Context: I am not necessarily advocating a curve-fit approach to every problem like this. There are times when a function-based model does not estimate actual measurements with sufficient accuracy, or it is simply preferred to use another approach such as piecewise linear or more complex fits.
That said, I was working with the data in this example to show a few different options for generating function-based models with Excel. The data table and chart below shows four different models, with a visual depiction of their performance based on residuals. The residual is just the difference between the model's estimation and the actual measurement at each known measurement value.
The four examples are: (1) Linear, as a baseline to which improvement is desired, (2) Poly 2, a second order polynomial, (2) Poly 2+, also second order, but with the 0 and 100 level measurements repeated 4 times, and (3) Poly 3, a third order polynomial.
One take-away is that you can improve the fit (reduce the residual) over certain regions of the fit by repeating those measurements in the curve fit routine. This was the point of Poly 2 vs. Poly 2+ which reduced residuals at the ends, but increased them in other regions.
Another is that the third order fit was great until about 40% on the input, where the residuals took off (literally) exponentially.
Since the piecewise linear model, by definition, sets the estimate to the actual at each point, it is not really possible to compare its performance in a similar manner. And since the values between each measurement are not known, it is not really possible to precisely assess the error due to measurement non-linearity between those points. Of course, the more points the better. (The extreme being just the end points, which is the linear model shown below.)
In any case, if the model (linear, curve, piecewise) error is significantly less than the instrument measurement error, it will not make that much difference in overall performance which is selected. In that case, other factors such as programability, supportability, run-time load, documentation, etc. would drive the decision on which to use.