Linear regression is described in every statistics book, and is performed by every statistics program. The purpose of linear regression is to find the line that comes closest to your data. More precisely, the linear regression program finds values for the slope and intercept that define the line that minimizes the sum of the square of the vertical distances between the points and the line. The equations used to do this can be derived with no more than high-school algebra (shown in many statistics books). Put the data in, and the answers come out. There is no chance for ambiguity. You could even do the calculations by hand, if you wanted to.

Many relationships in biology (and other fields of science) do not follow a straight line. To analyze such data, you have two choices:

	•	Do mathematical transformations, such as those used in Scatchard or Lineweaver-Burk plots, to force the data into a linear relationship. Then use linear regression. Although these techniques are commonly used, you should avoid them. They are less accurate than nonlinear regression, and are not any easier.

	•	Use nonlinear regression, as explained in this web site.

Nonlinear regression is a general technique to fit a curve through your data. It fits data to any equation that defines Y as a function of X and one or more parameters. It finds the values of those parameters that generate the curve that comes closest to the data (minimizes the sum of the squares of the vertical distances between data points and curve). Except for a few special cases, it is not possible to directly derive an equation to compute the best-fit values from the data. Instead nonlinear regression requires a computationally intensive, iterative approach. You can't really follow the mathematics of nonlinear regression unless you are familiar with matrix algebra. But you can use nonlinear regression without understanding exactly how it works.

Some scientists and students are afraid to approach nonlinear regression, because it seems so complicated. From a scientist's point of view, however, nonlinear regression is no more complicated than linear regression. You put in data, choose a few options, and interpret the results. The choice of using linear or nonlinear regression should be determined by the scientific problem you are trying to solve. Don't use linear regression because you are afraid to learn nonlinear regression. It really isn't very complicated.