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

Our study consists of 5 factors that are presumed to shape Statistics and Probability scores: Advanced Math scores, self-studying time per day, interest in the subject, classroom partici

FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS

Vũ Nam Khánh - 1814450045

Vũ Minh Hồng - 1816450041

ABSTRACT

Statistics and Probability is a subject with a long history of development The subject has been acknowledged as one of the foundation subjects for first-year economics students around the world because of its immense applicability

Therefore, our group has decided to conduct in-depth research on the determinants that influence the Statistics and Probability scores of economics students

Our study consists of 5 factors that are presumed to shape Statistics and Probability scores: Advanced Math scores, self-studying time per day, interest in the subject, classroom participation and attention to the lesson After analyzing data running from STATA, it is concluded that only attention to the lesson does not leave a strong impact on Statistics and Probability scores whereas the four remaining factors do At the end of the report, some resolutions andrecommendations are given to further assist in improving economics freshmen's Statistics and Probability scores

INTRODUCTION

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 In addition, most introductory business statistics courses require one or more math courses to provide the necessary mathematical foundation for statistics However, despite these prerequisite math courses, many students do poorly in their business and economics statistics (hereafter, business statistics) course It has even been alleged that "…Business Statistics is the most hated, most unpopular course in the business 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 statistics course

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

Several studies have previously examined the impacts of mathematics skills and topics on student performance in business statistics To our knowledge,however, this is the first study to examine the effect of alternative prerequisite math course 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 by the 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 in Advanced Math with lead to higher scores in Statistical and Probability scores

- Self-study hours per day on Statistics and Probability subject: Self-study is a great 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 areencouraged to explore more topics that interest them, developing stronger research skills Therefore, the more time students spend self-study to review and practice the subject, the higher their score will be

- Interested in the topic of Statistics and Probability: Because of interest in the subject, students make more efforts to study or learn more about this topic

Therefore, the higher the interest in Statistics and Probability, the higher the score 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; In addition, contributing to the lesson by asking questions requires students to

think logically and help them understand the lesson deeply Therefore, themore 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 is used when we want to predict the value of a variable based on the value of two or more other variables The variable we want to predict is called the dependent variable (or sometimes, the outcome, target or criterion variable)

The variables we are using to predict the value of the dependent variable are called the independent variables (or sometimes, the predictor, explanatory or regressor 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 in science, industry or social issues, it is usually starting with studying a statistical overall or a statistical model

The word probability is derived from the Latin word probate and means "to prove, to verify" Put simply, probably is one of many words referring to uncertain facts or knowledge, aimed at defining "ability" These are 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 be experimental, experimental, and random quantities, real-life randomprocesses When solving a problem we often make assumptions, then we need to see how much the assumption is true, then we have to perform the test 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 of high school math that we have ever studied and it is intended for undergraduate students It is based on basic knowledge of generalmathematics such as spatial geometry, statistical probability or quantities in mathematics and upgrades them to other tiers more difficult, so it is called advanced mathematics Advanced mathematics is a difficult subject that requires students to study hard to be able to do their exercises In fact, advanced math is often used for business majors such as business

administration, finance goods, accounting …

2.3. Self-study

Self-studying is a learning method where students direct their own studying—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 methods help students learn and retain information better, helping boostcomprehension, grades, and motivation

Using self-study, students are able to go beyond simply learning what their 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 or someone Interest in Statistics and Probability subject is the feeling of wanting to pay more attention and time to learn or research about this subject

2.5. Attention focus

Paying attention means to listen to, watch, or consider something or someone very carefully That means students focus carefully on the Statistics and 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 progress during the term), comparative assessments (what members of the samesection, or class, demonstrate is possible), and contextual assessments (what students whose work have been evaluated over the years suggests about thefull spectrum of class contribution performances) It is also defined as regularly 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 advanced statistics courses

Probability and statistics, the branches of mathematics concerned with the laws governing random events, including the collection, analysis, interpretation, anddisplay of numerical data Probability has its origin in the study of gambling and insurance in the 17th century, and it is now an indispensable tool of both social and natural sciences Statistics may be said to have its origin in census counts taken thousands 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 actions and later in that century as the mathematical tool for analyzing such numbers For technical information on these subjects, see probability theory and statistics

2 Object

For economics students, countless factors influence the test score instatistical and probability Among the factors that stand out is the time to study the subject yourself, the way you listen to the lectures of the teachers that must be effective in the learning process and the score of the advanced mathematics

Sometimes, students think that their self-study time is not suitable for test scores because there is an injustice between students who have bad self-study and students who have low self-study So, we want to ask the question, "Whether or not all the factors aforementioned affects how the score in Statistics and Probability subject of economics students"

3 Constructing economics model

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

in which:

amscore: Scores of the Advanced Math subject interest: student’s interest in Statistics and Probability subject class: Contribution to the Statistics and Probability classes study: Self-study hours per day on Statistics and Probability subject attention: attention paying to lecturers

4 Specifying economics model

s coreP = β0+ β1amscore+ β2interest+ β3class+ β4study+ β5attention+ μ

In which β0: ​is the intercept of the regression model

βi : ​is the slope coefficient of the independent variable

μ : ​is the 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 tertiary level It requires students to make their efforts in a long time In the process, there are the main factors affecting the GPA and their degree including good and bad

factors In modern life, students are often distracted by several external factors which have adverse affection on their studies In fact, these factors are constantly increasing They affect the six factors mentioned above However, a lot of universities manage to avoid such situations For example, in the period of2007-2011 4,22% of students of Pedagogy University (Da Nang University) had average results Graduation results of the University of Foreign Language (Da Nang University) had only 4,8% average students At Da Nang University of Science and Technology, course 2006-2011 graduated with 82% of graduates having gooddegree or higher At Duy Tan University, a number of students receiving good or higher 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%) In addition, Ho Chi Minh City University of Technology, the number of students receiving 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 individuals received excellent degree, 386 students received good, accounting for 36% It is clear 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 get the 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 statistic description about the dependent variable and independent variables, byrunning ​des ​command expressed as “​des spscore amscore interest attention study class​”

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

amscore float %8.0g interest byte %8.0g attention byte %8.0g study float %8.0g class byte %8.0g

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

Variables Explanation Type of variable Format spscore Score of Statistics

and Probability subject

Dependent variable Quantitative %8.0g

amscore Scores of the

Advanced Math subject

Independent variable Quantitative %8.0g

interest Interest in Statistics

and Probability classes

Independent variable (Dummy variable)

Qualitative %8.0g

Class Contribution to the

Statistics and Probability Classes

Independent variable (Dummy variable)

Qualitative %8.0g

study Self-study hours per

day on Statistics and Probability subject

Independent variable Quantitative %8.0g

attention Attention paying on

the lectures

Independent variable (Dummy variable)

Qualitative %8.0g

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:

Obs​ is 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 spscore 150 8.03 1.272093 6 10 amscore 150 7.36 1.455284 4 10 interest 150 0.56 0.498099 0 1 class 150 0.5333333 0.500559 0 1 study 150 0.4033333 0.3603534 0 2.5

2 Estimation of econometrics model

According to our hypothesis mentioned above: We expect β​1​, β​2​, β​3​, β​4​, β​5​ 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 using​ Corr​ command in Stata,

we have:

(obs=150)

spscore amscore interest attention study class

spscore 1.0000 amscore 0,7464 1.0000 interest 0,7519 0.4422 1.0000 attention 0,5217 0.7190 0.3310 1.0000

The table illustrates that:

The correlation coefficient between ​spscore​ and ​amscore​ is: 0,7464 The correlation coefficient between ​spscore​ and​ interest​ is: 0,7519 The correlation coefficient between​ spscore​ and ​attention​ is: 0,5217 The correlation coefficient between ​spscore​ and ​study​ is: 0,8153 The correlation coefficient between ​spscore​ and ​class​ is: 0,7125 From this statement, It can be easily seen that the correlation among variables is less than 1 so that there is not a strong correlation among variables in the model

3.2 Regression run

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

F(5, 144) = 197.58 Prob > F = 0.0000 R-squared = 0.8728 Adj R-squared = 0.8684 Root MSE = 0.46154

attention 0.0270072 0.1169929 0.23 0.818 -0.2042381 0.2582525

study 1.217141 0.1512262 8.05 0.000 0.918231 1.516051

class 0.5057395 0.1017541 4.97 0.000 0.3046149 0.7068642

_cons 4.869813 0.2761929 17.63 0.000 4.323897 5.415729

Analysis of regression coefficients:

β​1 ​= 0.2693326: Other determinants are held constant When the score of Advanced Math (amscore) increases (decreases) by one score, the score of Statistics and Probability increases (decreases) 0.2693326 score

β​2 ​= 0.7293491: Other determinants are held constant Statistics and Probabilityscores of students who have interest in this subject is higher by 0.2693326 than those of students who do not have interest

β​3​= 1.217141: Other determinants are held constant When the number of hours for studying Statistics and Probability increases (decreases) by one hour, the score of statistics and probability (spscore) increases (decreases) by 1.217141 score

β​4 ​= 0.3826367: Other determinants are held constant Statistics and Probabilityscores of students who pay attention to the lectures in this this subject is higher by 0.3826367 than those of students who do not pay attention

β​5 ​= 0.0270072 Ceteris paribus, Statistics and Probability scores of students who 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 class amscore 1.0000

interest 0.4422 1.0000

attention 0.7190 0.3310 1.0000 study 0.6011 0.6028 0.4052 1.0000 class 0.4901 0.5976 0.2811 0.5482 1.0000

Based on the result, we can observe that the independent variables do not correlate strongly with each other and there is no multicollinearity in the model

- Variance Inflation Factor (VIF) Running ​vif ​command, we have the result:

Step 1:​ Run regression model

F(5, 144) = 197.58 Prob > F = 0.0000 R-squared = 0.8728 Adj R-squared = 0.8684 Root MSE = 0.46154

Residual 30.6744795 144 0.21301721

9

Step 2: ​ Run ​rvfplot ​command

Based on the graph, the points do not distribute regularly, which is a sign of possible 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

chi2(17) = 120.01 Prob > chi2 = 0.0000 Cameron & Trivedi's decomposition of IM-test

Prob (>chi2) = 0.0 < α = 0.05 so we do not accept H​0​ (homoscedasticity)

There is heteroskedasticity in this set of data

5 Coefficients testing

Test each coefficient to know whether it is meaningful to the model, in other words, we test the significance of each independent variable on the dependent one (spscore) Two hypotheses for hypothesis testing:

5.1 P-value

If P-value of an independent variable is smaller than the confidence level, we reject H​0​, accept H​1​ It means this variable has significance on ​spscore​

Test for overall significance of β​1​:

Prob (β​1​) = 0.000 < 0.05, we cannot reject H​0​ at level of significance α = 5%

Therefore, ​study​ is statistically significant on ​spscore​

Test for overall significance of β​2​:

Prob (β​2​) = 0.000 < 0.05, we reject H​0​ at level of significance α = 5% Therefore, β​2

is statistically significant at 5%

Test for overall significance of β​3​ :

Prob (β​3​) = 0.818 > 0.05, we do not reject H​0​ at level of significance α = 5%

Therefore, β​3​ is not statistically significant at 5%

Test for overall significance of β​4​ :

Prob (β​4​) = 0.000 < 0.05, we reject H​0 ​at level of significance α = 5% Therefore, β​4

is statistically significant at 5%

Test for overall significance of β​5​ :

Prob (β​5​) = 0.000 < 0.05, we reject H​0​ at level of significance α = 5% Therefore, β​5

is statistically significant at 5%

In conclusion, ​attention​ does not have significant impact on spscore, ​study​,

interest ​, ​class​ and ​amscore​ have​ ​significant impact on spscore

5.2 Confidence Interval

Variables Coefficient Significant Level Confidence Interval const B​0 5% (4.323897;5.415729) amscore B​1 5% (0.1818351;0.3568301) interest B​2 5% (0.5229854;0.9357129) attention B​3 5% (-0.2042381;0.2582525) study B​4 5% (0.918213;0.7068642) class B​5 5% (0.3046149;0.7068642)

For the all the coefficients, 0 doesn’t belong to the confidence interval, so we reject the hypothesis H​0​ in the 5 pairs of hypothesis above Therefore, the all the coefficients are statistically significant with the confidence level of 95%

0.025​=1.985 |t​qs​| > t​150​

0.025​=1.984 interest B​2 6.99 t​150​

0.025​=1.985 |t​qs​| > t​150​

0.025​=1.984 attention B​3 0.23 t​150​

0.025​=1.985 |t​qs​| > t​150​

0.025​=1.984 study B​4 8.05 t​150​

0.025​=1.985 |t​qs​| > t​150​

0.025​=1.984 class B​5 4.97 t​150​