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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eral 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.
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 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.
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:
where C = Students’ expenditure
= 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.
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. 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)
b) Regression model:
- Population regression function:
(PRF):
(Ui: disturbance term)
- Sample regression function:
(SRF): (ei: residual)
2. COEFFICIENTS PREDICTION
- : positive – A generous student (CHA = 1) tends to spend more than an economical one (CHA = 0)
- : 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)
- : positive – If monthly family financial support increases, student’s monthly expenditure increases too.
- : positive – If a student’s monthly income increases, his/her expenditure increases too.
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
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
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
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
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
- = -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.
- = 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.
- = 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.
- = 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.
- = 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 :
Formula:
If , then
Since | t | = 0.2209 < t0.05(78) = 1.66, we accept H0. There is sufficient sample evidence to claim that , that is, the intercept is not significant.
- Slope :
Formula:
If , then
Since | t | = 1.972 > t0.05(78) = 1.66, we reject H0. There is insufficient sample evidence to claim that , that is, the slope is significant.
- Slope :
Formula:
If , then
Since | t | = 0.2035 < t0.05(78) = 1.66, we accept H0. There is sufficient sample evidence to claim that , that is, the slope is not significant.
- Slope :
Formula:
If , then
Since | t | = 18.45 > t0.05(78) = 1.66, we reject H0. There is insufficient sample evidence to claim that , that is, the slope is significant.
- Slope :
Formula:
If , then
Since | t | = 16.38 > t0.05(78) = 1.66, we reject H0. There is insufficient sample evidence to claim that , that is, the slope is significant.
b) The relevance of the regression function:
Formula:
If , then
Since F = 63.2313 > , we reject H0. There is insufficient sample evidence to claim that , that is, the regression function is relevant.
4. FIRST CURE: FOR THE REGRESSION MODEL
a) The coefficient and the variable HOM:
- From the above analysis, when conducting T-test with respect to , we have sufficient evidence to conclude that , that is, the slope is not significant.
- If the variable HOM is omitted, we obtain the following result when running a regression model having three independent variables: CHA, FFS, INC.
Model 1: OLS, using observations 1-83
Dependent variable: EXP
Coefficient
Std. Error
t-ratio
p-value
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, increases from 0.867792 to 0.869396
The variable HOM will be omitted.
b) The intercept :
- From the above analysis, when conducting T-test with respect to , we have sufficient evidence to conclude that , that is, the intercept is not significant.
- If the variable X1 (X1 = 1) is omitted, or in other words the intercept , we obtain the following result when running a regression model having three independent variables: CHA, FFS, INC.
Model 2: OLS, using observations 1-83
Dependent variable: EXP
Coefficient
Std. Error
t-ratio
p-value
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, increases from 0.869396 to 0.975876
The variable X1 = 1 will be omitted.
The regression function has the intercept .
c) New regression function
(SRF) EXPi = 154.635 CHAi + 0.859465 FFSi + 0.816912 INCi + ei (2)
d) Meaning of the regression coefficients:
- = 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.
- = 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.
- = 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.
- = 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 :
Formula:
Since | t | = 2.049 > t0.05(78) = 1.66, we reject H0. There is insufficient sample evidence to claim that , that is, the slope is significant.
- Slope :
Formula:
Since | t | = 24.41 > t0.05(78) = 1.66, we reject H0. There is insufficient sample evidence to claim that , that is, the slope is significant.
- Slope :
Formula:
Since | t | = 19.58 > t0.05(78) = 1.66, we reject H0. There is insufficient sample evidence to claim that , that is, the slope is significant.
- The relevance of the regression function:
Formula:
If , then
Since F = 539.755 > , we reject H0. There is insufficient sample evidence to claim that , that is, the regression function is relevant.
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
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
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 (), we can claim that multicollinearity does not exist.
- Conclusion: Multicollinearity does not exist.
b) Testing heteroskedasticity with White’s test:
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
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 >
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:
Model 1: OLS, using observations 1-83 (n = 78)
Missing or incomplete observations dropped: 5
Dependent variable: newEXP
Coefficient
Std. Error
t-ratio
p-value
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
***
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
From the above result, we obtain the following regression function:
(SRF) newEXPi = 0.79607 + 184.888 newCHAi + 0.928624 newINCi + (3)
- Testing heteroskedasticity with White’s test:
White's test for heteroskedasticity
OLS, using observations 1-83 (n = 78)
Missing or incomplete observations dropped: 5
Dependent variable: uhat^2
Omitted due to exact collinearity: sq_newFFS X1_X2 X1_X3
coefficient std. error t-ratio p-value
-----------------------------------------------------------------------------------
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
Unadjusted R-squared = 0.223913
Test statistic: TR^2 = 17.465190,
with p-value = P(Chi-square(5) > 17.465190) = 0.003697
From the above analysis:
nR2 = 78 x 0.223913 = 17.465190 >
p-value = 0.003697 < 0.05
Therefore, there still exists heteroskedasticity.
b) Dividing both sides of the regression function by INC:
- Constructing new regression function:
Model 1: OLS, using observations 1-83 (n = 45)
Missing or incomplete observations dropped: 38
Dependent variable: newEXP
Coefficient
Std. Error
t-ratio
p-value
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
4.195698
S.E. of regression
0.316066
R-squared
0.941516
Adjusted R-squared
0.938731
F(2, 42)
338.0709
P-value(F)
1.28e-26
Log-likelihood
10.46867
Akaike criterion
26.93734
Schwarz criterion
32.35733
Hannan-Quinn
28.95786
From the above result, we obtain the following regression function:
(SRF) newEXPi = 0.707631 + 269.765 newCHAi + 0.928624 newFFSi + (4)
- Testing heteroskedasticity with White’s test:
White's test for heteroskedasticity
OLS, using observations 1-83 (n = 45)
Missing or incomplete observations dropped: 38
Dependent variable: uhat^2
Omitted due to exact collinearity: sq_newINC X1_X2 X1_X3
coefficient std. error t-ratio p-value
-------------------------------------------------------------
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
Unadjusted R-squared = 0.047598
Test statistic: TR^2 = 2.141907,
with p-value = P(Chi-square(5) > 2.141907) = 0.829182
From the above analysis:
nR2 = 45 x 0.047598 = 2.141907 <
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
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 = 22
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