APPENDIX II FITTING OF DATA TO EQUATIONS
The purpose of fitting equations are several fold.^ a) To
summarize a mass of data in order to obtain predictive equations,
formulas and calibration curves? b) To confirm or refute an established
theory or relationship by comparing and evaluating several sets of data
in terms of certain parameters and c) To develop a theoretical model.
A good method of fitting data to equations should^1
a) Use all relevant data.
b) Have resonable economy in the number of parameters chosen.
c) Take into account the error in the data.
d) Find outliers, if any.
e) Provide some measure how well the equation will predict future
events.
Least square (LS) estimation. The method of least square is used to
estimate the values of the parameters in an equation that will minimize
the sum of squared deviations of the observed values from those
predicted by the equation.
Linear LS estimation. By definition, the requirement for linear
least square estimation is that the equation chosen is linear in all its
coefficients, i.e.,
C = aX + bY + . + c Eq. A1
where X, Y,. . are the independent variables and a, b,. . are the
constant coefficients. These coefficients are linear as they can be
calculated directly from the values of the independent and dependent
variables.
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