Finding reduced chi^2 for independent variable?

[khkwang]

Homework Statement

I have a function V = kI
where k is some constant
I_err = 0.005 A
V_err = 0.00005 V

A fit was then made, but a problem occurs when I try to calculate the reduced chi^2.
Since the error of the dependent variable V is so small, the resultant reduced chi^2 is fairly large; with good reason because the vertical error bars clearly don't overlap with the fit data.

However, the large error in the independent variable I is large enough to compensate and so the data agrees with the fit within error. If I flip the independent and dependent variables, I get a perfect reduced chi^2. However for the purposes of the fit, it would be strange to do so.

Is there a way to include the independent variable in the calculation for reduced chi^2?

Homework Equations

The equation I'm using right now is:
chi^2 = sum(((V_exp - V_fit) / V_err)^2)
reduced chi^2 = chi^2/((# of values in V_exp) - (# of parameters))

The Attempt at a Solution

No attempt thus far except switching independent and dependent variables. Which gives a good reduced chi-squared but is not what I want.

 

[mark726]

Hello there,

Thank you for sharing your problem with us. It seems like you are trying to fit a function to experimental data and are having trouble calculating the reduced chi-squared value due to large errors in the independent variable. In this case, it may be helpful to use a weighted least squares fitting method, which takes into account the errors in both the dependent and independent variables.

The weighted least squares method involves assigning weights to each data point based on the magnitude of its error. In your case, since the error in the independent variable is larger, those data points should have a higher weight compared to the data points with smaller errors. This will help to balance out the effect of the large error in the independent variable on the chi-squared value.

Another option could be to use a different fitting method, such as a Monte Carlo simulation, which also takes into account the errors in both variables. This method involves generating a large number of data sets with random variations based on the errors in the original data, and then fitting the function to each data set. The average of the fitted parameters from all the simulations can then be used as the final result.

I hope this helps. Let me know if you have any further questions or if you need any clarification.