there are some points you should consider before doing so.
If it's just random data, everything will be O.K. But there are a lot of problems you may run into, including heteroscedasticity, autocorrelation etc. You should run some tests on your data to know if it has these problems. If it has them, there are different implications. With some problems, your curve will be all right, but your approximated standard deviation will be useless; in other cases the whole results will be meaningless unless you use special ways for estimation (robust variance-covariance matrices etc.)
If you wish to get further into the topic, I recomend you to read some textbooks. One of the seminal works for econmetrics is written by Greene, and appeared 2003 by Prentice Hall. It could be a bit difficult to read, if you don't have the necessary mathematical background. The perhaps better book for starting would be "Introduction to econometrics" by Stock and Watson.
If you don't want to get a deeper understanding, but you just have one task you must solve, I would propose two ways. The easier one is: find a suitable software package, like EViews (commercial), or R (I think it's open source), feed in your data, estimate your equation choosing some kind of non-linear least sqares estimating option, and hope your residuals are homoscedastic and non-correlated and your model was well defined. If it the outcome is very important, you should go to the nearest college or university, go to the economics or to the mathematics faculty, and ask which professor is involved with econometric studies. Then get an appointment with a junior member of his staff (the prof wouldn't normally have the time for such a thing), tell him you are studying at another faculty and you have this special problem you need to solve for an important homework, and ask him how it is done, if you are lucky he will help you.

Answer 3

there is no best way.

You probably do not have one curve but a family of curves and you want to select the best member of the family

One way to do it is to minimizing the sum of the absolute errors
another way to do is to use a varionatial method

Answer 4

use a narrow interval axies in the numbers of 10 in the gap of 10 in ur graph.

prefferable use a less distance graphs.

Answer 5

Suppose we have "n" points (say {x_0,...,x_n}) ,let F(x)=a0+....+a_nx^n be the curve formula then you should find min value of \sum F(x_i)