Calculate the chi-squared probability for the fit

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SUMMARY

The discussion focuses on calculating the chi-squared probability for a linear fit of displacement (D) against voltage (V) using experimental data. The fitted equation derived from Excel is y = 474.82x + 8.3818. Participants debate whether to use this equation for theoretical values in the chi-squared calculation or to assume the relationship should pass through the origin, indicating a direct proportionality between V and D. The uncertainty in displacement measurements is noted as ±5um, while voltage uncertainty is negligible.

PREREQUISITES
  • Understanding of chi-squared statistics
  • Familiarity with linear regression analysis
  • Proficiency in using Excel for data analysis
  • Basic knowledge of piezoelectric materials and their behavior
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  • Learn how to calculate chi-squared values using experimental data
  • Explore linear regression techniques in Excel
  • Study the implications of fitting a line through the origin versus a non-zero intercept
  • Investigate the properties of piezoelectric materials and their linearity
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Homework Statement



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

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?
 
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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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