In statistics and regression analysis, an independent variable, which can only take two possible values, is called a dummy variable. For example, it can be set to 0 if an observation is of a white subject, or 1 if the observation is of a black subject. The two possible categories related to the two possible values are mutually exclusive, so that no observation falls into more than one category, and the categories are exhaustive, so that each observation falls into a category. Sometimes there are three possible categories that exclude themselves in pairs and are collectively exhaustive – for example, under 18, 18 to 64, and 65 or older. In this case, a large number of dummy variables are constructed, each dummy variable having two mutually exclusive categories and are exhaustive together – in this example, a dummy variable (called D1) would be equal to 1 if the age is less than 18 years, and otherwise it would be equal to 0; A second dummy variable (called D2) would be equal to 1 if the age is between 18 and 64, and 0 otherwise. In this configuration, pairs of dummy variables (D1, D2) can have the values (1.0) (less than 18), (0.1) (between 18 and 64) or (0.0) (65 or more) (but not (1.1), which would mean it would make senseless for an observed subject to be between 18 and 18 and 64). Then, dummy variables can be included in a regression as independent (explanatory) variables. A clear example is the amount of results of a single coin throw that can lead to either the head or the tail, but not both. When an entity is about to choose between mutually exclusive options, it must consider the opportunity costs that the company would abandon to follow each option. The concepts of opportunity costs and mutual exclusivity are intrinsically linked, as any mutually exclusive option requires the sacrifice of all the gains that could have been made by choosing the alternative option. Suppose a company has a budget of $50,000 for expansion projects. If available Projects A and B each cost $US 40,000 and Project C costs only $10,000, Projects A and B are mutually exclusive. If the company follows A, it also cannot afford to follow B and vice versa.
.
