Tiểu luận Kinh tế chuyển nhượng: The factors affecting monthly expenditure of FTU's studen

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 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. 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. 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 = 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) Formula: If , then Since F = 163.944 > , we reject H0. There is insufficient sample evidence to claim that , that is, the regression function is relevant. 7. FINAL REGRESSION MODEL From all of the above analysis and results, we obtain the following final regression model: - Population regression function: (PRF): (Ui: disturbance term) - Sample regression function: (SRF) newEXPi = 0.707631 + 269.765 newCHAi + 0.928624 newFFSi + (: new residual) in which: + + + + + 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: - 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