0

I have a set of samples with an age given with some uncertainty (x $\pm$ dx) and that have some measured property with some given uncertainty (y $\pm$ dy). I would like to fit a curve that begins at $(x_o,y_o)$ and ends at $(x_f,y_f)$. I know the values of $y_o$ And $y_f$ and have a range of values to test for $x_o$ And $x_f$.

For similar data that only had uncertainty in the measured data, I generated lines that fit the data that had the form $y(x)=ax^2+bx+c$ and determined their goodness of fit using a reduced chi-squared statistic. Is there a way to calculate a similar goodness of fit of a line to data that have uncertainties in both x and y?

I did find this answer. However that assumes that a line fits the data. I know that the data require a nonlinear fit. Does anyone know of a similar method for a nonlinear function? Could I use the same process as in the linked answer except with a nonlinear function? To keep this specific, what would this look for the quadratic I gave above?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
js16
  • 49
  • 5
  • Do you want GoF for *the data* or for the NLS model that you are trying to fit? For the data, you have to assume the probability model for the joint data and create some appropriate metric for it. For instance, if $(X,Y)$ are joint normal, then the statistic $[X-\mu_x, Y-\mu_y]^T \hat{\Sigma}^{-1} [X-\mu_x, Y-\mu_y]$ has a limiting chi-square density with 2 degrees of freedom. – AdamO Dec 06 '21 at 17:25

0 Answers0