Nonlinear Data (Curve Fitting)

• In many cases, data from experimental tests are not linear, so we need to fit to them some function other than a first-degree polynomial.
• Popular forms are the exponential form
  $$y=ax^b~~ or~~y =ae^{bx}$$

• The exponential forms are usually linearized by taking logarithms before determining the parameters, for the case $y=ax^b$:
  $$ln y = ln a + b ln x ~~ or~~ln y = ln a + bx$$

• We now fit the new variable $z= ln y$ as a linear function of $ln x$ or $x$ as described earlier.
• Here we do not minimize the sum of squares of the deviations of $Y$ from the curve, but rather the deviations of $ln Y$.
  • In effect, this amounts to minimizing the squares of the percentage errors, which itself may be a desirable feature.