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ODULE
6
M
ULTIPLE
R
EGRESSION

2
C
ONTENTS
:
M
ODULE
6
1. Introduction
2. Matrix Notation
3. Forecasting
4. Data Problems
4.1 Multicollinearity
4.2 Measurement Errors
4.3 Outliers and Undue Influence
5. The F Test for Linear Restrictions
5.1 The Redundant Variables Test
5.2 The Linear Restrictions or Wald Test
5.3 The Chow Test
6. Dummy Variables
6.1 Introduction
6.2 Generating Dummy Variables and Time Trends in Eviews
6.3 Interpreting the Coefficients of Dummy Variables
6.4 Comparing Regression Models
6.5 An Event Study
7. Financial Applications
7.1 Testing the CAPM
7.1.1 The Fama-MacBeth Approach
7.1.2 The Black-Jensen-Scholes Approach
7.2. The Predictability of Share Returns
7.3. Using the APT Model
7.3.1 Introduction
7.3.2 Estimating and Testing the APT Model
7.4. Testing Market Timing and Stock-Selection Performance

3
R
EFERENCES
Gujarati, Ch 7,8,9,and 10
Johnson and Di Nardo, Ch 3
Thomas, Ch 7 and 9
Wooldridge, Ch 4.4-4.5,7.2-7.3, 9.4, Appendices D&E
Other Useful References
Z.Y.Bello and V.Janjigian (1997) A Reexamination of the Market-Timing and Security-
Selection Performance of Mutual Funds
, Financial Analysts Journal,
September-October, p 24 - 30.
E.R.Berndt (1991) The Practice of Econometrics: Classic and Contemporary
, Ch 2
W.Daniel (1990) Applied Nonparametric Statistics
, Duxbury, Boston, p 63 - 66.
M.Grinblatt and S.Titman (1998) Financial Markets and Corporate Strategy
, Chs 5-6
M.Kritzman (1994)
What Practitioners need to know about Serial Dependence
Financial Analysts Journal, March-April, p 19 - 22

4
1.
I
NTRODUCTION
When there are two or more independent variables we have what is called a Multiple
Regression model. Where there are k = 2 independent variables we write this model
either as:
E(Y|X
1i
, X
2i
) =
β
0
+
β
1
X
1i
+
β
2
X
2i
or
Y
i
=
β
0
+
β
1
X
1i
+
β
2
X
2i
+
u
i
(i = 1 , .
.. , n)
The coefficients
β
1
and
β
2
in this model are what we call
partial derivatives
. This
means that a coefficient such as
β
1
tells us the impact on Y of a unit change in X
1
,
when the values of all other independent variables are held constant.
Once we have two or more independent variables the formula used can become very
large and very complicated. It is possible to write these formulae more concisely if we
use the matrix notation discussed in the next subsection. The formula needed when
forecasting with this type of model are discussed in the next section.
There are many situations in which the data we have to work with leads to problems
with these estimators so that they no longer possess the desired properties. The key
data problems that we need to take into consideration are discussed in section 4.
When we estimate a multiple regression model the estimates of the coefficients are
not independent if the independent variables are related to each other.
Because of
this the t statistics are not always reliable so we will often use F statistics instead.

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