How is this expression checking the linearity of the measurement? Looks to me like you subtracted the average from the average. And your measurements are just complementary sequences (by description and by value), how is this establishing the deviation from a slope? By your description of the experiment, the v2 set should be negative; why isn't it?
Assuming the resistors are exactly equal (you didn't mention if this was established or not), the results should be spaced exactly linear, i.e., V1(i + 1) = V2(N - i) = i * Vsrc / N (for each i in the range 0:(N - 1), taking N measurements from N-1 exactly equal resistors).
You can perform a ratiometric test by calibrating each resistor relative to the other, i.e., measuring from tap j to j-1 (j = 1 to N-1). These ideally will be equal measurements, but until linearity is established, cannot be calculated from the element-to-element differences in the v1 or v2 series. You can then perform the j to j-2 measurements (j = 2 to N-2), and so on, until you've built a triangle of differences. Then you can compare the respective sums to their measured values and establish linearity at these discrete points.
Note that this does not guarantee linearity for an arbitrary real-valued input, i.e., it only proves the error at the points shown, and not the complete transfer curve y = f(x) and its possible deviation from y_ideal = m*x + b. Doing an exhaustive proof point-by-point would of course be prohibitive (impossible on the reals, but possible for a digital converter -- if extremely tedious), but if continuous-time approaches are suitable, you can use some analysis to get a better confidence range on that figure.
For example, if it's a sampled ADC, apply a known low-distortion sine wave, at a frequency within its passband, and after gathering many sample points (10^3 to 10^6+), compute THD+N. This works well for higher sample rate converters (1k to 100M+), because the sine wave can be prepared with known stability and purity (such as crystal oscillators and passive (and low distortion) filters), and the acquisition period is brief. This doesn't work so well at low sample rates, where the sine wave becomes difficult to generate (noisy RC oscillators, drifty filters, amplifier distortion), especially to the required precision. Triangle waves are also a possibility (using a square wave of known stability, followed by a precision integrator; error can simply be computed as the time difference, x[t] - x[t - 1], averaged over the rising, then falling slopes, each, cutting off the peaks as needed).
Note that, unless you can guarantee that two converters should necessarily have different kinds of nonlinearity, it is not sufficient to simply cross-check their results. Using one DMM to calibrate another of the same model would be kind of silly, as they would be expected to exhibit the same nonlinearities in the same places. One might take a small significance by comparing, say, a SAR ADC to a D-S type. But, one point does not make a statistical study. A representative establishment of true linearity could only be made by averaging over many very different measurement methods, hopefully with orthogonal nonlinearities, which is the real point to drive at here. The best way is to use true linearity whenever possible; measuring voltage differences directly, rather than trying to infer them through disparate methods. Hence the triangle table of voltage drops earlier.
Tim
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