Transforms

Linearized regression is not to be confused with linear regression.

Consider an example: the Dow Jones Industrial Average from 1945 through 2002. The Normal Plot shows that the data is not linear. However, the Log Plot shows linearity. A linear regression in this space, shown in purple, fits the data. When transformed back into the Normal Plot, the purple line is curved, and fits the data. We have achieved a nonlinear fit using linearized regression.

In the analogous way, petrophysical relationships that are nonlinear can be linearized. Although we never use it, the relationship known as Gardner's Equation makes a good example. If you believe that the density, D, and the compressional velocity, V, are related by D=0.23 * V ^ 0.25, or any equation of the same form, then the velocity values should be raised to the 0.25 power before being plotted.

Our log calibration techniques use linearized regression in multiple dimensions simultaneously.