tiểu luận kinh tế lượng ECONOMETRICS REPORT factors affect students’ GPA

TABLES OF FIGURESExhibit 1: Difference in personal information and GPA...5 Exhibit 2: Difference in time-spending compared to GPA...5 Exhibit 3: Definition of variables in the GPA model.

ECONOMETRICS

REPORT

Class: KTEE309.2

Instructor: PhD Dinh Thi Thanh Binh

Nguyễn Nam Anh - 1811150046 Vũ

Tuấn Đức - 1810150006 Nguyễn

Văn Trọng - 1811150138

FACTORS THAT

AFFECT STUDENTS’ GPA

TABLES OF CONTENT

I, Introduction 3

II, Literature review 4

1 Question of interest 4

2 Some background analysis into the topic 4

3 Methodology 6

4 Procedure and program used 6

III Economic model 8

1 Specifying the object for modeling 8

2 Defining the target for modeling by the choice of the variables to analyze, denote {xi} 8

3 Embedding that target in a general unrestricted model (GUM) 8

IV Econometric model 10

V Data collection 11

1 Data overview 11

2 Data description 12

VI Estimation of econometric model 13

1 Checking the correlation among variables 13

2 Regression run 15

VII Diagnosing the model problem 18

1 Normality 18

2 Multicollinearity 19

3.Heteroscedasticity 20

VIII Hypothesis postulated 24

IX Result analysis & Policy implication 26

TABLES OF FIGURES

Exhibit 1: Difference in personal information and GPA 5

Exhibit 2: Difference in time-spending compared to GPA 5

Exhibit 3: Definition of variables in the GPA model 9

Exhibit 4: Statistic indicators of variables in the GPA model 12

Exhibit 5: Correlation matrix 13

Exhibit 6: Scatterplot of variables in GPA model 14

Exhibit 7: Regression model 15

Exhibit 8: Histogram plot indicating normality 18

Exhibit 9: Skewness/ Kurtosis tests for normality 19

Exhibit 10: Multicollinearity test 20

Exhibit 11: Heteroscedasticity test 21

Exhibit 12: Residual-versus-fitted plot of the model 22

Exhibit 13: Correcting heteroscedasticity 23

I, INTRODUCTION

Studying well always remains as a personal concern for students, no matterwhat level of education they are in From our perspective of view, we believe thatstudying at university requires a lot of interpersonal skills as well as flexibleapplication of different methods of study to get good result As this topic is

popular and practical among students, we choose the topic: Factors affect

students’ GPA to present in this report.

To reach the goal, our team members have conducted a survey and useeconometrics model to analyize the situation This report will show our workingprocess, which begins by collecting data, processing data and then applyingeconometrics model to analyze these factors and end up by giving somerecommendations and suggestions for students to manage to get better GPA in thefuture

Since the duration of the research was very limited, there are stilldeficiencies in this report Therefore, we do hope to have the review and comment

of Dr Dinh Thi Thanh Binh to develop the topic and improve this report

All after all, we do believe that this report would help students’s

performance at school in some way and it can provide readers with a decent view

of the data set as well as the knowledge we have gained through the course

II, LITERATURE REVIEW

1, Question of interest

As we have stated above, learning technique is one of the most commonconcerns for students, especially undergraduates at university It is common andeasy to understand that due to the change in the learning environment as well asthe difference in social circumstances, campus students are incapable ofperforming their best at school, as a result, having low academic scores – GPA.Hanoi University of Science and Technology, or National University of CivilEngineering, for example, about 40% of students can graduate with the exactnumber of course years, and up to 15% are expelled from school due to very lowacademic result

Therefore, in this research, we will analyze the factors that affect students’GPA by using Regression model running and hypothesis testing to trulyunderstand these effects Since we have conducted survey on social network, allthese 152 observations (answers) are updated and the result would be objectiveenough to count on

2, Some background analysis into the topic

When we found the materials for this research, we come across an articale

named «Derterminants of academic performance for undergraduate in Can Tho University of Technology» published on 27 October, 2016 The following are some

results that the article had pointed out, using median hypothesis testing

Exhibit 1: Difference in personal information and GPA (Source: sj.ctu.edu.vn)

Criteria Choices GPA (out of 4) Difference (a –b)

Exhibit 2: Difference in time-spending compared to GPA (Source: sj.ctu.edu.vn)

Criteria Choices GPA (out of 4) Difference (a –b)

*,**,***: having meaning with the confidence interval of 99%, 95%, 90% respectively.

ns: no meaning with the confidence interval of 90%

As it is shown in the above tables, we can see that girls have higher GPA thanboys in general; monitors/class operators/students joining clubs also have higherGPA than others and all this factors have the meaning in terms of statistics withthe confidence interval of 99% Research suggests that time for revisions/skipping class/groupstudy also affect the academic result with statistical meaning.With the help of the last research, we are now conducting another research tosee these factors’ effect into students’ GPA.

4, Procedure and program used

a, The procedure for analyzing include:

Step 1: Question of interest

Step 2: Economic model

Step 3: Econometrics model

Step 4: Data collection

Step 5: Estimation of econometric model

Step 6: Check multicollinearity and heteroscedasticity

Step 7: Hypothesis postulated

Step 8: Result analysis & Policy implication

b, Program used for the whole research

Google Forms: To collect data & carry out the survey.

Google Drive: To store all materials we have collected for this report, which

includes lots of folders & files

Microsoft Excel: To present data & replace some answers to match the Stata The

data set will be attached with this report

Stata: To analyze the data and run the regression

III, ECONOMIC MODEL

As data are provided up front, the economic model used in this report is anempirical one Note that the fundamental model is mathematical; with an empiricalmodel, however, data is gathered for the variables and using accepted statisticaltechniques, the data are used to provide estimates of the model's values

Empirical model discovery and theory evaluation are suggested to involve fivekey steps, but for the limitation of purpose and resources, this part of the reportonly follows three of them:

1) Specifying the object for modelling

2) Defining the target for modelling

3) Embedding that target in a general unrestricted model

1 Specifying the object for modeling

GPA= ( )

As such, this report find the relationship between GPA, which is the object

for modeling, and each of relating factors

2 Defining the target for modeling by the choice of the variables to

analyze, denote { }

After thorough research, our group have been chosen ten significant factors: years

of education at university, gender, time for clubs, jobs, entertainment, sleep, study and hanging out, number of credits and impact of teachers

self-3 Embedding that target in a general unrestricted model (GUM)

In its simplest acceptable representation (which will later be specified in

the econometric model), the GUM of is determined to be:

GPA = (educ, female, tclb, tjob, tentertain, tsleep, tstudy, tout, ncre, tchimp)

III, ECONOMIC MODEL

Exhibit 3: Definition of variables in the GPA model

Variables Definition

IV, ECONOMETRICS MODEL

To determine the relationship between GPA and other factors, the regression

function can be constructed as follows:

0 is the intercept of the regression model

is the slope coefficient of the independent variable xi

is the disturbance of the regression model

is the estimator of

is the residual (the estimator of

From this model, this report is interested in explaining GPA in terms of each of theten independent variables:

(educ, female, tclb, tjob, tentertain, tsleep, tstudy, tout, ncre, tchimp

Econometrics Report – KTEE309.2 Ha Noi, December 2019 Page 10

V, DATA COLLECTION

1, Data overview

This set of data is a primary one, collected from a recent survey

Survey source: http://bit.ly/2PYZl1H

This survey was conducted in 2019 and is a set of 152 observations which are 152 students at different universities It shows their GPA in 2019 and also the correlative factors, including factors that we have mentioned above in our model The data set would be attached with this report in APPENDIX part The survey was made by following these steps:

Step 1: Set the goals for the survey: We hope to find out the relationships

between the GPA of the students and their living and studying behaviors Step 2:

Set the parameters of the survey: The people who are asked to take the survey

are 152 random students at Foreign Trade University (FTU) The survey wastaken in December, 2019

Step 3: Decide on the survey method: The survey was an online form which was

convenient and time-saving for both the researching group and the students whotook the survey The structure of researching data is cross-sectional data toobserve several factors in a period of time

Step 4: Match questions to the objectives: The questions were arranged so that

they covered most of the significant factors that might affect the study results ofthe students These included the time spending for clubs, jobs, entertainment, self-

Step 5: Maintain records: All of the answers were recorded automatically at

Google Forms so that the survey could be checked later for researching purpose

2, Data description

To get statistic indicators of the variables, in Stata, the following command

is used:

sum gpa educ female tclb tjob tentertain tsleep tstudy

tout ncre tchimp

The result is shown in Exhibit 4.

Exhibit 4: Statistic indicators of variables in the GPA model

Where:

• Obs is the number of observations.

• Mean is the expected value of the variable.

• 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.

VI, ESTIMATION OF ECONOMETRIC MODEL

1 Checking the correlation among variables

First of all, the correlation of gpa and educ, female, tclb, tjob, tentertain,

tsleep, tstudy, tout, ncre, tchimp is checked by calculating the correlation

coefficient among these variables The correlation coefficient r measures the

strength and direction of a linear relationship between two variables on ascatterplot In Stata, the correlation matrix is generated with the command:

corr gpa educ female tclb tjob tentertain tsleep tstudy

tout ncre tchimp

The result is shown in Exhibit 5.

Exhibit 5: Correlation matrix

From the correlation matrix, it can be inferred that the correlation betweengpa and each of the independent variable is decent enough to run the regressionmodel Specifically:

- gpa and tclb have a weak downhill relationship.

- gpa and tjob have a weak uphill relationship.

- gpa and tentertain have a moderate downhill relationship.

- gpa and tsleep have a weak downhill relationship.

- gpa and tstudy have a moderate uphill relationship.

- gpa and tout have a weak uphill relationship.

- gpa and ncre have a weak downhill relationship.

- gpa and tchimp have a weak uphill relationship.

The correlation between each pair of them can be visualized using scatter

lot graph in Stata The result is shown in Exhibit 6.

Exhibit 6: Scatterplot of variables in GPA model

2 Regression run

Having checked the required condition of correlation among variables, the

regression model is ready to run In Stata, this is done by using the command:

reg gpa educ female time1 time2 time3 time4 time5 time6

ncre tchimp

The result is shown in Exhibit 7.

Exhibit 7: Regression model

From the result, it can be inferred that:

➢ We have the regression function:

= + + .

− .− .

− .− + .+ .− + .+

in which, regression coefficients:

❖ 0 = 3.308301 : When all the independent variables are zero, the expected value of GPA is 3.308301.

❖ 1 = 0.0328137: When years of education at university increases by one year, the expected value of GPA increases by

0.0328137.

❖ 2 = 0.0436706: Expected value of GPA in is lower than that in male 0.0436706 unit.

❖ 3 = −0.0505358: When increases by one hour, the expected value of GPA decreases by 0.0505358.

❖ 4 = −0.0046487: When increases by one hour, the expected value of GPA decreases by 0.0046487.

❖ 5 = −0.1089011: When the increases by one hour, the expected value of GPA decreases by 0.1089011

❖ 6 = −0.0008117: When increases by 1 hour, the expected value of GPA decreases by 0.0008117.

❖ 7 = 0.1164687 : When − increases by 1 hour, the expected value of GPA increases by 0.1164687.

Econometrics Report – KTEE309.2 Ha Noi, December 2019 Page 16

❖ 8 = 0.0147472 : When ℎ increases by 1 hour, the expected value of GPA increases by 0.0147472.

❖ 9 = −0.0147472 : When í increases by 1 credit per student, the expected value of GPA decreases by 0.0147472.

❖ 10 = 0.0878932 : When ℎ increases by 1 unit, the expected value of GPA increases by 0.0878932.

❖All independent variables (educ, female, tclb, tjob, tentertain, tsleep, tstudy,

tout, ncre, tchimp) jointly explain 41.32% of the variation in the dependent

variable (gpa).

❖Other factors that are not mentioned explain the remaining 58.68% of the

variation in the gpa.

Other indicators:

❖ Adjusted coefficient of determination adj R- squared= 0.3716

❖ Total Sum of Squares TSS= 33.2980886

❖ Explained Sum of Squares ESS = 13.7604018

❖ Residual Sum of Squares RSS = 19.53768681

❖ The degress of freedom of Model Dfm = 10

❖ The degree of freedom of residual Dfr = 141

Econometrics Report – KTEE309.2 Ha Noi, December 2019 Page 17

VII, DIAGNOSING THE

PROBLEMS

1 Normality

We have this following hypothesis:

H0: ui is normally distributed H1: ui is not normally distributed

To test this hypothesis, we can use histogram in Stata, which is generated usingthese commands:

predict resid, residual histogram resid, normal

The result is shown in Exhibit 8.

Exhibit 8: Histogram plot indicating normality

We can also test normality using Skewness Kurtosis test for normality, using thecommand:

Sktest resid

The result is shown in Exhibit 9.

Exhibit 9: Skewness/ Kurtosis tests for normality

At the 5% significance level, both p-values of Skewness and Kurtosis are smallerthan 0.05 so we have enough evidence to reject H0

However, our sample has 152 observations in total, which is really big that eventhough ui is not normally distributed, this model can still give us good results andcan still be used for statistic analysis

2 Multicolinearity

Multicollinearity is the high degree of correlation amongst the explanatoryvariables, which may make it difficult to separate out the effects of the individualregressors, standard errors may be overestimated and t-value depressed The

problem of Multicollinearity can be detected by examining the correlation matrix

of regressors and carry out auxiliary regressions amongst them In Stata, the vif

command is used, which stand for variance inflation factor Exhibit 10 shows the