Regression Analysis 133demand. With uncontrolled markets, however, many factors change at the same
time. How, then, can a firm judge the effect of any single factor? Fortunately,
statisticians have developed methods to handle this very problem.
During the last 20 years, firms have increasingly used sophisticated com-
puter-based methods to gather market data. Today more than three-quarters of
all supermarkets employ check-out scanners that provide enormous quantities
of data about consumer purchases. Internet purchases provide an expanding
universe of additional data on consumer preferences and purchasing behavior.
Gathering this (relatively uncontrolled) data is quick and cheap—as little as
one-tenth the cost of controlled market tests. Today, using computers featuring
massively parallel processors and neural networks, companies can search
through and organize millions of pieces of data about customers and their buy-
ing habits, a technique known as data mining.
Finally, firms can also purchase data and access publicly available data. For
example, the University of Michigan publishes surveys of consumer buying
plans for durable items, and the U.S. Bureau of the Census disseminates
Consumer Buying Intentions. Often the firm spends less using published or pur-
chased forecasts than gathering and processing the data itself. Firms frequently
need off-the-shelf forecasts as inputs to its own firm-generated model. For
example, a firm may have determined, via its own studies, that gross domestic
product (GDP) greatly affects the demand for its product. The firm may pur-
chase forecasts of GDP that are more accurate than those it could produce
itself at a comparable cost.REGRESSION ANALYSIS
Regression analysis is a set of statistical techniques using past observations to
find (or estimate) the equation that best summarizes the relationships among
key economic variables. The method requires that analysts (1) collect data on
the variables in question, (2) specify the form of the equation relating the vari-
ables, (3) estimate the equation coefficients, and (4) evaluate the accuracy of
the equation. Let’s begin with a concrete example.Ordinary Least-Squares Regression
In the central example of Chapter 3, an airline’s management used a demand
equation to predict ticket sales and to make operating decisions along a
Texas–Florida air route. Let’s examine how the airline can use regression analy-
sis to estimate such an equation. The airline begins by collecting data. The sec-
ond column of Table 4.1 shows the average number of coach seats sold per
flight for each quarter (i.e., 90 days) over the last four years. Sales vary quarter
by quarter. In the best quarter, customers bought 137 seats on each flight; inc04EstimatingandForecastingDemand.qxd 9/13/11 10:43 AM Page 133