FINANCE Corporate financial policy and R and D Management

The coefficient of determination, R^2 , is the percentage of the variance of the
dependent variable explained by the independent variable. The coefficient of
determination cannot exceed one nor be less than zero. In the case of R^2 = 0,
the regression line’s Y= Yand no variation in the dependent variable is ex-
plained. If the dependent variable pattern continues as in the past, the model
with time as the independent variable should be of good use in forecasting.
The firm can test whether the a^and b

^
coefficients are statistically dif-
ferent from zero, the generally accepted null hypothesis. A t-test is used to
test the two null hypotheses:

H 0 : a^= 0

HA: a^≠ 0

H 0 : b

^

= 0

HA: b

^

≠ 0

The H 0 represents the null hypothesis while HArepresents the alternative
hypothesis. To reject the null hypothesis, the calculated t-value must ex-
ceed the critical t-value given in the t-tables. The calculated t-values for a^
and b

^

are found by:

(5.13)

The critical t-value, tc, for the .05 level of significance with N– 2 degrees of
freedom can be found in a t-table in any statistical econometric text.

If ta> tc, then reject H 01.

If tb> tc, then reject H 02.

The null hypothesis is that =0 can be rejected and therefore is statistically
different from zero. The t-value of bleads to the rejection of =0, and is sta-
tistically different from zero. One has a statistically significant regression
model if one can reject H 02.
We can create 95 percent confidence intervals for aand b, where the
limits of aand bare:

t

a

S

NM

MNX

t

b

S

M

N

a

e

XX

XX

b

e

XX

=

−

+

=

−

ˆ ()

()

ˆ ()

α

β

2

78 AN INTRODUCTION TO STATISTICAL ANALYSIS AND SIMULTANEOUS EQUATIONS