3-1 Probabilistic Models

Deterministic models describe the connection between independent variables and a dependent variable. They are so named because they allow us to determine the value of the dependent value from the values of the independent variables. These deterministic models are usually from the natural sciences. Some examples of deterministic models are as follows:

• E = mc ², where E = energy, m = mass, and c = the speed of light

• F = ma, where F = force, m = mass, and a = acceleration

• S = at ²/2, where S = distance, t = time, and a = gravitational acceleration

• D = vt, where D = distance, v = velocity, and t = time.

An automobile traveling at a constant speed of fifty miles per hour will travel the distances shown in Table 3-1 for the given times.

Probabilistic models are more realistic for most real-world situations. For example, suppose we know that, in a given city, most lots sell for about $20,000 and that the cost of building a new house costs about $70 per square foot. The average cost, y, of a house of 2500 square feet is

y = 20,000 + 70(2500) = $195,000

This is still...