The graphs on the left show examples of the problem using a simple line fit expression to describe the uncertainty data. The first graph shows the contribution from all sources listed in the uncertainty budget with the constant and length dependent components identified in different colors. The combined value from the two types of sources produces a curve. 

The second graph shows the problem with trying to describe the curved uncertainty shape using only a best fit line. The biggest concern with this is that the line at length zero (Y Intercept) is almost always lower than what could potentially be achievable by the laboratory. In some cases this value may even show as a negative if the curve is pronounced enough. 

The third graph shows a set of actual uncertainty data compared to the curve fit representation. Although the fit is not perfect it is much better at describing the actual shape then what would be possible using only a line. The expression used to generate the shape is displayed below the graph with L representing the position in meters. 