How to find the uncertainty of a slope (using software)?

[dilloncyh]

I've just done an experiment and need to calculate the slope of the best fit straight line, but I'm having some trouble with it.

First, let me briefly describe the experiment. I need to vary the distance two metal plates and find the capacitance of it. I tried to record the value a few points on the curve (time and voltage) shown on the oscilloscope, and then plot the graph of ln(V/V0) against t, and the slope equals -1/RC. Then, after I got the values of C for a few different distances, I plotted another graph C against 1/d, and the slope equals permittivity times area of the plate.

Here comes the problem. When I used the software origin to plot the graph, it calculates the slope and the standard error. However, standard error only depends on the deviation of the data point from the best fit line (correct me if I'm wrong), but each data point (voltage, time, and so the calculated C) has uncertainty, and the size of the error bar will not affect the standard error, leading to a smaller slope uncertainty that I believe. I can get a value of something like -3 +/- 0.5 for ln(V/V0), and if I draw the max and min slope that fit within the error bar, the uncertainty is definitely larger than the standard error that origin calculates. So, my question is, are there other methods to estimate the uncertainty of the slope other than using standard error, like drawing two more slopes with the maximum and minimum values? I'm expecting some ways of doing it using the computer(like using origin or other software), as I will need to attach the graph to the soft copy of my lab report.

thanks

 

[Simon Bridge]

You want to use some form of weighted least squares regression.
http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd143.htm
... if the program used the errors on each data point as part of the calculation, then it has likely already done this.
i.e. MATLAB has this ability: http://au.mathworks.com/help/curvefit/least-squares-fitting.html