The link referred to in this thread
contains an equation trying to fit cost index data from 1950 onwards to a sixth degree polynomial. Come on! This is not good engineering practice for any such set of data.
1. Most of the parameters in that sixth degree equation are not significant
2. A cost or price index curve should be expected to be exponential, rather than polynomial, as this would be the case for a constant growth rate (or rate of inflation in this case).
3. Looking at the data they seem best described by one exponential (i.e. constant rate of inflation) for the years 1950-80, then a new exp curve (reduced inflation rate) for the years thereafter
4. Any model should be tested by its ability to predict. The polynomial predicts a sharp price increase in 2003 and the years ahead. Is that credible? If you just want to interpolate, a simple linear interpolation between adjacent points will do.
A footnote on item 2: I once saw an attempt to fit gas density vs. temperature (constant pressure) by using a high degree polynomial, disregarding the ideal gas law which tells us that including a 1/T term would explain most of the variation (not to mention the work done on equations of state to model deviations from this ideal behavior). Linear regression (aka curve fitting) is a wonderful tool, but a little insight and critical sense are necessary too.