Anon

274 The Basics of financial economeTrics

method applied to simple or multiple regressions under standard assump-
tions is the OLS method to distinguish it from weighted and generalized
least squares that we will describe shortly.
Standard assumptions of simple and multiple regression require that
residuals have the same variances and that they are mutually uncorrelated
and uncorrelated with the regressors. Under these assumptions, the OLS
method estimates the regression parameters by minimizing the sum of
squared residuals. We have seen in Chapter 3 that the regression equation
(3.8), which is reproduced as equation (13.1):

yX=+β e (13.1)

This can be estimated by finding the value of b that minimizes the sum of
squared residuals:

Sei
i

n

=

=

∑

2

1

(13.2)

0 2 4 6 8 10 12

−12

−10

−8

−6

−4

−2

0

2

4

6

x

y

FigUre 13.5 Scatterplot of Sample Data and Plot of the Best Fitting Polynomial of
Degree 10