I'm asked to find the Reaction Rate when t = 120 seconds (which involves differentiation) for a Generic Chemical Equation. The rate of a chemical reaction is defined as:
R = dC/dt (Differentiation of Concentration with respect to time)
I'm given a set of 11 points (x= time, y= Concentration) which I need to plot in order to find a general trend for them.
After plotting all points and observing the resulting graph, I tried performing multiple different Regression Analyses in order to find a Function (C(t)) that best fits the plotted points.
For each of the Functions I obtained from each individual Regression...
1) I derived each one
2) Evaluated each resulting derivative for t = 120, in order to obtain the Reaction Rate for each case.
Finally, I compared each result (Reaction Rate) with the Literature Value, and calculated an error percentage for every case.
These were my results:
My question is:
Many sources (including my book) claim that a High-Degree Polynomial Regression (Cubed Regression and above) is not appropriate for describing a Physical Phenomenon, even when the Regression Fit is perfect (R=1).
However, based on the table above, the most accurate answer I got was obtained through a Quartic Regression, while the rest had considerably higher error percentages.
Am I missing something or is it just an exception? Any clarification would be much appreciated!