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Lecturer :Ms.Dao Binh Tutor: Ms.Tran Kim Anh

Factors affecting the final result of FMT students

Group members:

Nguyễn Thị Loan 0804000062

Chu Thị Phượng 0804010069

Nguyễn Thùy Linh 0804010036

Nguyễn Hải Yến 0804040183

Thọ Thị Yến 0804010114

Bùi Doãn Mai Phương 0707030070

Hoàng Thị Thùy Linh 0704040042

Cao Thị Anh Thương 0704040086

 

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Table of Contents

Introduction1

Model specification2

Estimated equation

Hypothesis Testing4

3

6

5 Testing the violation of OLS assumptions

Conclusion & Evaluation

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Introduction

Sample size : 30 BA_08 students Purpose of the project: Apply Econometric and Macroeconomic theories into

reality Obtain a comprehensive view of Average mark and some

other factors :

IELTS score

IQ index

Self study time

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Model specification

From the graph: The highest mark of BA08-block D 8.5 The lowest mark : 5.5Large difference in average mark among students above.

(Table 1) From the survey 9 students spend 2 hours /day 1/3 students spending: 3 hours for self-study. only one student study 6 hours per day and the self–study time

of others are about 4 or 5 hours per day.

(Table 2)

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Table 1

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Table 2

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Model specification

IQ Index: 1/3 students got the mark of 23 1/3 got 21 to 22.5. 4 students: 24 to 24.5 3 students : reaching very high score 27 and 28

(Table 3) IELTS mark: 12students: 6.0 9 students: 5.5 2 students: over 7.0

(Table 4)

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Table 3

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Table 4

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Estimated equation AM = β1+β2*T+ β3*IQ+ β4*IE + u

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Hypothesis Testing

Testing individual partial coefficients Testing the overall significant of all coefficients Test the drop variable

Note: level of significant: α = 0.05

LOGOTesting individual partial

coefficients

Holding IQ & IE constant: whether T has effect on average mark?

Ho: β2 = 0

Ha: β2 ≠ 0

Value of t-statistic = 2.495128

t-critical = = 2.056

Since >

→ Reject Ho

Answer: Self-study time has effect on the average mark

Holding T & IE constant: whether IQ has effect on AM?

Ho: β3 = 0

Ha: β3 ≠ 0

Value of t-statistic = 2.285119

t-critical = = 2.056

Since >

→ Reject Ho

Answer: IQ has effect on the average mark

ctt

ct 26,025.0ct 26,025.0

t ct

LOGOTesting individual partial

coefficients

Holding IQ & T constant: whether IE has effect on AM?

Ho: β4 = 0

Ha: β4 ≠ 0

Value of t-statistic = 1.325721

t-critical= = 2.056

Since: <

→ Do not reject Ho

Answer: IELTS score doesn’t significantly affect on the average mark

ct 26,025.0t

ct

LOGOTesting the overall significant of

all coefficients

4 variable cases:Ho: β2 = β3 = β4 = 0 (all variables are zero effect)Ha: β2#0 or β3#0 or β4#0 (Not all slope coefficients are

simultaneously zero)

Value of F- statistic = =7.968662 = 2.98Since: >→ reject Ho

Answer: At least one independent variable has effect on dependent variable

*F cF

cF 26,3,05.0

cknkF ,1,

*F

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Test drop variable

The unrestricted model:

Ln(AM)= β1 + β2 *Ln(T) + β3 *Ln(IQ) + β4 *Ln(IE) + u1

Or Ln (AM) = -0.387926 +0.111639* Time + 0.557299*IQIndex + 0.256894*IELTS mark

(Table 5) Run the restricted model:

Ln(AM)= α1 + α 2 *Ln(T) + α3 *Ln(IQ) + u2

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Table 5Dependent Variable: LOG(AM)

Method: Least Squares

Date: 11/16/11 Time: 21:22

Sample: 1 30

Included observations: 30

Variable Coefficient Std. Error t-Statistic Prob.

C -0.387926 0.607985 -0.638053 0.5290

LOG(T) 0.111639 0.048855 2.285119 0.0307

LOG(IQ) 0.557299 0.223355 2.495128 0.0193

LOG(IE) 0.256894 0.193777 1.325721 0.1965

R-squared 0.479020 Mean dependent var 1.960752

Adjusted R-squared 0.418907 S.D. dependent var 0.099503

S.E. of regression 0.075850 Akaike info criterion -2.196544

Sum squared resid 0.149585 Schwarz criterion -2.009717

Log likelihood 36.94815 F-statistic 7.968662

Durbin-Watson stat 2.084685 Prob(F-statistic) 0.000626

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Test drop variable

Explaining the worth of dropping X (IE)

Testing the variable X4 whether it’s relevant or not?

H0 : β4 = 0

H1 : β4 ≠ 0

= 1.7575

Fc(0.05,4-3,30-4) = Fc

(0.05,1,26) = 4 F* > Fc not reject H0

The variable X4 is not relevant to the regression equation we keep the unrestricted model New estimated equation Ln (AM) = -0.377992 +0.112059* Time + 0.700605*IQIndex(Table 6)

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Table 6

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Errors

1

Multicollinearity

2

Heteroskedasticity

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Multicollinearity

Detecting multicollinearity: Auxiliary regression Regress X4 (IE mark) on X2 (Time), X3 (IQ index)

R2 = 0.242077 ( Table 7) F-statistic = 4.31

= F(0.05,2,27) = 3.34

Since F-statistic > Fc

There is a linear relationship between 3 independent variables X2 (Time), X3 (IQ index) and X4(IE mark)

2. Remedial measures

Because Multicollinearity is essentially a deficiency problem and our objective is only for prediction so we would prefer doing nothing.

cknkF ,1,

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Table 7

Dependent Variable: LOG(IE)

Method: Least Squares

Date: 11/15/11 Time: 21:32

Sample: 1 30

Included observations: 30

Variable Coefficient Std. Error t-Statistic Prob.

C 0.038669 0.603776 0.064046 0.9494

LOG(T)

LOG(IQ)

0.001634

0.557839

0.048519

0.194117

0.033671

2.873729

0.9734

0.0078

R-squared 0.242077 Mean dependent var 1.799379

Adjusted R-squared 0.185934 S.D. dependent var 0.083492

S.E. of regression 0.075331 Akaike info criterion -2.239210

Sum squared resid 0.153219 Schwarz criterion -2.099090

Log likelihood 36.58815 F-statistic 4.311833

Durbin-Watson stat 2.042182 Prob(F-statistic) 0.023710

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Checking multicollinearity again in the new model

Checking multicollinearity again

Using Axiliary regression

Regressing X4 on X2, X3

Running Eview and got the results: (Table 8)

R2 =

F-stat =

Fc(4-1,30-3) = F-stat > Fc

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Table 8

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Heteroelasticity

Detect of heteroscedasticity

The white test Ho: var(ui) = σ2

Ha: var(ui) = σ2i

Running Eview and got the results W = n*R2= 3.359 χ2(0.05, 9)= 16.919 W < χ2 Not reject Ho There is no Heteroscedasticity (Table 9)

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Table 9White Heteroskedasticity Test:F-statistic 0.280215 Probability 0.972708Obs*R-squared 3.359310 Probability 0.948332

Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 11/17/11 Time: 08:27Sample: 1 30Included observations: 30

Variable Coefficient Std. Error t-Statistic Prob. C -2.730839 2.947207 -0.926586 0.3652

LOG(T) -0.137090 0.479113 -0.286132 0.7777(LOG(T))^2 -0.005217 0.017129 -0.304598 0.7638

(LOG(T))*(LOG(IQ)) 0.062854 0.183781 0.342004 0.7359(LOG(T))*(LOG(IE)) -0.027382 0.115665 -0.236732 0.8153

LOG(IQ) 1.547363 2.162482 0.715550 0.4825(LOG(IQ))^2 -0.338254 0.513849 -0.658274 0.5179

(LOG(IQ))*(LOG(IE)) 0.280586 0.771352 0.363759 0.7199LOG(IE) 0.420459 1.782130 0.235931 0.8159

(LOG(IE))^2 -0.349590 0.329793 -1.060029 0.3018R-squared 0.111977 Mean dependent var 0.004986Adjusted R-squared -0.287633 S.D. dependent var 0.008827S.E. of regression 0.010016 Akaike info criterion -6.107991Sum squared resid 0.002007 Schwarz criterion -5.640925Log likelihood 101.6199 F-statistic 0.280215Durbin-Watson stat 1.780083 Prob(F-statistic) 0.972708

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Conclusion & Evaluation

Limitations: Inaccurate data Drawbacks of questions Small sample size Other factors affecting final average result

Findings: the positive relationship between the result studying major in FMT and other factors (IELTS score, self-study time, IQ score)

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References

Damodar N. Gujarati, 2003, Basic Econometrics, 4th edition, McGraw-Hill

Jaccard, James and Robert Turrisi. 2003. Interaction Effects in Multiple Regression Second Edition. Thousand Oaks: Sage Publications. Available on URL:

http://www.gwu.edu/~gwipp/presentations/Interactive%20Variables%20Talk.ppt

Garry Young (GW Institute of Public Policy.) January 25, 2006. A Practical Guide to Multiplicative Interaction Variables in Policy Research. Available on URL:

http://www.pdfebooksdownloads.com/ppt/dummy-research~0

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