# Calculate the chi-squared probability for the fit

1. Oct 11, 2011

### blueyellow

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. Oct 11, 2011

### blueyellow

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