tiểu luận kinh tế lượng ANALYSIS OF THE DETERMINANTS INFLUENCING THE STATISTICS AND PROBABILITY SCORES OF ECONOMICS STUDENTS

Thesubject has been acknowledged as one of the foundation subjects for first-yeareconomics students around the world because of its immense applicability.Therefore, our group has decided

FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS

Vũ Nam Khánh - 1814450045

Vũ Minh Hồng - 1816450041

4.Multicollinearity and heteroskedasticity testing 14

Statistics and Probability is a subject with a long history of development Thesubject has been acknowledged as one of the foundation subjects for first-yeareconomics students around the world because of its immense applicability.Therefore, our group has decided to conduct in-depth research on the determinantsthat influence the Statistics and Probability scores of economics students

Our study consists of 5 factors that are presumed to shape Statistics andProbability scores: Advanced Math scores, self-studying time per day, interest in thesubject, classroom participation and attention to the lesson After analyzing datarunning from STATA, it is concluded that only attention to the lesson does notleave a strong impact on Statistics and Probability scores whereas the fourremaining factors do At the end of the report, some resolutions andrecommendations are given to further assist in improving economics freshmen'sStatistics and Probability scores

There is a general consensus that leads to the difference in the performance

of economics students Virtually all accredited business schools require theirstudents to take one or more courses in both mathematics and business statistics Inaddition, most introductory business statistics courses require one or more mathcourses to provide the necessary mathematical foundation for statistics However,despite these prerequisite math courses, many students do poorly in their businessand economics statistics (hereafter, business statistics) course It has even beenalleged that "…Business Statistics is the most hated, most unpopular course in thebusiness program." Potential reasons cited for poor student performance includestatistics anxiety, inadequate statistics instruction, inadequate math preparationbefore matriculation and inadequate math prerequisites prior to taking the statisticscourse

In this study, we focus on the importance of math prerequisites for studentperformance in the business statistics course Specifically, we use an ordered probitmodel to examine the relationship between alternative math course sequences andthe grades earned by students the first time they complete the business statisticscourse We then show how imposing a minimum grade requirement of C- for theprerequisite math course would be expected to affect student performance inbusiness statistics

Several studies have previously examined the impacts of mathematics skillsand topics on student performance in business statistics To our knowledge,however, this is the first study to examine the effect of alternative prerequisite mathcourse sequences on student performance It is also the first study to demonstrate

the effect on student success in business statistics of imposing a minimum grade requirement for the prerequisite math course.

I Overview of the topic (Review of economic theories and statement of research hypotheses)

1 Foundation for variables and model choosing

1.1 Foundation of choosing variables

Our assumption is that the Statistical and Probability Scores are affected bythe following variables: Advanced Math scores, self-studying time per day, interest

in the subject, classroom participation and attention to the lesson

- Advanced Math Score: Because Advanced Math includes the skills andknowledge to study Statistics and Probability, we expect that higher scores inAdvanced Math with lead to higher scores in Statistical and Probabilityscores

- Self-study hours per day on Statistics and Probability subject: Self-study is agreat method that students can use to enhance their learning experience.Using self-study, students can go beyond simply learning what theirtextbooks and instructors teach By practicing self-study, they are encouraged

to explore more topics that interest them, developing stronger research skills.Therefore, the more time students spend self-study to review and practice thesubject, the higher their score will be

- Interested in the topic of Statistics and Probability: Because of interest in thesubject, students make more efforts to study or learn more about this topic.Therefore, the higher the interest in Statistics and Probability, the higher thescore of this course

- Attention in class: It is believed that the more attention students pay for in the lesson, the higher the score will be

- Class contribution: A successful lesson built on student contributions; Inaddition, contributing to the lesson by asking questions requires students to

think logically and help them understand the lesson deeply Therefore, the more contributions a student has to make, the higher the subject score.

1.2. Foundation of choosing models

- Multiple regression model: is an extension of simple linear regression It isused when we want to predict the value of a variable based on the value oftwo or more other variables The variable we want to predict is called thedependent variable (or sometimes, the outcome, target or criterion variable).The variables we are using to predict the value of the dependent variable arecalled the independent variables (or sometimes, the predictor, explanatory orregressor variables) (statistics.laerd.com)

2 Definitions

2.1 Statistics and Probability subject.

Statistics are the study of a wide range of areas, including analysis,interpretation, presentation and data organization When applying statistics inscience, industry or social issues, it is usually starting with studying astatistical overall or a statistical model

The word probability is derived from the Latin word probate andmeans "to prove, to verify" Put simply, probably is one of many wordsreferring to uncertain facts or knowledge, aimed at defining "ability" Theseare two related but separate academic disciplines Statistical analysis oftenuses probability distributions, and the two topics are often studied together.Learning about the probability we will work with tests, is considered to beexperimental, experimental, and random quantities, real-life randomprocesses When solving a problem we often make assumptions, then weneed to see how much the assumption is true, then we have to perform thetest The testing of such a hypothesis is called a statistical hypothesis test,whose test results are calculated based on actual, calculated data

2.2. Advanced Mathematics in college.

Advanced math is a subject with a level of advanced than the type ofhigh school math that we have ever studied and it is intended forundergraduate students It is based on basic knowledge of generalmathematics such as spatial geometry, statistical probability or quantities inmathematics and upgrades them to other tiers more difficult, so it is calledadvanced mathematics Advanced mathematics is a difficult subject thatrequires students to study hard to be able to do their exercises In fact,advanced math is often used for business majors such as businessadministration, finance goods, accounting …

2.3. Self-study.

Self-studying is a learning method where students direct their ownstudying—outside the classroom and without direct supervision Sincestudents are able to take control of what (and how) they are learning, self-study can be a very valuable way for many students to learn these methodshelp students learn and retain information better, helping boostcomprehension, grades, and motivation

Using self-study, students are able to go beyond simply learning whattheir class textbooks and instructors teach them By practicing self-study,they are encouraged to further explore topics they are interested in,developing stronger study skills as a result

2.4. Interest.

Interest is the state of wanting to know or learn about something orsomeone Interest in Statistics and Probability subject is the feeling ofwanting to pay more attention and time to learn or research about thissubject

2.5. Attention focus.

Paying attention means to listen to, watch, or consider something orsomeone very carefully That means students focus carefully on the Statisticsand probability lessons

2.6. Class contribution.

Class contribution is a combination of a combination of three modes

of assessment: individual assessments (a student's development and progressduring the term), comparative assessments (what members of the samesection, or class, demonstrate is possible), and contextual assessments (whatstudents whose work have been evaluated over the years suggests about thefull spectrum of class contribution performances) It is also defined asregularly attending class not just for filling a seat

II Model Specification

1 Literature review

The purpose of the present study was to identify factors that may contribute

to economics students who are having difficulty in introductory and advancedstatistics courses

Probability and statistics, the branches of mathematics concerned with thelaws governing random events, including the collection, analysis, interpretation, anddisplay of numerical data Probability has its origin in the study of gambling andinsurance in the 17th century, and it is now an indispensable tool of both social andnatural sciences Statistics may be said to have its origin in census counts takenthousands of years ago; as a distinct scientific discipline, however, it was developed

in the early 19th century as the study of populations, economies, and moral actionsand later in that century as the mathematical tool for analyzing such numbers Fortechnical information on these subjects, see probability theory and statistics

2 Object

For economics students, countless factors influence the test score in

statistical and probability Among the factors that stand out is the time to study thesubject yourself, the way you listen to the lectures of the teachers that must beeffective in the learning process and the score of the advanced mathematics.Sometimes, students think that their self-study time is not suitable for test scoresbecause there is an injustice between students who have bad self-study and studentswho have low self-study So, we want to ask the question, "Whether or not all thefactors aforementioned affects how the score in Statistics and Probability subject ofeconomics students"

3 Constructing economics model

spscore =f (amscore, interest, class, study, attention)

in which:

amscore: Scores of the Advanced Math subjectinterest: student’s interest in Statistics and Probability subjectclass: Contribution to the Statistics and Probability classesstudy: Self-study hours per day on Statistics and Probability subjectattention: attention paying to lecturers

4 Specifying economics model

scoreP = β0 + β1amscore + β2interest + β3class + β4study + β5attention + μ

In which β 0 :isthe intercept of the regression model

β i : isthe slope coefficient of the independent variable

μ : isthe disturbance of the regression model

III Estimated model and statistical inferences

GPA or score is the biggest goal when a student decides to get the tertiarylevel It requires students to make their efforts in a long time In the process, thereare the main factors affecting the GPA and their degree including good and bad

factors In modern life, students are often distracted by several external factorswhich have adverse affection on their studies In fact, these factors are constantlyincreasing They affect the six factors mentioned above However, a lot ofuniversities manage to avoid such situations For example, in the period of 2007-

2011 4,22% of students of Pedagogy University (Da Nang University) had averageresults Graduation results of the University of Foreign Language (Da NangUniversity) had only 4,8% average students At Da Nang University of Science andTechnology, course 2006-2011 graduated with 82% of graduates having gooddegree or higher At Duy Tan University, a number of students receiving good orhigher degrees accounted for 94,5% Another example is the 58th school year(2008-2012) of Hanoi National University of Education, among 1,547 students,only 9 students graduated with an average degree (accounting for 0,58%) Inaddition, Ho Chi Minh City University of Technology, the number of studentsreceiving good, excellent degree was 27,6% As for Van Hien University, at the end

of 2012, graduation ceremony gave degrees to 1155 graduates, only 27 individualsreceived excellent degree, 386 students received good, accounting for 36% It isclear that the GPA or Statistic and Probability Scores in FTU witnessed the change.This reported is supposed to clarify this problem

1 Data overview

- This set of data is a primary one, as it is collected from our survey We getthe data from our survey on FTU students and gain 150 qualifiedobservations after cleaning all sets of data

- We use des command to give a general description of the variables The most important information obtained after running des command is the meaning of

the variables Here is the result that our group got when doing a statisticdescription about the dependent variable and independent variables, by

running des command expressed as “des spscore amscore interest attention

study class”

variable name storage type display format value label variable labelspscore float %8.0g

We had a summarizing table based on the above result in the table:

Variables Explanation Type of variable Formatspscore Score of Statistics Dependent variable Quantitative %8.0g

interest Interest in Statistics Independent variable Qualitative %8.0g

and Probability (Dummy variable)

classes

Class Contribution to the Independent variable Qualitative %8.0g

Statistics and (Dummy variable)

attention Attention paying on Independent variable Qualitative %8.0g

the lectures (Dummy variable)

The description: We run Sum command in Stata in order to get statistics

indicators of the variables

After processing, the result we have:

In which:

Obsis the number of observations

Std.Dev is the standard deviation of the variable

Min is the minimum value of the variable

Max is the maximum value of the variable

variable Obs Mean Std Dev Min Max

2 Estimation of econometrics model

According to our hypothesis mentioned above: We expect β, β, β, β, β to

be positive (+)

3 Building the experimental model

3.1 Checking correlation among variables

First and foremost, we have to analyze the correlation of variables,

determining the correlation coefficients then specifically consider whether there is

multicollinearity among variables in the model With usingCorrcommand in Stata,

we have:

(obs=150)

The table illustrates that:

The correlation coefficient between spscoreand amscoreis: 0,7464

The correlation coefficient between spscoreandinterestis: 0,7519

The correlation coefficient betweenspscoreand attentionis: 0,5217

The correlation coefficient between spscoreand studyis: 0,8153

The correlation coefficient between spscoreand classis: 0,7125

From this statement, It can be easily seen that the correlation amongvariables is less than 1 so that there is not a strong correlation among variables inthe model

3.2 Regression run

With using Reg command in Stata, we have a sample regression model:

attention 0.0270072 0.1169929 0.23 0.818 -0.2042381 0.2582525

Analysis of regression coefficients:

β = 0.2693326: Other determinants are held constant When the score of Advanced

contribute to classes in this this subject is higher by 0.0270072 than those of

students who do not contribute

4 Multicollinearity and heteroskedasticity testing

4.1 Multicollinearity Testing

- Using corr command:

amscore interest attention study classamscore 1.0000

interest 0.4422 1.0000

- Variance Inflation Factor (VIF)

Running vif command, we have the result:

Step 1:Run regression model

Step 2:Run rvfplot command

Based on the graph, the points do not distribute regularly, which is a sign ofpossible Heteroscedasticity

- Apply White test:

Run imtest, white command, we have the result as following:

imtest, white

White's test for Ho: homoskedasticity

against Ha: unrestricted heteroskedasticity

Prob (>chi2) = 0.0 < α = 0.05 so we do not accept H (homoscedasticity).

5.1 P-value

If P-value of an independent variable is smaller than the confidence level, we

reject H0, accept H1 It means this variable has significance on spscore.

Test for overall significance of β 1 :

Prob (β1) = 0.000 < 0.05, we cannot reject H0 at level of significance α = 5%

Therefore, studyis statistically significant on spscore.

Test for overall significance of β 2 :

Prob (β2) = 0.000 < 0.05, we reject H0 at level of significance α = 5% Therefore, β2

is statistically significant at 5%

Test for overall significance of β 3 :

Prob (β3) = 0.818 > 0.05, we do not reject H0 at level of significance α = 5%.Therefore, β3is not statistically significant at 5%

Test for overall significance of β 4 :

Prob (β4) = 0.000 < 0.05, we reject H0 at level of significance α = 5% Therefore, β4

is statistically significant at 5%

Test for overall significance of β 5 :

Prob (β5) = 0.000 < 0.05, we reject H0 at level of significance α = 5% Therefore, β5

is statistically significant at 5%

In conclusion, attentiondoes not have significant impact on spscore, study,

interest, classand amscorehavesignificant impact on spscore.

5.2 Confidence Interval

Variables Coefficient Significant Level Confidence Interval

For the all the coefficients, 0 doesn’t belong to the confidence interval,

so we reject the hypothesis H in the 5 pairs of hypothesis above Therefore, the all the