FINANCE Corporate financial policy and R and D Management

Y, given the value of X, is a linear function of X. In other words, the mean

value of the dependent variable is assumed to be a linear function of the

independent variable. Put still differently, the means of the conditional

probability distributions are assumed to lie on a straight line:

μy⋅x= A+ BX

The straight line is called the population regression line or the true regres-

sion line.

Second, regression analysis assumes that the standard deviation of the

conditional probability distribution is the same, regardless of the specified

value of the independent variable. The characteristic (of equal standard de-

viations) is called homoscedasticity.

Third, regression analysis assumes that the values of Yare independent

of one another. For example, if one observation lies below the mean of its

72 AN INTRODUCTION TO STATISTICAL ANALYSIS AND SIMULTANEOUS EQUATIONS

FIGURE 5.2 Fitting the Population Regression Line

10

8

6

4

2.95

2

0

Cost
(thousands
of dollars)

Probability

distribution

of Y, given X – 9

Population regression line (A + BX)

Probability distribution

of Y, given

X = 2

Mean

of Y,

given

X = 2

Mean of Y,

given X – 9

Y

X

2 4 6 9

Output (tons)