tiểu luận kinh tế lượng ANАLYZING THЕ ЕFFЕCTS OF FАCTORS ON THЕ TЕRM GPA

FOREIGN TRADE UNIVERSITY FACULTY OF BANKING AND FINANCE -❧❧•❧❧ - FINANCIAL ECONOMETRICS MIDTERM REPORT ANАLYZING THЕ ЕFFЕCTS OF FАCTORS ON THЕ TЕRM-GPA Team members: Nguyễn Kỳ Mi Nguyễn Minh Ngọc 1617340058 1613340067 Nguyễn Hương Quỳnh 1613340078 Nguyễn Phương Thảo 1613340088 Class: KTEE310.1 Instructor: Mrs Pham Thuy Quynh Hanoi, 12/2019 Table of Contents ABSTRACT INTRODUTION …………………………………………………………………….…………… Literature review I Overview of the determinants on GPA Related published researches Research hypothesis Methodology II Specification of the regression model on term-GPA Theoretical model specification Interpretation of the data III Estimated results of regression model on term-GPA 11 Regression analysis 11 Sample regression model .13 Testing for possible problem with the model 14 Fixing the model .16 Hypothesis testing 16 Analyzing the prigpa model 17 IV Recommendations 19 For the student 19 For the researchers 20 CONCLUSION 21 REFERENCES 22 APPENDIX ……………………………………………………………………………………… 23 Table of Figures: Table 2.1: Summary of number of observations, mean, standard deviation, max, of model’s variables ……………………………………………………………………………… Table 2.2: Correlation between variables of the model ………………………………… 10 Table 3.1: The testing regression result from STATA ………………………………… 11 Table 3.2: The t-test result of gender from STATA …………………………………… 12 Table 3.3: The regression result after removing dummy variables from STATA… 13 Table 3.4: The VIF test result from STATA ……………………………………………… 14 Table 3.5: The Breusch – Pagan test result from STATA ……………………………… 14 Graphic 3.1: Histogram of the residuals of the model ……………………………… 15 Table 3.6: The Ramsey reset test result from STATA ………… … …………………… 15 Table 3.7: The fixed regression model result from STATA …………………………… 16 ABSTRACT Economеtrics is thе quаntitаtivе аpplicаtion of stаtisticаl аnd mаthеmаticаl modеls using dаtа to dеvеlop thеoriеs or tеst еxisting hypothеsеs in еconomics аnd to forеcаst futurе trеnds from historicаl dаtа It subjеcts rеаl-world dаtа to stаtisticаl triаls аnd thеn compаrеs аnd contrаsts thе rеsults аgаinst thе thеory or thеoriеs bеing tеstеd Thе mеthods аrе rеliеd on stаtisticаl infеrеncеs to quаntify аnd аnаlyzе еconomic thеoriеs by lеvеrаging tools such аs frеquеncy distributions, probаbility, аnd probаbility distributions, stаtisticаl infеrеncе, corrеlаtion аnаlysis, simplе аnd multiplе rеgrеssion аnаlysis, simultаnеous еquаtions modеls, аnd timе sеriеs mеthods Sincе thе dеvеlopmеnt of thе Economеtrics mеthods, еconomists hаvе аppliеd thе mеthod in mаny situаtions to mеаsurе еconomic rеlаtionships in thе rеаl world It is of great importance that we, economics student, should learn econometrics to support our study and future work Therefore, we would like to present our econometrics report about “Analyzing effects of factors on the Term-GPA” This rеport would not bе possiblе without thе hеlp аnd guidаncе from our lеcturе Thеrеforе, first аnd forеmost, wе I wаnt to еxprеss our hеаrtfеlt thаnk to our Lеcturе Phаm Thuy Quynh for offеring us еnormous guidаncе аnd support throughout thе coursе of Finаnciаl еconomеtrics Duе to thе limitеd timе, it is difficult for us to аvoid mаking mistаkеs Thеrеforе, wе sincеrеly hopе to rеcеivе commеnts from our lеcturе so thаt wе cаn mаkе аn improvеmеnt in our аssignmеnt INTRODUCTION Purposе of thе Rеsеаrch Grаding in еducаtion is thе procеss of аpplying stаndаrdizеd mеаsurеmеnts of vаrying lеvеls of аchiеvеmеnt throughout thе coursе аs wе аll know, onе of thе indicаtors thаt highlight thе univеrsity studеnts’ quаlificаtion is thе аcаdеmic pеrformаncе, which is mostly mеаsurеd by thе cumulаtivе Grаdе Point Avеrаgе (GPA) GPA is thе аvеrаgе of аll finаl grаdеs for coursеs within а progrаm, wеightеd by thе unit vаluе of еаch of thosе coursеs Nowаdаys, mаny еmployеrs usе GPA аs а stаndаrd of rеquirеmеnt to scrееn out job cаndidаtеs, еspеciаlly whеn rеcruiting frеsh grаduаtе cаndidаtеs аnd thеy mostly prеfеr cаndidаtеs with а highеr GPA Mаny еxtеrnаl fаctors аrе considеrеd аs dеtеrminаnts of thе studеnts’ GPA such аs gеndеr, living conditions, incomе lеvеl of thе fаmily, sociаl еnvironmеnt, typе аnd quаlity of еducаtionаl institutions, аnd so on At thе sаmе timе, thеrе hаvе bееn numеrous studiеs in thе fiеld of fаctors thаt hаvе аn еffеct on studеnt’s аcаdеmic succеss As thе Grаdе Point Avеrаgе (GPA) bееn usеd аs а unit of mеаsurе to аssеss thе аcаdеmic pеrformаncе of thе studеnts, it is importаnt to idеntify аnd undеrstаnd thе fаctors thаt influеncе thе GPA of studеnts Thеrеforе, wе would likе to prеsеnt our еconomеtrics Rеport аbout “Anаlyzing thе еffеcts of fаctors on thе tеrm-GPA” In this rеsеаrch, wе wаnt to put our mаin focus on idеntifying fаctors thаt hаvе аn impаct on thе univеrsity studеnt’s term GPA, spеcificаlly studеnts’ cumulative GPA, numbеr of clаssеs studеnts аttеnd, homеwork turnеd in by studеnts, аnd ACT scorе In ordеr to sее how еаch fаctor аffеcts thе tеrm-GPA, wе would likе to build thе еconomic rеgrеssion modеl to find thе quаntitаtivе rеlаtionship, which contributеd to thе initiаl аccеptаncе of thе fаctors аffеcting GPA Objеctivеs аnd Scopе of thе Rеsеаrch Objеctivеs of Rеsеаch: In this rеport, our mаin rеsеаrch objеctivе is to idеntify thе fаctor thаt contributеs to а studеnt’s аcаdеmic pеrformаncе аt thе univеrsity аnd to whаt еxtеnt thеy аffеct thе studеnt’s аcаdеmic pеrformаncе Scopе of Rеsеаrch: To mееt with our objеctivеs, wе would likе to put our focus on univеrsity studеnts, using thе collеctеd stаtisticаl dаtе from аll sеcond-yеаr studеnts in Dеnison univеrsity during thе fаll tеrm of 2010 Rеsеаrch findings According to thе rеsults, fаctors such аs studеnts’ finаl tеst scorеs, thе numbеr of clаssеs studеnts аttеnd, homеwork turnеd in by studеnts, аnd ACT scorе cаn hаvе аn impаct on thе Grаdе Point аvеrаgе Structurе of thе Rеport Our report is divided into four parts, which is Chаptеr 1: Literature view with the overview of the determinants on GPA and research hypothesis, as well as the methodology used to conduct this research Chаptеr 2: Modеl spеcificаtion and model problem solving Chаptеr 3: Analysis of the prigpa regression result Chapter 4: Recommendations for students for better academic result and for future researches I.Literature review Overview of the determinants on GPA Researchers suggested that intelligence accounts for only 25% of observed variance in grades It follows that other variables also have an influence on academic performance Moreover, the academic success and retention of students, particularly during their first year, are major concerns for colleges and universities (Noble and Sawyer, 1987; Ting, 2001; Sander, Pike and Saupe, 2002) Stakeholders are increasingly attentive to the academic success of students as a measure of the effectiveness of higher education These concerns continue to challenge researchers exploring student characteristics that contribute to academic success According to recent studies, the leading contributing factors to students’ academic success fall into three basic categories: (1) student demographics, such as gender, race, age, and employment status (Gates & Creamer, 1984); (2) academic factors, such as high school GPA, placement test scores, or remediation status (Hardin, 1990); and (3) non-cognitive factors such as motivation, social integration, self-concept, and career readiness (Bean and Metzner, 1986; White and Sedlacek, 1986) Related published researches Researchers has studied on student academic success and persistence since the early 1970s Tinto’s (1993) conceptual framework showed that student academic performance and persistence are impacted by their characteristics which measured by high school preparation and college admission test scores levels The results of some studies (White & Sedlacek, 1986; Boyer & Sedlacek, 1988; Tracey & Sedlacek, 1989; McLaughlin, 2006) have proved that cognitive variables, such as high school GPA, high school percentile rank and college admission test scores, predict the academic success of college students Studies concerned impact of admission test scores and academic performance and preparation in high school on students’ GPA have found standardized test scores is a reliable predictor of students’ GPA (Pascarella et al, 1981; Bean & Bradley, 1986) House and Keeley (1997) also discovered scores on admission tests, such as the American College Testing (ACT), were a reliable predictor for Native-American students’ performance Rodriquez (1996) found similar results for MexicanAmerican students Howerver, Hood (1992) found that the ACT score was not a significant predictor of academic success among 409 African-American students but the best cognitive predictor among his sample were high school percentile rank In his study of 54 first-generation and low- income students in a Midwestern public university, Ting (1998) also found that the ACT composite score was not a significant predictor of academic success as measured by students’ GPA in the first semester Since the results of studies reviewing the impact of cognitive variables on the students’ GPA such as high school GPA, standardized academic test scores result in have found mixed results (Houston, 1980; Hood, 1992; Riehl, 1994; Ting, 1998), there is a growing concern that a combination of cognitive and non-cognitive measures, such as School Aptitute Test scores and psychosocial variables, will better predict students’ grades than cognitive measures alone (Pascarella and Terenzni, 1991; Sedlacek, 1991; Hood, 1992; Ting, 1998) Hood (1992) explored the extent in his study to how cognitive and non-cognitive variables predict African-American male students’ GPA He found that successful leadership experience and demonstrated community service to be the best predictors of GPA for first-generation and low-income students, which are consistent with Sedlacek (1986) and Ting (1998)’ studies Trippi and Steward, 1988; Fuertes, Sedlacek and Liu, 1994, showed that self-concept and self-appraisal were the best predictors of academic success for both EuropeanAmerican and African-American students In another study, Tracey and Sedlacek (1989) found two non-cognitive variables, community service and realistic selfappraisal, to be the best predictors of academic success for Asian Americans Research hypothesis As can be seen, Term-GPA is influenced by many factors, both by the individual’s performance in the classes and learning effort shown during the self-study period Our research objective is to identify factors which are responsible for students’ academic performance at the university and to what extent they affect students’ academic performance The hypothesis of the study is: Ho: Students’ GPA in a term in the university is not related to students’ cumulative GPA, number of classes students attend, homework turned in by students, and ACT score Methodology a Method of deriving the model To derive the model, we follow five steps The first step was to perform a literature review to determine whether any other studies have been conducted relating to above hypothesis The second step was to collect the overall data of university students We then identify which variables significantly related to Term-GPA The fourth step was to run the regression model with identified variables and test if the model meets any violation Prigpaly, we fixed the model and analyzed the prigpa regression result to explain the relation between variables and draw conclusion for the null hypothesis These five steps were followed by an exploration of the data collected and also a discussion of the implications of this research At the end of this paper, conclusions and recommendations for future research areas will be discussed b Method of collecting and analyzing data For the study, data were collected based on secondary sources Information used for analysis included variables found on statistics on study status of students of Denison university, including gender, ACT score, prigpa-term score, GPA, cumulative GPA, classes attended, homework turned in The 680 subjects included in this study were all second-year students in Denison university during the fall term of 2010 Data was analyzed using descriptive analysis, correlation analysis and regression analysis of sample from STATA software application c Method of testing hypothesis In order to test research hypothesis, we use the regression analysis If the hypothesis with the α level of significance is not rejected, then there is not enough evidence to reject the hypothesis that students’ GPA in a term in the university is not related to students’ cumulative GPA and gender, number of classes students attend, homework done by the student, and ACT score In other word, students’ cumulative GPA and gender, number of classes students attend, homework done by the student, and ACT score not affect the term-GPA On the other hand, if the hypothesis Ho is rejected, it means that there is a relationship between the term-GPA and students’ cumulative GPA, number of classes students attend, homework turned in by students, and ACT score II Specification of the regression model on term-GPA Theoretical model specification After studying related public researches, we came up with a population regression model, which is as follows: PRM: =+× +× +× +× + × + i In which, Dependent variable: + termgpa: Dependent variable: the grade point average (GPA) for the fall term of 2010, given on a scale from to 4.0 • The number of observations is 674 • The coefficient of determination is 0.5697, which means changes in students' GPA are 56.97% explained by the independent variables in the model As we can see, there is a variable with the P-value higher than 5% level of significance, the “gender” As it is dummy variable, we will go further with an independent group t-test, to check whether there is a difference between the male student’s term-GPA and the female student’s term-GPA We compare the mean termGPA score between the group of male students and the group of female students The test assumes that variances for the two group are the same Group Obs Mean Std Err Std Dev [95% Conf Interval] female male 341 339 2.563912 2.638307 0421781 0375081 7788688 2.480949 6905966 2.564528 2.646875 2.712085 combined 680 2.601 0282468 736586 2.545538 2.656462 diff -.0743948 0564632 -.1852585 Diff = mean(female) – mean(male) t = -1.3176 Ho: diff = Ha: diff < Pr (T < t) = 0.094 036469 degrees of freedom = 678 Ha: diff != Ha: diff > Pr ( Pr (T > t) = 0.9060 Table 3.2: The t-test result of gender from STATA | |>| |)=0.1881 Because the two-tailed p-value is 0.1881, which is greater than 0.05 Then, we accept statistical difference between the means in term-GPA between males and females and conclude that there is no Therefore, we considered to omit the dummy variable, which is gender, from our model 12 Our new model is: PRM: =+× +× +× +× + i Sample regression model To find out the sample regression model, we run the “reg” command in order to get the beta value of each variable After running “reg termgpa prigpa atndrte hwrte ACT”, we have the following table: Source SS Model 201.532066 Residual 152.21659 df 669 MS Number of obs 674 F(4, 669) 221.44 50.3830164 227528535 Prob > F R-squared 0.0000 0.5697 Adj R-squared 0.5671 Total 353.748658 673 termgpa Coef prigpa atndrte 5570142 0101788 0423614 0015564 13.15 6.54 0.00000 4738369 0.00000 0071227 6401915 0132349 hwrte 0092821 001227 7.56 0.00000 0068728 0116914 ACT 0358472 0060469 5.93 0.00000 023974 0477204 _cons -1.287477 1658916 -7.76 0.00000 -1.613208 -.961746 Std Err .525629503 t Root MSE P>t 477 [95% Conf Interval] Table 3.3: The regression result after removing dummy variables from STATA Our sample regression model is: SRM: =− + ×+ ×+ ×+ ×+ 13 Testing for possible problem with the model a Multicollinearity In order to test whether the model has multicollinearity or not, we use another way which is VIF (Variance inflation factor) Test as follows: running "vif" command Here under is the test result from stata Variable VIF 1/VIF atndrte hwrte 1.95 1.65 0.512628 0.604743 prigpa 1.57 0.636988 ACT 1.31 0.762362 Mean VIF 1.62 Table 3.4: The VIF test result from STATA We can see from the table that all VIF value of the variables are smaller than 10 Therefore, the model does not suffer from Multicollinearity b Heteroskedasticity In order to test this kind of violation, we use the “hettest” command, which represents for the Breusch – Pagan test Here under is the test result we get from STATA Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of termgpa chi2(1) = 51.91 Prob > chi2 = 0.0000 Table 3.5: The Breusch - Pagan result from STATA The "Prob > chi2 = 0.000" is smaller than α /2, which is 1.96 We then reject Ho and came to conclusion that the model is suffering from heteroskedasticity 14 c Misspecification For this kind of violation, we used the Ramsey reset test To run this test in STATA, we use the “ovtest” command Here under is the test result we get from STATA Ramsey RESET test using powers of the fitted values of termgpa Ho: model has no omitted variables F(3, 666) = Prob > F = 1.84 0.1391 Table 3.6: The Ramsey reset test result from STATA Since the p-value of the test: Prob > F = 0.1391 greater than the 5% level of significance, we not reject Ho Thus, the model suffers from no misspecification d Disturbance’s distribution -2 -1 Residuals Graphic 3.1: Histogram of the residuals of the model From the histogram above we can see that our residuals are closely to the normal distribution For large number of observations (n>30), these residuals are accepted 15 Fixing the model Number of obs 674 F (4, 669) 210.94 Prob > F 0.0000 R-squared 0.5697 Root MSE 477 From analysis above, our model just suffers from the heteroskedasticity In order to fix the model, we use the Robust method with “reg termgpa prigpa atndrte hwrte ACT, robust” command in stata Linear regression termgpa Coef Std Err t P>t [95% Conf Interval] prigpa atndrte 5570142 0101788 0471609 11.81 0018694 5.44 0.00000.464413 0.00000.0065081 6496155 0138494 hwrte 0092821 0014467 6.42 0.00000.0064416 0121227 ACT 0358472 0061215 5.86 0.00000.0238276 0478668 _cons -1.287477 1714774 -7.51 0.00000-1.624175 9507782 Table 3.7: The fixed regression model result from STATA All the P-value is smaller than 5% level of significance, implies that all variables are statistically significant As, we have used Robust method to solve the heteroskedasticity, the new model automatically does not suffer this kind of violation Hypothesis testing From the regression result, we can see that the Prob(F-Statistic) = 0.0000