GVHD: TS. Phùng Đức Nam

Chapter 4
Further development and analysis of the classical linear regression model

Phan Tuyết Trinh

Lâm Bá Du

Tô Thị Phương Thảo

Lê Chí Cang

Nguyễn Hoàng Minh Huy

Huỳnh Thái Huy


1. Generalising the simple model to multiple linear regression

2. The constant term

3. How are the parameters calculated in the generalised case?

4. Testing multiple hypotheses: the F-test

5. Sample output for multiple hypothesis tests

6. Multiple regression using an APT-style model

7. Data mining and the true size of the test

= the number of parameters that are estimated in the regression equation.


4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
The elements of the β vector

•●  SRF(Sample Regression Function)

, where:,
T×1

T×3

3×1


4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?

Ordinary least squares (OLS)

•

 

●

(: an estimate of the variance of the errors - )


-1

2

-1

-2

-1

1

1

-1

0


4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?

Example

•

 


4.3 How are the parameters (the elements of the β vector) calculated in the generalised

 

 
 

 
 
 
 
 

 
 
 
 
 

 

 

 
 

 
 

 
 



 

Std. Error

 

t-Statistic

 

Prob.  

  

  

 

 

 
 

  
 

X2

0.294118

0.466252
0.466252
-1.248510
-1.248510

0.892103

0.263752

0.8167

 

 

 

 

 

 
 

 
 

 
 


•

Mô hình gốc/Mô hình không ràng buộc – UnRestricted



Ước lượng bằng OLS thu được tổng bình phương các phần dư URSS, có bậc tự do df (degree of freedom) =

 

T–k

●

Mô hình có ràng buộc (Mô hình bị thu hẹp, mất đi m hệ số hồi quy) – Restricted



Ước lượng bằng OLS thu được tổng bình phương các phần dư RRSS, có df = T – (k – m) = T – k + m

●

Khi đó: RRSS – URSS có df = T – k + m – (T – k) = m

●

Với giả thiết cho trước, ta có:


4.4 F-test

 

●
●
●




k=2
k=3
k=4
:

m=1

: và

m=2

:

m=3

:
:

Phi tuyến nên không dùng F-test
được


Step 1: Open a new Eviews workfile
Step 2: Import the data
Step 3: Generate variables:

The APT posits that the stock return can be explained by reference to the unexpected
changes in the macroeconomic varibles rather their levels
Unexpected value = Actual value – expected value


4.6 Multiple regression using an APT-style model

Generate variables

•

Genr

Dspread = baa_aaa_spread – baa_aaa_spread(-1)
Dcredit = consumer_credit – consumer_credit (-1)
Rmsoft = 100*dlog(microsoft)
Rsandp = 100*dlog(sandp)
Dmoney = m1money_supply – m1money_supply(-1)
Inflation = 100*dlog(cpi)
Term = ustb10y – ustb3m
Dinflation = inflation – inflation(-1)
Mustb3m = ustb3m/12
Rterm = term – term(-1)
Ermsoft = rmsoft – mustb3m
Ersandp = rsandp – mustb3m


Tes t Statis tic
F-s tatis tic
Chi-s quare

Value

df

Probability

0.852936
4.264679

(5, 316)
5

0.5131
0.5120

Null Hypothes is : C(3)=0, C(4)=0, C(5)=0, C(6)=0,C(7)=0
Null Hypothes is Sum m ary:
Norm alized Res triction (= 0)
C(3)
C(4)
C(5)
C(6)
C(7)

Value


The simplest is the uni-directional forwards method.
No variables => first variable(the lowest p-value) =>the next lowest pvalue....


4.6 Multiple regression using an APT-style model

Stepwise regression

•
•
•
•
•

Object/New Object

•

Option: Forward, p-value: 0.2

Equation: Msoftstepwise
Method: STEPLS- Stepwise Least Square
Dependent variable: ERMSOFT C
Explanatory variables: ERSANDP DPROD DCREDIT DINFLATION DMONEY
DSPREAD RTERM