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Calculate the chi-squared probability for the fit

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data

    an experiment is performed to test whether the displacement D produced on a piezoelectric drive behaved linearly with the potential voltage V applied across it. The following data are obtained:

    V (volts) D (um)
    0.1 50
    0.2 101
    0.3 151
    0.4 198
    0.5 249
    0.6 298
    0.7 346
    0.8 393
    0.9 438
    1 181
    1.1 521

    the uncertainty on the voltage setting can be considered negligible. While the displacement measurements are performed with a linear encoder with an uncertainty of +-5um

    calculate the chi-squared probability for the fit

    3. The attempt at a solution
    when I plotted the graph the equation Excel displayed was:
    y=474.82x+8.3818

    I have thought about two possibilities:

    when calculating chi-squared, the values of V(subscript theory) be taken by using the equation on the least-squared-fitted graph on Excel?

    y=474.82x+8.3818

    or does one assume that V is supposed to be proportional to D and that the graph is meant to go through the origin?

    Should I use the above equation to work out what Dis supposed to be in theory when working out chi-squared? or should I assume it's supposed to go through the origin?
     
  2. jcsd
  3. Oct 11, 2011 #2
    by the way, I had trouble getting the values in the table to look presentable on the screen, but I'm sure you can guess what I meant
     
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