FINANCE Corporate financial policy and R and D Management

 To discuss the role of the computer in calculating multiple regressions

with any number of independent variables, and to indicate in detail

how computer printouts should be interpreted and used.

Whereas a simple regression includes only one independent variable, a
multiple regression includes two or more independent variables. Basically,
there are two important reasons why a multiple regression must often be
used instead of a simple regression. First, one can often predict the depen-
dent variable more accurately if more than one independent variable is
used. It may be reasonable to assume that

E(Yi) = A+ B 1 X 1 i+ B 2 X 2 i

where Yiis capital expenditures for the ith quarter, X 1 iis the GNP for that
quarter, and X 2 iis the interest rate at the end of the quarter.

Least Squares Estimates of the Regression Coefficients

The first step in multiple-regression analysis is to identify the independent
variables and to specify the mathematical form of the equation relating the
expected value of the dependent variable to these independent variables.
The relationship between the expected value of the dependent variable and
these independent variables is linear. Having carried out this first step, we
next estimate the unknown constants A, B 1 , and B 2 in the true regression
equation. Just as in the case of simple regression, these constants are esti-
mated by finding the value of each that minimizes the sum of the squared
deviations of the observed values of the dependent variable from the values
of the dependent variable predicted by the regression equation.
To understand more precisely the nature of least squares estimates of
A, B 1 , and B 2 , suppose that ais an estimator of A, b 1 an estimator of B 1 ,
and b 2 an estimator of B 2. Then the value of the dependent variable Yipre-
dicted by the estimated regression equation is

and the deviation of this predicted value from the actual value of the de-
pendent variable is

YYYabX bXii i−=−− −ˆ 11 i2 2i

YabX bXˆiii=+ 11 +2 2

80 AN INTRODUCTION TO STATISTICAL ANALYSIS AND SIMULTANEOUS EQUATIONS