FINANCE Corporate financial policy and R and D Management

(5.5)

To assure that a minimum is reached, the partial derivatives of the squared
error terms function

will be taken with respect to aand b.

The partial derivatives will then be set equal to zero.

(5.6)

(5.6)

∂

∂

∂

∂

e

a

YabX

e

b

YX X b X

i

N

i

i

N

i

i

N

i

N

i

N

ii

i

N

i

N

i

N

1

2

1

111

1

2

1

1

2

1 1 1

20

20

=

===

=

= = =

∑

∑∑∑

∑

∑ ∑ ∑

=− − −











=

=− − −











=

∂

∂

e

b

Y a bX X

YX X b X

i

N

iii

i

N

ii

i

N

i

i

N

i

N

1

2

1

1

11

1

2

1

2

2

=

=

===

∑

∑

∑∑∑

=−−−

=− − −













()()

∂

=−−−

=− − −













=

=

== =

∑

∑

∑∑ ∑

e

a

YabX

YabX

i

N

ii

i

N

i

i

N

i

N

i

i

N

1

2

1

1

11 1

21

2

∂

()()

[(YbXii)]

i

N

−+

=

∑ α

2

1

eYY Y bX

i

N

ii i i

i

N

i

N

1

2

1

22

=== 1 1

∑∑∑[ −= −+

ˆ][( )]α

The Linear Regression Model 75