A Complete Guide to the Futures Market, 2nd Edition

Appendix D

The Multiple Regression Model

In our description of nature the purpose is not to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience.

—Niels Bohr

■ Basics of Multiple Regression

In practice, it is rarely possible to explain the behavior of a dependent variable adequately with only one explanatory variable. For example, hog slaughter alone will provide only a rough indication of hog prices. A more satisfactory model would also incorporate other independent variables, such as broiler slaughter. The multiple regression equation is a straightforward extension of simple regression and describes the linear relationship between the dependent variable and two or more independent variables.

The meaning of linear, which might not be intuitively obvious beyond the two-dimensional case, is that all the variables are of the first degree and are combined only by addition or subtraction. For example, in terms of Z as a function of X and Y, Z = 2X + Y + 3 is a linear equation, while Z = X² + 2y² + 4, Z = XY, and Z = log X + log Y are nonlinear equations. A basic characteristic of a linear equation is that a one-unit change in an independent variable will result in a constant magnitude change in the dependent variable, regardless of the independent variable value. In other words, in a linear equation, the slope in each dimension is constant. When there are only two variables, as is ...