MODEL vs. METHOD
We have come this far without making any assumptions about the nature of the causal relationships at play. The set of these assumptions – about how we believe Sales respond to the causal forces – gives us a regression model. The standard is the classical linear regression model described in a later section of this tutorial. A model provides us with a basis for checking the statistical reliability of the regression equation, calculating prediction intervals, which reveal the margin for error in a forecast and, most fundamentally, selecting the set of variables to include in the regression.
Positing a model to underlie the regression equation is not the only means of assessing reliability and enabling calculation of prediction intervals. Monte Carlo simulation procedures are an alternative that is growing in use and feasibility. As with a model, Monte Carlo requires a set of assumptions about the relationships at work, but these are far less restrictive than the assumptions typically required for statistical modeling. Sam Sugiyama’s article in Foresight (2007) offers a general tutorial on Monte Carlo and specific applications to regression forecasting.