Anon

270 The Basics of financial economeTrics

points on the line. In this case, the sum for a generic a and b can be writ-
ten as:

()()()

()()()

()()

()()

= −−× + −−× + −−×

+ −−× + −−× + −−×

+ −−× + −−×

+ −−× + −−×

S.ab .ab.ab

.ab.ab .ab

.ab.ab

.ab.ab

07 0.81 31 .8 11 2.9

17 4.21 65 .5 14 6.7

16 7.41 78 .1

21 9.22 4 10.6

222

222

22

22

It is possible to find the value that minimizes the above expression ana-
lytically by equating to zero the partial derivatives of S:

∂

∂

=

∂

∂

=

S

a

S

b

00

However, commercial econometric software uses iterative programs
that find the minimum of S by an iterative searching procedure. For
example, we can perform the above operation in MATLAB using the polyfit

0 2 4 6 8 10 12

0

0.5

1

1.5

2

2.5

x

y

FigUre 13.2 Scatterplot of Sample Data and the Plot of the Straight Line
y = 0.05 + 0.1x