This time consider linear regression, the most frequently used form of regression analysis. Linear regression models describe the functional relationship between a phenomenon, y, and a set of variables, x 1, x 2, . . . All x 's are raised to the first power and all x 's are combined with all other x 's additively. The next one unit increase in x 1 also leads to a ten unit increase in y, as does each additional one unit increase in x 1 . Similarly, each one unit increase in the variable x 2 leads to a four unit increase in the phenomenon under study.
Proportionality is a comfortable thing.
It lets us know that when we change one side of a linear equation, the other side changes at a constant rate. In other words, changes to the inputs of a system lead to constant changes in the output of that system. Such a relationship between inputs and outputs is simple, easily understood, and predictable. For example, proportionality exists when each five percent increase in the DoD budget translates into a one percent increase in military readiness, or when each one percent increase in the Federal Funds rate results in a one-half percent decrease in inflation. Because proportionality is simple and easy to understand, we rely on it heavily in our traditional thinking.