CHAPTER
5An Introduction to Statistical Analysis and Simultaneous Equations
I
n this chapter, we introduce the reader to the techniques of statistical
modeling and analysis including single variable regression, multiple re-
gression, and simultaneous equations. We will use these estimation tech-
niques in Chapters 6 and 7.
The horizontal line is called the x-axis and the vertical line the
y-axis. Regression analysis looks for a relationship between the Xvari-
able (sometimes called the independent or explanatory variable) and
the Yvariable (the dependent variable). For example, Xmight be the
aggregate level of gross national product (GNP) in the United States and
Ywould represent capital expenditures in the United States. (See Figure
5.1.) By looking up these numbers for a number of years in the past,
we can plot points on the graph. Each point represents one year or quar-
ter. More specifically, regression analysis seeks to find the “line of best
fit” through the points. The term “best” has a very specific meaning in
this context. Specifically, the regression line is drawn to best approxi-
mate the relationship between the two variables. Techniques for estimat-
ing the regression line (i.e., its intercept on the y-axis and its slope)
are the subject of this chapter. Forecasting using the regression line as-
sumes that the relationship that existed in the past between the two vari-
ables will continue to exist in the future. There may be times when this
assumption is inappropriate; the forecaster must be aware of this poten-
tial pitfall.
Regression analysis can be expanded to include more than one inde-
pendent variable; this is called multiple regression. For example, the fore-
caster might believe that capital expenditures depend not only on GNP but
also on the level of interest rates. Historical data on these three variables