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At the moment I am trying to find a best fit equation to radial velocity data vs. time of a planet HD17156b. The paper with the Authors fit parameters (I am trying to mimic the fit) has the arXiv ref number of :0704.1191v2

From this paper I extract their data, which is on the final few pages and take note of their fit parameters.

I use the relevant equations to make a continuous curve using there fit parameters. They say in the paper they achieve a fit with a normalised Chi squared value = 1.17

When I plot the data, and the continuous curve I note that the fit is definitely not close to 1. I believe this is because of the nature of the equations used are highly non-linear and the error in their fit parameters are throwing off the continuous curve.

When I try to find a best fit using the Newton-Raphson method in conjunction with the Levenberg-Marquardt Algorithm I use their best fit parameters as my initial starting point. Assuming surely this would find a good fit to the data. But I achieve a horrible fit. Anybody have any ideas that could help me achieve a better fit similar to the original Authors fit?

Below is a plot of the original Data and the Authors best fit parameters leading to the continuous curve on the plot.

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# Fitting Highly Non-linear Data

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