A Complete Guide to the Futures Market, 2nd Edition

Appendix C

Checking the Significance of the Regression Equation

Factual evidence can never “prove” a hypothesis; it can only fail to disprove it, which is what we generally mean when we say, somewhat inexactly, that the hypothesis is “confirmed” by experience.

—Milton Friedman

■ The Population Regression Line

In Appendix A we discussed the derivation of a regression line on the basis of empirical data. While it was premature to raise the subject then, the fitted line provided by the regression formula is actually a sample of the true population line, which is not known. For example, the regression line relating hog slaughter to the pig crop was a sample of the true relationship between the two variables. The fitted line is a sample because it represents only one realization of an entire series of possible regression lines. The actual regression line realized will depend on measurement error in the data and the unknown influence of variables not included in the model.

The population or true regression model can be expressed as

where e is a randomly distributed error or disturbance term.

Even if we knew the true population regression line, the actual observed values Y_i would still deviate from the predicted level by an amount equal to the error term e. The key reason for this is that a regression equation is a highly simplified model for the behavior of the dependent variable. ...