Tiểu luận tiếng Anh Kinh Tế Chuyển Nhượng Các Yếu Tố Ảnh Hưởng Đến Chi Tiêu Hàng Tháng Của Sinh Viên FTU

Econometrics Assignment
- 1 -
ESSAY:
THE FACTORS AFFECTING MONTHLY
EXPENDITURE OF FTU’S STUDENT
TIỂU LUẬN TIẾNG ANH KINH TẾ CHUYỂN NHƯỢNG
CÁC YẾU TỐ ẢNH HƯỞNG ĐẾN CHI TIÊU HÀNG
THÁNG CỦA SINH VIÊN FTU
Nhận viết Tiểu Luận TIẾNG ANH
HOTLINE (ZALO/VIBER/TELE) 0936885877
DICHVULUANVANTRITHUC@GMAIL.COM
LUANVANTRITHUC.COM
LIÊN HỆ ĐỂ TẢI TÀI LIỆU NHANH

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TABLE OF CONTENTS
Page
I. INTRODUCTION ............................................................................................1
II. METHODOLOGY .........................................................................................2
1. DEFINITION ...............................................................................................2
1.1. Income..................................................................................................2
1.2. Expenditure..........................................................................................3
2. THEORIES OF CONSUMERS’ BEHAVIOR............................................3
3. THE KEYNESIAN CONSUMPTION FUNCTION ...................................5
III. ECONOMETRIC MODEL..........................................................................7
1. MODEL CONSTRUCTION........................................................................7
2. COEFFICIENTS PREDICTION .................................................................8
IV. DATA DESCRIPTION.................................................................................9
V. EMPERICAL RESULTS.............................................................................13
1. USING THE ABOVE DATA TO ESTIMATE
THE REGRESSION MODEL BY OLS METHOD......................................13
2. MEANING OF THE REGRESSION COEFFICIENTS............................14
3. TESTING THE SIGNIFICANCE OF THE
REGRESSION COEFFICIENTS AND THE
RELEVANCE OF THE REGRESSION FUNCTION ..................................14
4. FIRST CURE: FOR THE REGRESSION MODEL..................................17
5. TESTING THE CONFORMITY WITH
THE ASSUMPTIONS OF OLS METHOD...................................................21
6. SECOND CURE: FOR THE HETEROSKEDASTICITY ........................23
7. FINAL REGRESSION MODEL ...............................................................28
VI. CONCLUSION ............................................................................................29
VII. REFERENCES...........................................................................................30

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I. INTRODUCTION
Vietnam in recent years, along with nearly 200 countries around the world, has
been integrating into the trend of globalization and exercising national campaigns
towards the overall development in economic, political, social and cultural
aspects. In this context, human capital is considered one of the key factors for
Vietnam’s long-term revolution, and it is university students that make up an
indispensable part in the domestic labor force in the future.
Regarded as one of the most privileged universities in Vietnam, Hanoi Foreign
Trade University has long attracted thousands of students from North to South
every year. Each student, as a matter of fact, has his own family background,
distinctive personalities as well as certain level of knowledge and experience.
Such factors, certainly, have significant impacts on students’ daily life, in which
students’ expenditure should be mentioned first of all.
Therefore, after taking everything into consideration, we decided to choose and
study the project: “THE FACTORS AFFECTING MONTHLY EXPENDITURE
OF FTU’S STUDENT”. Although the government has tried to implement
financial aid programs for university learners, we, especially those coming from
provincial areas, have still met many difficulties in managing our spending every
day. It is really not easy to allocate our limited source of money into a range of
activities in the most effective way. Thus through our project, we would like to
provide you with more in-depth understanding about some main factors
dominating daily spending of FTU’s students. We hope that arguments and
statistics in this project will be helpful for you in drawing a reasonable plan of
expenditure for the time being.

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II. METHODOLOGY
In this project, we consider three factors that may affect students’ monthly
spending: income, students’ homeland and students’ characteristics.
Homeland and characteristics are two qualitative variables. In general they
have certain impacts on the ways students plan their expenditure. For instance, a
student coming from rural area may consume less than one coming from a big
city. Similarly, the amount of spending depends on whether the student is
generous or thrifty, shopping-lover or shopping-averse.
Income, by contrast, is a quantitative variable. It can be said that income and
expenditure are two critical elements of the market economy, as everyone has to
consider how to spend their disposable income in the most reasonable way. There
also exists a close-knit relationship between those two factors, thus we will use
microeconomic and macroeconomic theories and models to interpret it.
1. DEFINITIONS
1.1. Income
There are two main types of income, which can be listed as personal income
and disposable income.
1.1.1. Personal income (PI)
Personal income is the income earned by households and non-corporate
businesses. Unlike national income, it excludes retained earnings, which is the
amount of revenue corporations have earned but have not paid out to stockholders
as dividend. It also subtracts corporate income taxes and contributions for social
insurance (mostly Social Security taxes). In addition, personal income includes
interest income, the amount households receive from their holdings of government
debt, and transfer payment, the amount they get form government transfer
program such as welfare and social security.

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1.1.2. Disposable income (DI)
Disposable personal income is the net income that households and non-
corporate businesses earn after fulfilling all their obligations to the government. It
equals personal income minus personal taxes and certain non-tax payments (such
as traffic tickets).
DI = PI – personal taxes
In the scope of our project, however, our studied subjects are FTU’s students
who have no obligation to pay income tax. Thus they have entire disposal of what
they earn, which means that their personal income also equals their disposable
income. Besides, students’ earnings generally come from two main sources:
family financial support and income from part-time jobs. Family financial support
is the monthly amount supported by students’ families so that they can fulfill their
daily life. Income from part-time jobs is what students earn when participating in
the labor market, which is tax-free.
1.2. Expenditure
Expenditure is the sum of money each individual uses for the purchase of
goods and services to satisfy their needs.
For instance, each month students have to pay for some urgent needs such as
food, clothing, traveling fees, housing expenses (if students have to rent a
house), and so on. Those all aim at responding to personal needs of students.
2. THEORIES OF CONSUMERS’ BEHAVIOR
 We assume that university students always try to maximize their own utility
by using a number of certain resources. This means that although there are many
ways of planning expenditure, students will only follow the choice that is most
likely to optimize their satisfaction. Moreover, as there always exists a limit to

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students’ income, they have to consider how to allocate that restricted source for a
variety of daily activities.
In short, this part of our project has two main objectives. The first one is to
study how students use their income to bring about maximum benefit for
themselves. And the second one is to explain how income affects expenditure
theoretically and realistically.
 The theories of consumers’ behavior, in microeconomics, begin with three
basic assumptions about consumers’ preference.
Firstly, preferences are complete. This means that consumers can rank their
baskets of goods based on personal preferences or different levels of utility they
may provide. Prices of goods have no effects on consumers’ choice in this case.
Secondly, preferences are transitive. If a person prefers good A to good B, and
good B to good C, certainly he will prefer good A to good C.
Thirdly, in case of normal goods, consumers always prefer more to less. This is
an obvious argument, because everyone feels more satisfied when consuming
more goods and services.
 Generally our project still relies on those basic assumptions, but instead of
goods, we aim to study different ways of planning expenditure of FTU’s students.
Thus in the scope of this project, we will adjust the three assumptions as follows.
Firstly, students can compare and rank different choices of spending based on
their satisfaction.
Secondly, of a student prefers choice A to choice B, and choice B to choice C,
this means that he prefers choice A to choice C.
Thirdly, students will choose the choice of expenditure that benefits them
most.

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3. THE KEYNESIAN CONSUMPTION FUNCTION
In general, the basic form of consumption function is as follows:
C = f(Yd)
with Yd representing disposable income. But as afore-mentioned, since there is
no personal income tax levied on university students, their disposable income also
equals their personal income. In this case, the consumption function can be
rewritten as :
C = f(Y)
This reflects the relationship between planned expenditure and disposable
income.
Generally students’ spending increases when income increases, but it is
assumed to rise less quickly than income. The reason is that students tend to divide
their earnings into two parts: consumption and savings. This means that they do
not spend all their money on the purchase of goods and services but tend to save a
small amount to deal with unexpected incidents in the future, such as illnesses,
burglaries, house-moving, etc. This is a popular psychological phenomenon of
almost every student in Vietnam, especially those coming from provincial areas to
big cities to further their study.
If consumption rises at a lower speed than income does, the ratio
consumption/income will decrease as income increases. We use a linear function
in the form of y = a + bx to build the consumption function.
In particular, we have the standard Keynesian consumption function as
follows:
1( ) .
C f Y C MPC Y
  
where C = Students’ expenditure

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C = Autonomous consumption. This is the level of
consumption that will take place even if income is zero. If an
individual's income falls to zero, some of his existing
spending can be sustained by using savings. This is known as
dis-saving spending.
MPC = Marginal propensity to consume. This is the change
in consumption divided by the change in income, or in other
words, it determines the slope of the consumption function.
The MPC reflects the effect of an additional VND of
disposable income on consumption.
C
MPC
Y



As you can see from the graph above, we always have: 0 < MPC < 1. If MPC
equals to 1, this means that students’ spending always equals students’ income,
which is irrational in reality. Actually when a student’s income reaches a certain
level, he will not spend all the money but keep a certain amount as savings.

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Certainly, savings will increase as income increases, thus MPC can never equal to
1.
In conclusion, there is a positive relationship between disposable income (Yd)
and students’ spending (C). The gradient of the consumption curve gives the
marginal propensity to consume. The intercept gives the autonomous
consumption, which exists even if students have no current disposable income.
III. ECONOMETRIC MODEL
1. MODEL CONSTRUCTION
a) Variables:
- Dependent variable:
EXP: Student’s monthly expenditure (unit: thousand dong)
- Independent variables:
+ CHA (dummy): Student’s character
Generous = 1
Economical = 0
+ HOM (dummy): Student’s homeland
Urban area = 1
Rural area = 0
+ FFS: Family financial support (unit: thousand dong)
+ INC: Student’s monthly income (from tuition, part-time jobs, etc) (unit:
thousand dong)

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b) Regression model:
- Population regression function:
(PRF): 1 2 3 4 5
. . . .
i i i i i i
EXP CHA HOM FFS INC U
    
     
(Ui: disturbance term)
- Sample regression function:
(SRF): 1 2 3 4 5
ˆ ˆ ˆ ˆ ˆ
. . . .
i i i i i i
EXP CHA HOM FFS INC e
    
      (ei: residual)
2. COEFFICIENTS PREDICTION
- 2
 : positive – A generous student (CHA = 1) tends to spend more than an
economical one (CHA = 0)
- 3
 : positive – A student who comes from an urban area (HOM = 1) tends to
spend more than one who comes from a rural area (HOM = 0)
- 4
 : positive – If monthly family financial support increases, student’s
monthly expenditure increases too.
- 5
 : positive – If a student’s monthly income increases, his/her expenditure
increases too.

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IV. DATA DESCRIPTION
The primary data is collected from a survey which has been conducted among
83 FTU students in April 22, 2011. The dataset is interpreted as cross-sectional.
The results of the survey has been obtained as follows:
No CHA HOM FFS INC EXP
1 1 0 2000 0 2000
2 1 1 2000 0 2000
3 1 0 1500 0 1500
4 0 1 2000 0 2000
5 1 1 1000 0 1000
6 1 1 1500 0 1500
7 0 1 400 0 400
8 1 1 500 0 500
9 1 1 600 0 600
10 1 0 2500 500 3000
11 1 1 1500 500 2000
12 1 1 0 2000 1500
13 1 1 2000 0 2000
14 1 0 500 1500 3000
15 1 1 2000 0 1500
16 1 0 3000 900 3700
17 1 1 300 1000 1300
18 0 1 1000 0 900

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19 0 1 500 0 500
20 1 0 1500 0 1500
21 0 1 500 0 500
22 0 0 600 0 500
23 0 1 500 400 600
24 1 1 0 1500 1500
25 1 1 2000 1000 3000
26 1 0 500 500 1000
27 1 1 3000 0 2500
28 0 1 500 1000 1200
29 1 1 2000 0 1500
30 1 0 2000 1000 3000
31 1 1 500 1000 1500
32 1 0 2000 1000 3000
33 0 0 1000 0 700
34 0 1 2000 0 1500
35 0 1 0 1200 800
36 1 1 400 0 400
37 1 1 500 900 1200
38 0 1 1000 1000 1000
39 1 1 2000 0 1500
40 0 1 400 4000 4000
41 1 1 1000 1000 2000

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42 1 1 400 400 700
43 1 1 1000 1200 2000
44 1 1 1000 1500 2500
45 0 1 1000 0 1000
46 0 1 1000 0 700
47 1 0 2000 1000 2000
48 1 0 2000 0 2000
49 1 1 2000 600 2500
50 0 0 2000 500 2000
51 0 0 700 0 600
52 0 0 2000 0 2000
53 1 1 3000 1000 3500
54 1 1 2000 500 2300
55 1 1 1000 1000 2000
56 1 1 0 2000 1500
57 0 1 3000 0 3000
58 1 0 2000 1000 3000
59 0 0 1000 0 800
60 1 1 2500 1000 3000
61 1 0 1500 0 1200
62 1 0 3000 0 2000
63 1 1 2000 500 2500
64 1 1 3000 0 3000

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65 1 0 1500 1300 2500
66 1 0 2000 1600 2000
67 1 0 2000 0 2000
68 0 1 0 2000 1500
69 1 0 1000 1800 2800
70 1 1 1800 1200 3000
71 1 0 2000 1000 2000
72 1 1 600 1000 1500
73 1 1 3500 0 3500
74 1 0 2000 0 2000
75 0 1 500 1500 1500
76 1 1 1000 2000 2500
77 0 0 400 500 800
78 1 0 2000 0 2000
79 0 1 200 1000 1200
80 0 1 700 2500 2500
81 1 0 1500 1200 2000
82 1 1 1500 0 1500
83 0 1 2000 0 1800

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V. EMPERICAL RESULTS
1. USING THE ABOVE DATA TO ESTIMATE THE REGRESSION
MODEL BY OLS METHOD
Model 1: OLS, using observations 1-83
Dependent variable: EXP
Coefficient Std. Error t-ratio p-value
const -23.7348 107.466 -0.2209 0.82578
CHA 158.541 80.3945 1.9720 0.05215 *
HOM 15.2599 74.9691 0.2035 0.83924
FFS 0.864879 0.0468649 18.4547 <0.00001 ***
INC 0.81998 0.0500468 16.3843 <0.00001 ***
Mean dependent
var 1803.614
S.D. dependent var
870.3021
Sum squared resid 7810729 S.E. of regression 316.4452
R-squared 0.874241 Adjusted R-squared 0.867792
F(4, 78)
135.5590
P-value(F) 2.67e-
34
Log-likelihood -
593.0369
Akaike criterion
1196.074
Schwarz criterion
1208.168
Hannan-Quinn
1200.933
Excluding the constant, p-value was highest for variable 2 (HOM)
From the above result, we obtain the following regression function:
(SRF) EXPi = -23.7348 + 158.541 CHAi + 15.2599 HOMi + 0.864879 FFSi +
0.81998 INCi + ei (1)
2. MEANING OF THE REGRESSION COEFFICIENTS
- 1
ˆ
 = -23.7348 means that if an economical student who comes from an rural
area has no family financial support and no income, he/she will spend -23.7348
thousand dong on average every month.

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- 2
̂ = 158.541 means that a generous student will spend 158.541 on average
more than an economical one, provided that they come from the same homeland
areas and have the same family financial support and income every month.
- 3
ˆ
 = 15.2599 means that a student who comes from an urban area spend
15.2599 on average more than another student who comes from a rural area,
provided that they have the same character, family financial support and income
every month.
- 4
̂ = 0.864879 means that every month if the family financial support of one
student increases (or decreases) by one thousand dong, he/she will spend 0.864879
dong more (or less) on average; provided that his/her character, homeland and
monthly income remain unchanged.
- 5
ˆ
 = 0.81998 means that every month if the income of one student increases
(or decreases) by one thousand dong, he/she will spend 0.81998 dong more (or
less) on average; provided that his/her character, homeland and monthly family
financial support remain unchanged.
3. TESTING THE SIGNIFICANCE OF THE REGRESSION
COEFFICIENTS AND THE RELEVANCE OF THE REGRESSION
FUNCTION
a) The significance of the regression coefficients:
- Intercept 1
 :
0 1
1 1
: 0
:
: 0
H
Hypothesis
H







Formula: 1
1
ˆ 0 23.7348 0
0.2209
ˆ 107.466
( )
t
SE


  
   
If 0.1
  , then 0.05 (78) 1.66
t 

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Since | t | = 0.2209 < t0.05(78) = 1.66, we accept H0. There is sufficient sample
evidence to claim that 1 0
  , that is, the intercept is not significant.
- Slope 2
 :
0 2
1 2
: 0
:
: 0
H
Hypothesis
H







Formula: 2
2
ˆ 0 158.541 0
1.972
ˆ 80.3945
( )
t
SE


 
  
If 0.1
  , then 0.05 (78) 1.66
t 
Since | t | = 1.972 > t0.05(78) = 1.66, we reject H0. There is insufficient sample
  , that is, the slope is significant.
- Slope 3
 :
0 3
1 3
: 0
:
: 0
H
Hypothesis
H







Formula: 3
3
ˆ 0 15.2599 0
0.2035
ˆ 74.9691
( )
t
SE


 
  
If 0.1
  , then 0.05 (78) 1.66
t 
Since | t | = 0.2035 < t0.05(78) = 1.66, we accept H0. There is sufficient sample
  , that is, the slope is not significant.
- Slope 4
 :
0 4
1 4
: 0
:
: 0
H
Hypothesis
H







Formula: 4
4
ˆ 0 0.864879 0
18.45
ˆ 0.0468649
( )
t
SE


 
  

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If 0.1
  , then 0.05 (78) 1.66
t 
- Slope 5
 :
0 5
1 5
: 0
:
: 0
H
Hypothesis
H







Formula: 5
5
ˆ 0 0.819980 0
16.38
ˆ 0.0500468
( )
t
SE


 
  
If 0.1
  , then 0.05 (78) 1.66
t 
b) The relevance of the regression function:
2
0
2
1
: 0
:
: 0
H R
Hypothesis
H R
 





Formula:
2 2
2 2
( ) (0.874241) (83-5)
63.2313
(1 )( 1) [1 (0.874241) ].4
R n k
F
R k

  
  
If 0.05
  , then 0.05 (4,78) 2.50
F 
Since F = 63.2313 > 0.05(4,78) 2.50
F  , we reject H0. There is insufficient
sample evidence to claim that 2
0
R  , that is, the regression function is relevant.
4. FIRST CURE: FOR THE REGRESSION MODEL
a) The coefficient 3
 and the variable HOM:
- From the above analysis, when conducting T-test with respect to 3
ˆ
 , we have
sufficient evidence to conclude that 3 0
  , that is, the slope is not significant.

- 19 -
- If the variable HOM is omitted, we obtain the following result when running
a regression model having three independent variables: CHA, FFS, INC.
Const -11.1501 87.3646 -0.1276 0.89877
CHA 157.774 79.8175 1.9767 0.05157 *
FFS 0.863175 0.0458309 18.8339 <0.00001 ***
INC 0.82031 0.049716 16.4999 <0.00001 ***
Mean dependent var
1803.614
S.D. dependent var
870.3021
Sum squared resid
7814878
S.E. of regression
314.5195
R-squared
0.874175
Adjusted R-squared
0.869396
F(3, 79)
182.9514
P-value(F) 1.85e-
35
Log-likelihood -
593.0589
Akaike criterion
1194.118
Schwarz criterion
1203.793
Hannan-Quinn
1198.005
After the variable HOM is omitted, 2
R increases from 0.867792 to 0.869396
 The variable HOM will be omitted.
b) The intercept 1
 :
- From the above analysis, when conducting T-test with respect to 1
ˆ
 , we have
sufficient evidence to conclude that 1 0
  , that is, the intercept is not significant.
- If the variable X1 (X1 = 1) is omitted, or in other words the intercept 1 0
  ,
we obtain the following result when running a regression model having three
independent variables: CHA, FFS, INC.

- 20 -
CHA 154.635 75.4656 2.0491 0.04373 **
FFS 0.859465 0.0352129 24.4077 <0.00001 ***
INC 0.816912 0.0417275 19.5773 <0.00001 ***
Mean dependent
var 1803.614
S.D. dependent var
870.3021
Sum squared resid
7816489
S.E. of regression
312.5798
R-squared
0.976464
Adjusted R-squared
0.975876
F(3, 80)
1106.357
P-value(F) 5.27e-
65
Log-likelihood -
593.0675
Akaike criterion
1192.135
Schwarz criterion
1199.391
Hannan-Quinn
1195.050
After the variable X1 = 1 is omitted, 2
R increases from 0.869396 to 0.975876
 The variable X1 = 1 will be omitted.
The regression function has the intercept 1 0
  .
c) New regression function
(SRF) EXPi = 154.635 CHAi + 0.859465 FFSi + 0.816912 INCi + ei (2)
d) Meaning of the regression coefficients:
- 1
ˆ
 = 0 means that if an economical student who comes from an rural area has
no family financial support and no income, he/she will spend zero every month.
- 2
̂ = 154.635 means that a generous student will spend 154.635 thousand
dong on average more than an economical one, provided that they have the same
family financial support and income every month.

- 21 -
- 3
ˆ
 = 0.859465 means that every month if the family financial support of one
student increases (or decreases) by one thousand dong, he/she will spend 0.859465
thousand dong more (or less) on average; provided that his/her character and
monthly income remain unchanged.
- 4
̂ = 0.816912 means that every month if the income of one student increases
(or decreases) by one thousand dong, he/she will spend 0.816912 thousand dong
more (or less) on average; provided that his/her character and monthly family
financial support remain unchanged.
e) Testing the significance of the regression coefficients and the relevance
of the regression function:
- Slope 2
 :
0 2
1 2
: 0
:
: 0
H
Hypothesis
H







Formula: 2
2
ˆ 0 154.635 0
2.049
ˆ 75.4656
( )
t
SE


 
  
- Slope 3
 :
0 3
1 3
: 0
:
: 0
H
Hypothesis
H







Formula: 3
3
ˆ 0 0.859465 0
24.41
ˆ 0.0352129
( )
t
SE


 
  

- 22 -
- Slope 4
 :
0 4
1 4
: 0
:
: 0
H
Hypothesis
H







Formula: 4
4
ˆ 0 0.816912 0
19.58
ˆ 0.0417275
( )
t
SE


 
  
- The relevance of the regression function:
2
0
2
1
: 0
:
: 0
H R
Hypothesis
H R
 





Formula:
2 2
2 2
( ) (0.976464) (83-4)
539.755
(1 )( 1) [1 (0.976464) ].3
R n k
F
R k

  
  
If 0.05
  , then 0.05 (3,79) 2.73
F 
Since F = 539.755 > 0.05(3,79) 2.73
0
5. TESTING THE CONFORMITY WITH THE ASSUMPTIONS OF
OLS METHOD
a) Testing multicollinearity:
- Correlation matrix:
Correlation coefficients, using the observations 1 - 83
5% critical value (two-tailed) = 0.2159 for n = 83
CHA FFS INC
1.0000 0.3252 0.0313 CHA
1.0000 -0.3549 FFS
1.0000 INC

- 23 -
From the above matrix, in which there is no rij ( 2,4; 2,4
i j
  ) greater than
0.8, we can claim that multicollinearity does not exist.
- Variance Inflation Factors (VIF) method:
The following result is obtained:
Variance Inflation Factors
Minimum possible value = 1.0
Values > 10.0 may indicate a collinearity problem
CHA 1.150
FFS 1.314
INC 1.177
VIF(i) = 1/(1 - R(i)^2), where R(i) is the multiple correlation coefficient
between variable j and the other independent variables
Properties of matrix X'X:
1-norm = 2.717891e+008
Determinant = 2.5333308e+017
Reciprocal condition number = 6.3086927e-008
From the above analysis, since VIF(i) < 10 ( 2,4
i  ), we can claim that
multicollinearity does not exist.
- Conclusion: Multicollinearity does not exist.
b) Testing heteroskedasticity with White’s test:
0
1
: The regression model is homoskedastic
:
: The regression model is heteroskedastic
H
Hypothesis
H



White's test for heteroskedasticity
OLS, using observations 1-83
Dependent variable: uhat^2
coefficient std. error t-ratio p-value
----------------------------------------------------------------------------------
CHA -59510.8 135663 -0.4387 0.6622
FFS 38.4485 77.7873 0.4943 0.6226
INC -2.86511 106.989 -0.02678 0.9787
X1_X2 12.6469 81.7329 0.1547 0.8774
X1_X3 111.923 94.6678 1.182 0.2408

- 24 -
sq_FFS -0.000733091 0.0327011 -0.02242 0.9822
X2_X3 0.0236958 0.0588971 0.4023 0.6886
sq_INC 0.00807122 0.0318929 0.2531 0.8009
Unadjusted R-squared = 0.255030
Test statistic: TR^2 = 21.167482,
with p-value = P(Chi-square(7) > 21.167482) = 0.003530
From the above analysis:
nR2
= 83 x 0.255030 = 21.167482 > 2 2
0.05 0.05
( 1) (8 1) 14.0671
k
 
   
p-value = 0.003530 < 0.05
Therefore, we reject H0. There is insufficient sample evidence to claim that the
regression model is homoskedastic.
In other words, there exists heteroskedasticity.
6. SECOND CURE: FOR THE HETEROSKEDASTICITY
Two variables FFS and INC are the cause of heteroskedasticity. We can cure
this problem by dividing both sides of the regression function by either FFS or
INC.
a) Dividing both sides of the regression function by FFS:
- Constructing new regression function:
2 3 4
. . .
i i i i i
i i i i i
EXP CHA FFS INC U
FFS FFS FFS FFS FFS
  
   
3 2 4
. .
i i i i
newEXP newCHA newINC
   
    
Model 1: OLS, using observations 1-83 (n = 78)
Missing or incomplete observations dropped: 5
Dependent variable: newEXP
newFFS 0.79607 0.0518096 15.3653 <0.00001 ***
newCHA 184.888 54.3363 3.4027 0.00107 ***
newINC 0.928624 0.0261405 35.5244 <0.00001 ***

- 25 -
Mean dependent
var 1.594811
S.D. dependent var
1.403971
Sum squared resid
8.121899
S.E. of regression
0.329077
R-squared
0.946488
Adjusted R-squared
0.945061
F(2, 75)
663.2784
P-value(F) 2.07e-
48
Log-likelihood -
22.45356
Akaike criterion
50.90711
Schwarz criterion 57.97724 Hannan-Quinn 53.73741
(SRF) newEXPi = 0.79607 + 184.888 newCHAi + 0.928624 newINCi + i
 (3)
- Testing heteroskedasticity with White’s test:
OLS, using observations 1-83 (n = 78)
Omitted due to exact collinearity: sq_newFFS X1_X2 X1_X3
-----------------------------------------------------------------------------------
newFFS -0.0485516 0.0880099 -0.5517 0.5829
newCHA 225.636 198.313 1.138 0.2590
newINC 0.114733 0.0964110 1.190 0.2379
sq_newCHA -165585 90068.7 -1.838 0.0701 *
X2_X3 168.063 64.1490 2.620 0.0107 **
sq_newINC -0.00985850 0.0111903 -0.8810 0.3813
nR2
= 78 x 0.223913 = 17.465190 > 2
0.05(5) 11.0705
 
p-value = 0.003697 < 0.05

- 26 -
Therefore, there still exists heteroskedasticity.
b) Dividing both sides of the regression function by INC:
- Constructing new regression function:
2 3 4
. . .
i i i i i
i i i i i
EXP CHA FFS INC U
INC INC INC INC INC
  
   
4 2 3
. .
i i i i
newEXP newCHA newFFS
   
    
Model 1: OLS, using observations 1-83 (n = 45)
Dependent variable: newEXP
newINC 0.707631 0.0792352 8.9308 <0.00001 ***
newCHA 269.765 88.1186 3.0614 0.00383 ***
newFFS 0.874051 0.0447625 19.5264 <0.00001 ***
Mean dependent
var 2.147920
S.D. dependent var
1.276898
Sum squared resid 4.19569
8
S.E. of regression 0.31606
6
R-squared
0.941516
Adjusted R-squared
0.938731
F(2, 42)
338.0709
P-value(F) 1.28e-
26
Log-likelihood 10.4686
7
Akaike criterion 26.9373
4
Schwarz criterion
32.35733
Hannan-Quinn
28.95786
(SRF) newEXPi = 0.707631 + 269.765 newCHAi + 0.928624 newFFSi + i
 (4)
- Testing heteroskedasticity with White’s test:
OLS, using observations 1-83 (n = 45)
Omitted due to exact collinearity: sq_newINC X1_X2 X1_X3

- 27 -
-------------------------------------------------------------
newINC 0.0439779 0.0571211 0.7699 0.4460
newCHA -13.4097 123.853 -0.1083 0.9143
newFFS 0.0908602 0.0712252 1.276 0.2096
sq_newCHA 7465.68 52197.7 0.1430 0.8870
X2_X3 -0.965074 34.3478 -0.02810 0.9777
sq_newFFS -0.0203834 0.0190389 -1.071 0.2909
nR2 = 45 x 0.047598 = 2.141907 < 2
0.05(5) 11.0705
 
p-value = 0.829182 > 0.05
Therefore, we can conclude that heteroskedasticity does not exist
- Testing (4) on multicollinearity:
+ Correlation matrix:
Correlation coefficients, using the observations 1 - 83
(missing values were skipped)
5% critical value (two-tailed) = 0.2159 for n = 83
newCHA newFFS
1.0000 0.5674 newCHA
1.0000 newFFS
From the above matrix, in which there is no rij greater than 0.8, we can claim
that multicollinearity does not exist.
+ Variance Inflation Factors (VIF) method:
The following result is obtained:
Variance Inflation Factors

- 28 -
Minimum possible value = 1.0
Values > 10.0 may indicate a collinearity problem
newCHA 1.475
newFFS 1.475
VIF(i) = 1/(1 - R(i)^2), where R(i) is the multiple correlation coefficient
between variable j and the other independent variables
Properties of matrix X'X:
1-norm = 223.38933
Determinant = 0.042566825
Reciprocal condition number = 5.7550166e-008
From the above analysis, since VIF(i) < 10, we can claim that multicollinearity
does not exist.
+ Conclusion: Multicollinearity does not exist.
- Testing the relevance of the regression function (4)
2
0
2
1
: 0
:
: 0
H R
Hypothesis
H R
 





Formula:
2 2
2 2
( ) (0.941516) (45-3)
163.944
(1 )( 1) [1 (0.941516) ].2
R n k
F
R k

  
  
If 0.05
  , then 0.05 (2,42) 3.23
F 
Since F = 163.944 > 0.05 (2,42) 3.23
0
7. FINAL REGRESSION MODEL
From all of the above analysis and results, we obtain the following final
regression model:
- Population regression function:
(PRF): 0.707631 269.765 0.928624
i i i i
newEXP newCHA newFFS U
   
(Ui: disturbance term)

- 29 -
- Sample regression function:
(SRF) newEXPi = 0.707631 + 269.765 newCHAi + 0.928624 newFFSi + i

( i
 : new residual)
in which:
+ i
i
i
EXP
newEXP
INC

+ i
i
i
CHA
newCHA
INC

+ i
i
i
FFS
newFFS
INC

+ i
i
i
INC
newINC
INC

+ i
i
i
e
INC
 
VI. CONCLUSION
From the above analysis and results, some conclusions are obtained as
follows:
 The variables newCHA and newFFS have impact on newEXP. However,
both newCHA and newFFS depend on CHA, FFS and INC; and newEXP depends
on EXP. Thus, generally EXP depends on CHA, FFS and INC. In other words, a
student’s monthly expenditure depends on his/her character, monthly family
financial support and monthly income.
 The brief steps of constructing the appropriate model:

- 30 -
- First, there exists inappropriate variables in the original regression function.
This problem is cured by omitting two variables: X1 = 1 and HOM.
- Second, the above-derived function has heteroskedasticity problem. This can
be cured by dividing both sides of the function by either of these two variables:
FFS and INC.
- Third, we try dividing both sides of the function by FFS. The results show
that heteroskedasticity has not been cured. Then again we divide both sides of the
function by INC. This time we obtain the final regression function
- Eventually, the final regression model is significant and appropriate and meet
all the assumptions of OLS. R2 = 0.941516 means that the regression function can
explain about 94.15% the student’s monthly expenditure in reality.
 Limitation: When curing heteroskedasticity problem, we have difficulty in
dividing both sides of the function by any independent variables. This results from
the fact that some of the observations for the variables FFS and INC may have
value zero (xi = 0). However, Gretl has automatically omitted these incomplete
observations and done analysis in a quite accurate way. To some extent, the
problems have been cured and we get the most suitable regression model.
VII. REFERENCES
 Introduction to Econometrics, Brief Edition – James H. Stock and Mark
W. Watson
 Econometrics – Nguyen Quang Dong
 Principles of Macroeconomics, 3rd edition – N. Gregory Mankiw
 Macroeconomics – Dr. Duong Tan Diep

- 31 -
 http://tutor2u.net/economics/content/consumption/consumption_theory.htm
 http://www.statcan.gc.ca/nea-cen/pub/guide/chap4-eng.htm

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