ASA University BangladeshProgram: BBA

- Assignment on-

Socio Economic Condition of ASAUB’s Student.

Course Title: Applied StatisticsCourse Code: Math 201

Submitted to:Md. Ashraful Alam

LecturerFaculty of Business

ASA University Bangladesh

Submitted by:

ID Name Sec Batch Mark071-12-214 Md. Fokrul Hasan Bhuiya C 1st

071-12-211 Nahid Raja C 1st

071-12-218 Md. Saruwar Hossain C 1st

071-12-198 Md. Rakibul Hasan C 1st

071-12-200 Md. Shahidul Islam C 1st

Date of Submission: 02/12/08

Date: December 23, 2008

To

Sheikh Mohammad Sayem

Lecturer

ASA University Bangladesh

Shyamoly, Dhaka-1215.

Subject: Application for submitting the term paper.

Sir,

Here is the term paper we have assigned for Applied Statistics(Math-202) as a

partial requirement of the course. The topic of the term paper is ”Socio Economic

Condition of ASAUB’s Studen”s.

We have collected reliable information from thee cluster data. Then we tried to

identify the over all economic condition of ASAUB’s student in different point of

view.

We would like to thank you for giving us the opportunity for allowing us to work

on such topic and for your constant guidance and support.

Sincerely yours

Md. Fokrul Hasan BhuiyaNahid RajaMd. Saruwar HossainMd. Rakibul HasanMd. Shahidul Islam

Chapter-1 Introduction

We know that Bangladesh is in the member of third world. Bangladesh is the development country. The economic condition of the country is very law. The per income of the people is not satisfactory at all. Now we are going to research about the economic condition of the people. But it is impossible to collect information from every people of Bangladesh. That’s why we collect information from some of the people as sample project. For this reason, we select the ASA University to survey over the students for researching the economic condition level of the students of the private University. We know that ASA University is the higher Middle Classes University of Bangladesh. Here most o f the students are belonging from higher middle classes family. In this University some of the students are studying with 100% waiver tuition fees, because of the obtaining good result in H.S.C. In the time of researching, we find that the students of the ASA University come from the higher middle classes. In the next port of the assignment we try to show the economic condition level of the students.

Motivation

Any comprehensive work, such as this term papers we credit to a multitude of people. Certainly, we should acknowledge the contribution of the pioneer persons who are directly or indirectly helps to prepare or accomplish this term paper. Specially we can give think to pour course coordinator Sheikh Mohammed Sayem who is giving some important instruction or indication for making this assignment. Obviously, it should be our proper instruction to accomplish this task. Actually, everything is not prepared accurately without the helping of anyone. Although it is prepared by without helping of anyone but can not extremely acceptance in the modern work. Actually when we are faced some problem, at this time, we are taking best help from him about this term paper. Most probably our class teacher possesses a frankly manner with us which is very helpful to make this task.

Objectives

The primary objective of this task is to analyze the socio economic condition of ASA University students. So the main objectives of this study are given below:

1) Method used in calculating socio economic condition.2) Differentiate the student’s economic conditions.3) To know about the Regression Analysis.4) To know about the coefficient of multiple determination.5) To know about the Global test.6) To find out the students economic condition.7) To know about the dependent variable and independent variable.

Limitation

In preparing this assignment, we need some fractural information that have some limitations in making our assignment. Actually the limitation varies some reason. The main reason is that first time; our group member was not mostly attentive about this assignment. At the last moment we are started our workings. The informers were not so friendly. They can not provide all of the information correctly. First of all, they are not agreeing to describe their economic condition. It is also informed that the time is so little. But at the eleventh hours, all we are doing this task heart and soul. In fact, it is not effective for us. On the other hand, when we are making this assignment, we have encountered scarcity of Lab. In spite of this condition, we tried to prepare the assignment with in a short time and try to show ourselves the best.

Data collection

We have followed two ways to collect the data and information. These data are collected from various sources. These are:

1. primary data collection and2. Secondary data collection.

Primary Data:Primary data means collect data from the informer directly. We collect data from the student of various section of the ASA University Bangladesh. The students are so flexible to provide data to us. We also gather knowledge about this. We also seek many books to write about this assignment. Most probably, we searched many sorts of renowned writer’s books.

Chapter-2

Literature Review

Regression Analysis:

In preparing this assignment, we use regression model or analysis to find the answers. Now we are going to discuss something about the Regression analyses that are given below:

The Regression analysis is a technique of analyzing or studying the dependence of the one variable on one or more variables. With a view to estimating or predicting the population mean or average value of forms in terms of the known or fixed values of the letter. For instance, economic condition mainly depends on income, expense and education etc.Multiple Regression Analysis:A statistical process by which several variable are used to predict another variables.

Multiple Regression Model:

. Where, Y is the response or dependent variable. are K regression coefficient which are called parameters. Assume that, €~N ( 0,σ )

Multiple Regression Equation:

Fitted or estimated multiple Regression Equation:

Where is the intersect, the value of Y when all the one Zero. is the amount by which Y changes when the particular increases by one unit

with all other values hold the same. The subscript j can assume values between 1 and k which is the number of independent variable.

Least Squares Method:

This method used to develop the estimated regression equation. If minimizes the sum of squared residuals. The population multiple regression model-

Coefficient of Variance:

For its observation, the difference between the observed value of the dependent variable. , is called its residual. The its residual represents the error in using , to

estimate . Thus, for its observation, the residual is - . The sum of squares of these residuals or error is the quantity that is minimized by the least square method. Thus quantity also known as the sum of square due to error is denoted by SSE.

SSE= - )

Correlation Coefficient:

We presented the equation for computing the sample correlation coefficient. If a regression analysis has already been performed and the coefficient of determination r has been computed the sample correlation coefficient can be computed as follows:Sample Correlation Coefficient,R= =

t- Test:the simple linear regression model is y . If x and y are linearly model related. We must have 0. The purpose of the t-test is to see whether we can conclude that . we will use the sample data to test the following hypothesis about the parameter .

we reject the if or .

Closeness of fit in multiple regressions:

The multiple regression models is,

under the assumption of classical linear regression model by using ordinary least square(OLS) method, the fitted regression equation is-

Analysis of variance (ANOVA): Analysis of variance is the process of partitioning and decomposing the total variance contained in the data set into different components each of which is attributed to an identifiable cause or sources of variation and a further component due to chance factor. Here, SST = SSE+SSRWhere, SST = Sum of square of total =

SSE = Explained sum of square =

SSR = Residual sum of square =

Coefficient of multiple determination : R = Explained sum of square_ 100 Total sum of square

Comment:-

R measure the proportion of percentage of the total variance in independent variable explained by the regression model, 0 < R < 1The adjust R : A measure of the goodness of fit of the estimated multiple regression equation that adjusts for the number of independent variables in the model and independent variables.

= 1 -

F test of Global test:- Testing the multiple regression models:-

The hypothesis is , : All the true regression coefficient are Zero : At least one of the coefficients is not Zero

Source Sum of square D.F Mean square F

Regression SSE K MSSE = F =

Error SSR n-k-1 MSSR =

At level of significance , k, n-k-1 is the critical value under the null hypothesis,

the test statistic, F =

Rejection rule: If , then is rejected.

These are about the regression analysis which topics are related with our assignment.

Chapter – 3

Statistical Analysis

In this chapter, we are going to discuss about statistical analysis. In fact, in statistical analysis, we try to explain Descriptive, Regression, Scatter plot, correlation, Global test, T- test etc. According to the following cluster sampling data (cluster data means select homogeneous data selecting from a sampling observation)

FMI FME FE FMI FME FE20,000.00 16,000.00 14.00 55,000.00 40,000.00 1460,000.00 40,000.00 14.00 150,000.00 70,000.00 450,000.00 40,000.00 15.00 30,000.00 25,000.00 1240,000.00 30,000.00 14.00 18,000.00 15,000.00 1440,000.00 38,000.00 14.00 25,000.00 25,000.00 050,000.00 35,000.00 14.00 35,000.00 28,000.00 1445,000.00 35,000.00 14.00 90,000.00 60,000.00 1435,000.00 25,000.00 15.00 30,000.00 25,000.00 1430,000.00 28,000.00 14.00 50,000.00 30,000.00 1240,000.00 32,000.00 15.00 20,000.00 18,000.00 1850,000.00 40,000.00 16.00 35,000.00 30,000.00 1840,000.00 35,000.00 14.00 30,000.00 28,000.00 1240,000.00 35,000.00 14.00 15,000.00 10,000.00 1450,000.00 30,000.00 14.00 40,000.00 25,000.00 1250,000.00 40,000.00 15.00 25,000.00 22,000.00 1220,000.00 15,000.00 14.00 40,000.00 35,000.00 1850,000.00 30,000.00 15.00 45,000.00 30,000.00 525,000.00 22,000.00 14.00 30,000.00 20,000.00 1820,000.00 18,000.00 14.00 20,000.00 25,000.00 1827,000.00 18,000.00 15.00 41,000.00 35,000.00 1650,000.00 45,000.00 15.00 20,000.00 19,000.00 1660,000.00 45,000.00 0.00 18,000.00 17,000.00 1245,000.00 40,000.00 14.00 30,000.00 28,000.00 1435,000.00 32,000.00 15.00 80,000.00 70,000.00 040,000.00 30,000.00 14.00 80,000.00 30,000.00 020,000.00 10,000.00 0.00 22,000.00 15,000.00 1220,000.00 10,000.00 14.00 1,00,000 40,000 1220,000.00 10,000.00 14.00 50,000 40,000 10FMI FME FE FMI FME FE45,000.00 30,000.00 14.00 50,000 20,000 040,000.00 30,000.00 14.00 1,00,000 90, 000 1455,000.00 40,000.00 14 30,000 25,000 16

FMI FME FE FMI FME FE25,000 25,000 12 30000 20000 1450,000 35,000 0 25000 22000 1450,000 40,000 0 21000 19000 1455,000 40,000 14 20000 15000 1280,000 50,000 16 30000 20000 1290,000 45,000 1630,000 20,000 1622,000 22,000 030,000 20,000 101,50,000 1,00,000 1630,000 25,000 1630,000 25,000 035,000 30,000 1620,000 17,000 1440,000 35,000 1640,000 20,000 1025,000 25,000 1418,000 12,000 1625,000 25,000 1023,000 22,000 1050,000 35,000 1620,000 20,000 1250,000 30,000 1220,000 19,000 1635,000 35,000 148000 10000 1640000 25000 1430000 22000 1425000 10000 1250000 45000 1425000 20000 1250000 40000 1226000 12000 1225000 20000 1420000 15000 1430000 23000 1430000 20000 1435000 30000 1450000 48000 16

We know that under the assumptions of classical linear regression model, by using ordinary least square(OLS) method, the fitted regression is –

Here,

Again, means the family expense (FME) is increased .530 times, if we change 1 unit of family income (FMI), when other variable are remain constant.

Means the family expense is increased 202.161times, if we change 1 unit of father education (FE), when other variable are remain constant.

Means, the family expense is fixed for 5581.254, if we hold all variables.

Descriptive

Descriptive statistics are used to describe the basic feature of the data. They provide simple survey about the sample and measurement.

Descriptive Statistics for Father Education (FE)

N Minimum Maximum Mean Std. DeviationFE 105 0 18 12.54 4.618Valid N (listwise) 105

Descriptive Statistics family income (FMI)

N Minimum Maximum Mean Std. DeviationFMI 102 8000 150000 37490.20 19574.051Valid N (listwise) 102

Descriptive Statistics family expense (FME)

N Minimum Maximum Mean Std. DeviationFME 103 10000 70000 28077.67 11774.590Valid N (listwise) 103

Graph for FME & FMI

140000120000100000800006000040000200000

FMI

70000

60000

50000

40000

30000

20000

10000

FM

E

CorrelationsCorrelations

FMI FMEFMI Pearson Correlation 1 .861(**)

Sig. (2-tailed) .000

N 102 102FME Pearson Correlation .861(**) 1

Sig. (2-tailed) .000N 102 103

** Correlation is significant at the 0.01 level (2-tailed).

From the graph we can say that it is a slight positive correlation because if we increase or decrease the FMI then FME variable is increased or decreased. We also say that two variable are positively correlated with other because their values are 1 & 0.861 .

Graph for FME & FE

20151050

FE

70000

60000

50000

40000

30000

20000

10000

FM

E

CorrelationsCorrelations

FME FE

FME Pearson Correlation 1 -.135

Sig. (2-tailed) .175

N 103 103FE Pearson Correlation -.135 1

Sig. (2-tailed) .175N 103 105

From the graph we can say that it is a negative correlation because if we increase or decrease the FME & FE then changes in both sides in same percentage. We also say that two variable are negatively correlated with other because their values are 1 & -0.135.

Regression

Now we are discussing about the Regression Analysis of model summary, coefficient and ANOVA.

Variables Entered/Removed(b)

ModelVariables Entered

Variables Removed Method

1 FE, FMI(a) . Enter

a All requested variables entered.b Dependent Variable: FME

Model Summary

Model R R SquareAdjusted R

SquareStd. Error of the Estimate

1 .864(a) .747 .742 5978.334

a Predictors: (Constant), FE, FMI

Means on an average 74.7% of total variation in dependent variable can be explain by the regression model. Therefore it can explain 74.7%, so we can say that this explanation is good.

= .747. We use adjusted R square for justifying reasonable independent variable. Here, adjusted R square is near to R square. So We can say that the measure is good fit to the estimated multiple regression.

Coefficients (a

Model Unstandardized

CoefficientsStandardized Coefficients t Sig.

B Std. Error Beta 1 (Constant) 5581.254 2316.129 2.410 .018 FMI .530 .031 .880 16.899 .000 FE 202.161 131.315 .080 1.540 .127

a Dependent Variable: FME

ANOVA (b)

Model Sum of

Squares df Mean Square F Sig.1 Regression 104595364

43.4172

5229768221.709

146.326 .000(a)

Residual 3538306693.838

99 35740471.655

Total 13997843137.255

101

a Predictors: (Constant), FE, FMIb Dependent Variable: FME

Global test ( F – Test ):

The hypothesis is,

At the level of , the critical value is 3.09. We reject “Null Hypothesis”, If

The test is, =

Here, F (146.33)> (3.09). Therefore we can reject “Null Hypothesis”So that there are enough evidence to say that every independent variable is actively played.

T- Test: For variable , the hypothesis is,

We reject null hypothesis, if or . And the critical value is 1.984.

The test is,

Here, t (16.899)> (1.984). Therefore we can reject “Null Hypothesis”So that there is enough evidence to say that the independent variable (FMI) is actively played.

For variable , the hypothesis is,

We reject null hypothesis, if or . And the critical value is 1.984.

The test is,

Here, t (1.540)> (1.984). Therefore we can reject “Null Hypothesis”So that there is enough evidence to say that the independent variable (FE) is actively played.

Conclusion: Our assignment topic is “Socio Economic Condition of ASAUB students”. To assign this we use only 2 variable but we need more variable to complete this. Here, family expense is depending on family income and father education of students. Here the variables are positively correlated. The independent variables are relevant according to R square and adjusted R

square. Moreover, independent variables are directly played role to influence the dependent variable. We can measure it by F test and t-test.