FINANCE Corporate financial policy and R and D Management

Rewriting these equations, one obtains the normal equations:

(5.7)

(5.7)

Solving the normal equations simultaneously for aand byields the least
squares regression estimates:

(5.8)

(5.8)

(5.8)

(5.8)

An estimation of the regression line’s coefficients and “goodness of fit”
also can be found in terms of expressing the dependent and independent
variables in terms of deviations from their means, their sample moments.
The sample moments will be denoted by M.

Mxxx

NX X

XX i

i

N

i

N

ii

i

N

i

N

==−

=−













= =

= =

∑ ∑

∑ ∑

1

22

1 1

1 1

2

()

bˆ

XY X Y

NX X

ii

i

N

i

i

N

i

i

N

i

N

i

i

N

=











−



































−













===

==

∑∑∑

∑∑

111

1

2

11

2

aˆ

XY XY

NX X

i

N

i

i

N

ii

i

N

i

N

i

i

N

=























−























−













== =

==

∑∑ ∑

∑∑

1

2

11 1

1

2

11

2

1 1 1

1

2

1 1 1

YabX

YX a X b X

ii

i

N

i

N

i

N

ii i

i

N

i

N

i

N

=+

=+

= = =

= = =

∑ ∑ ∑

∑ ∑ ∑

76 AN INTRODUCTION TO STATISTICAL ANALYSIS AND SIMULTANEOUS EQUATIONS