QMTH104 Quantitative Methods

QMTH104 Quantitative Methods

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QMTH104 Quantitative Methods

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QMTH104 Quantitative Methods

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Course Code: QMTH104
University: Kent Institute Australia

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Country: Australia

Question:

Business reports are practical learning tasks where students apply the theories they have been studying to real-world situations. The students are required to select a topic, collect information (Primary and/or secondary) and prepare a report describing a business problem or incident. This report should consist of (not inclusive) Abstract, Introduction, Objectives, Methodologies,Information Analysis, Findings, Recommendations, References, and Appendices.
Find out the linear relationship between any three expenditure items and monthly income.
Develop a scatter diagram and discuss about the casual relationship between those two variables by observing the overall trend of your plots of coordinates.

Understand ethics and ethical behaviour in undertaking a statistical study.
Interpret data by using descriptive statistics.
Explain probability, probability distributions and their applications in decision making.
Explain the concepts of statistical inference and its application.
Interpret results and make decisions through the use of appropriate statistical techniques

What is the average monthly income of the international students?
What factors predict the income of the international students’ income?
What is the average expenditure on various items such as rent, transport, entertainment, food and internet

Answer:

Introduction
Australia has a complex and lucrative industry in terms of international students it enrolls every year. It estimated that international students are the third largest contributor to the country’s economy with close to 16 billion dollars received in 2010/2011 (Cohen, et al., 2002). This has subsequently resulted to more job creations with an estimated 120,000 jobs available to Australian as a result of the enrolment of the international students (Boddy & Smith, 2009). The study sought to answer the following research questions;
Method of data collection
A survey of randomly selected international students was performed. A total of 20 international students was included in the sample. A structured questionnaire was used to collect data from the sampled participants (Wilcox, 2005). A copy of the questionnaire used is attached in the appendix. However, the following are the description of the variables (questions) in the questionnaire;
Table 1: Description of the variables

Variable

Measurement

Variable type

Variable type

Gender

Nominal

Qualitative variable

Independent variable

Country

Nominal

Qualitative variable

Independent variable

Marital status

Nominal

Qualitative variable

Independent variable

Rent

Ratio

Quantitative variable

Independent variable

Food

Ratio

Quantitative variable

Independent variable

Internet

Ratio

Quantitative variable

Independent variable

Entertainment

Ratio

Quantitative variable

Independent variable

Transport

Ratio

Quantitative variable

Independent variable

Income

Ratio

Quantitative variable

Dependent variable

Summary of the data set
The following is the data set for the randomly selected participants.
Table 2: Dataset

Gender

Country

Type of studies

Marital status

Rent

Food

Internet

Entertainment

Transport

Income

1

UAE

1

1

600

300

50

140

160

1500

1

UAE

1

1

680

400

60

180

170

1650

1

India

1

1

520

350

40

140

160

1400

2

India

2

1

630

300

60

170

165

1500

2

UAE

1

1

565

330

65

120

150

1400

1

Philippines

2

1

570

350

50

150

130

1450

1

UAE

1

2

700

550

70

170

180

1850

1

UAE

1

1

600

400

40

150

140

1500

1

Philippines

2

2

750

500

60

160

160

1800

2

Philippines

1

1

550

300

40

130

120

1300

1

UAE

1

1

660

350

50

135

140

1500

2

Nigeria

2

2

700

450

70

175

180

1750

2

Nigeria

2

2

650

300

45

170

160

1500

2

UAE

1

1

650

350

40

120

120

1450

2

UAE

2

1

600

300

50

150

150

1400

1

India

1

1

500

300

40

140

145

1300

1

India

2

2

600

400

70

140

140

1500

1

Philippines

1

2

650

450

80

180

170

1700

1

UAE

2

1

500

300

30

140

120

1250

1

UAE

1

1

630

300

60

170

165

1500

Key:
Table 3: Coding table

Code

Value

1

Male

0

Female

Code

Value

1

Undergraduate

0

Post-graduate

Code

Value

1

Single

0

Married

Descriptive data analysis
Before embarking on the inferential analysis, a descriptive analysis was performed. The results are presented in table 4 below.
Table 4: Descriptive statistics

 

Rent

Food

Internet

Entertainment

Transport

Income

Mean

615.25

364.00

53.50

151.50

151.25

1510.00

Standard Error

15.23

16.74

2.99

4.29

4.24

36.74

Median

615.00

350.00

50.00

150.00

155.00

1500.00

Mode

600.00

300.00

40.00

140.00

160.00

1500.00

Standard Deviation

68.12

74.86

13.39

19.20

18.98

164.32

Sample Variance

4640.72

5604.21

179.21

368.68

360.20

27000.00

Kurtosis

-0.44

0.58

-0.80

-1.18

-0.85

-0.13

Skewness

-0.05

1.15

0.21

0.01

-0.32

0.61

Range

250.00

250.00

50.00

60.00

60.00

600.00

Minimum

500.00

300.00

30.00

120.00

120.00

1250.00

Maximum

750.00

550.00

80.00

180.00

180.00

1850.00

Sum

12305.00

7280.00

1070.00

3030.00

3025.00

30200.00

Count

20

20

20

20

20

20

From the table, it can be seen that the average monthly income for the sampled international students was $1,510.00 with median income being $1,500.00
Frequencies
Gender
Majority of the participants in the study were the male students who represented 65% (n = 13), the female participants represented 35% (n = 7).

Figure 1: Pie chart for the gender
Country of origin
Respondents were asked to state their country of origin, majority of the participants (50%, n = 10) said to come for UAE, the countries with the second highest proportion of participants were India and Philippines with 25% (n = 4) each while 10% (n = 2) said to come from Nigeria.

Figure 2: Bar chart for the country of origin
Type of studies
Majority of the participants in the study were the undergraduate students who represented 60% (n = 12), the post-graduate students represented 40% (n = 8).

Figure 3: Pie chart for the type of studies
Marital Status
Most of the participants interviewed in the study were single and they represented 70% (n = 14), the married participants represented 30% (n = 6).

Figure 4: Pie chart for the marital status
 
Simple linear regression analysis
The study sought to identify the factors that predict the monthly income of the international students. To achieve this, a multiple regression was modelled. The model that the study sought to fix is given below;
Where
The results of the analysis are presented in the tables below;
Table 5: Regression summary statistics

 

 

Regression Statistics

Multiple R

0.994303

R Square

0.988638

Adjusted R Square

0.980375

Standard Error

23.01887

Observations

20

From table 5 above, the value of R-Square is 0.9886; this implies that 98.86% of the variation in the dependent variable (monthly income) is explained by the eight independent (explanatory) variables in the model.
Table 6: ANOVA Table

 

df

SS

MS

F

Significance F

Regression

8

507171.4

63396.43

119.6456

1.35E-09

Residual

11

5828.551

529.8683

 

 

Total

19

513000

 

 

 

Table 6 further shows the goodness of the model where it can be seen that the model is appropriate to predict the monthly average income (p < 0.05). Table 7: Regression coefficient table   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 140.486 76.367 1.840 0.093 -27.597 308.568 Gender 17.453 13.513 1.292 0.223 -12.290 47.195 Type of studies -1.560 13.654 -0.114 0.911 -31.613 28.492 Marital status -1.080 19.870 -0.054 0.958 -44.813 42.653 Rent 1.061 0.128 8.285 0.000 0.779 1.343 Food 0.891 0.137 6.518 0.000 0.590 1.191 Internet 0.574 0.631 0.910 0.382 -0.815 1.964 Entertainment 0.359 0.506 0.709 0.493 -0.755 1.474 Transport 1.967 0.540 3.644 0.004 0.779 3.155 From table 7 above, it is clear that out of the 8 explanatory variables in the model only 3 were significant in the model. This means that only 3 explanatory variables significantly influences the average income of the international students. The significant variables include; monthly rent expense, monthly food expense and monthly transport expense. The coefficient of monthly rent expense was found to be 1.061; this suggests that a unit increase in monthly rent expense would result to an increase in the monthly average income by 1.061. Similarly, a unit decrease in monthly rent expense would result to a decrease in the monthly average income by 1.061. The coefficient of monthly food expense was found to be 0.891; this suggests that a unit increase in monthly food expense would result to an increase in the monthly average income by 0.891. Similarly, a unit decrease in monthly food expense would result to a decrease in the monthly average income by 0.891. The coefficient of monthly transport expense was found to be 1.967; this suggests that a unit increase in monthly transport expense would result to an increase in the monthly average income by 1.967. Similarly, a unit decrease in monthly transport expense would result to a decrease in the monthly average income by 1.967. The intercept coefficient (constant coefficient) was also found to be insignificant in the model (p > 0.05).
Considering the significant variables only, the regression model for predicting the monthly average income would be as follows;
Conclusion
The main purpose of this research was to analyze determinants of international students’ expenditure using a survey of foreign students studying in Australian universities in 2018. A sample of 20 randomly selected students was used to answer the concerns of the researcher. Descriptive statistical analysis was performed on the demographic, monthly expenditure and average monthly income. Multiple linear regression was performed to determine what factors predict the international student’s income. Results showed that the factors that predict the international student’s income were expenditure on food, rent and transport. This clearly shows that the students are more concerned on spending on the basic needs and the spending were found to predict the income.
It is there recommended that the stakeholders should ensure that the prices of the basics needs such as rent, transport and food are on reach to the students.
References
Armstrong, J. S., 2012. Illusions in Regression Analysis.. International Journal of Forecasting (forthcoming), 28(3), p. 689.
Bagdonavicius, V. & Nikulin, M. S., 2011. Chi-squared goodness-of-fit test for right censored data. The International Journal of Applied Mathematics and Statistics, p. 30–50.
Boddy, R. & Smith, G., 2009. Statistical methods in practice: for scientists and technologists. p. 95–96.
Cohen, J., Cohen, P., West, S. G. & Aiken, L. S., 2002. Applied multiple regression/correlation analysis for the behavioral sciences.
Ryabko, B. Y., Stognienko, V. S. & Shokin, Y. I., 2004. A new test for randomness and its application to some cryptographic problems. Journal of Statistical Planning and Inference, Volume 123, p. 365–376.
Waegeman, W. & De Baets, B., 2008. ROC analysis in ordinal regression learning. Pattern Recognition Letters, 29(5), pp. 1-29.
Wilcox, R. R., 2005. Introduction to robust estimation and hypothesis testing.

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