University Data Analysis Report: Problem Analysis and Statistics

This report provides a comprehensive statistical analysis of tax return data, utilizing two datasets. Dataset 1, sourced from the Australian Taxation Office (ATO), explores the relationships between lodgement methods (agent vs. self-preparation), age groups, total income, and deduction amounts. The analysis includes frequency distributions, proportions, one-sample proportional Z-tests, correlation coefficients, and linear regression to uncover patterns and dependencies. Dataset 2, gathered through a survey, focuses on international students' preferences for lodgement methods. Comparative analyses between the two datasets are conducted using two-sample Z-tests to assess the equality of proportions. The report reveals insights into the factors influencing tax return lodgement choices and the relationships between various financial and demographic variables. The findings are presented with statistical summaries, confidence intervals, and visualizations, offering a detailed understanding of the data and its implications.

Running head: PROBLEM ANALYSIS AND STATISTICS
Problem Analysis and Statistics
Name of the Student:
Name of the University:
Author’s note:

1PROBLEM ANALYSIS AND STATISTICS
Table of Contents
1. Section 1: Introduction............................................................................................................................................................................................ 3
a) Brief introduction about the assignment:............................................................................................................................................................3
b) Dataset 1:........................................................................................................................................................................................................... 3
c) Dataset 2:............................................................................................................................................................................................................. 3
2. Section 2: Lodgement Method-Dataset 1...............................................................................................................................................................3
A) Part a................................................................................................................................................................................................................... 3
B) Part b................................................................................................................................................................................................................... 4
C) Part c................................................................................................................................................................................................................... 4
3. Section 3: Lodgement Method-Dataset2.................................................................................................................................................................4
A) Part a................................................................................................................................................................................................................... 4
B) Part b................................................................................................................................................................................................................... 5
C) Part c................................................................................................................................................................................................................... 5
4. Section 4: Lodgement Method and Age group-Dataset1:........................................................................................................................................6
A) Part a................................................................................................................................................................................................................... 6
B) Part b................................................................................................................................................................................................................. 10
C) Part c................................................................................................................................................................................................................. 11
5. Section 5: Lodgement Method and Total Income Amount-Dataset1:....................................................................................................................11
A) Part a................................................................................................................................................................................................................. 11
B) Part b................................................................................................................................................................................................................. 13
6. Section 6: Total Income Amount and Deduction Amount-Data set 1:...................................................................................................................16
A) Part a................................................................................................................................................................................................................. 16
B) Part b................................................................................................................................................................................................................. 19
Correlation:....................................................................................................................................................................................................... 19
Regression:........................................................................................................................................................................................................ 19
7. Section7: Conclusion.............................................................................................................................................................................................. 20
A) Part a................................................................................................................................................................................................................. 20
B) Part b: Further Research................................................................................................................................................................................... 20
References:................................................................................................................................................................................................................ 21
Appendices:............................................................................................................................................................................................................... 22
Dataset 1:.............................................................................................................................................................................................................. 22
Dataset 2:.............................................................................................................................................................................................................. 36

2PROBLEM ANALYSIS AND STATISTICS
1. Section 1: Introduction
a) Brief introduction about the assignment:
Many people need to lodge a tax return after the end of the financial year in Australia. Australians could arrange and lodge an own tax
return or pay a registered tax agent for doing it for themselves. By utilising a subset of the sample-file from the Australian Taxation Office (ATO),
we are shortly elaborating and analysing different hidden facts of lodgement method.
The report is constructed by elaborating two datasets. The first dataset is consists of five variables that are Gender, age_range,
Lodgement_method, Tot_inc_amt and Tot_ded_amt. We are keen to be aware about the proportion of people who prefer to lodge a tax return
utilising a tax agent. We are also keen to observe the difference among the age groups with accordance to corresponding lodging group. We are
testing whether there is an inherent relevance between total income and lodgement method or not. At last, we are testing whether there is an
relationship between total income and deduction amount or not.
A tax agent to lodge a tax return in the future constructs the second dataset with primary survey. The dataset2 is a collection of
preference of international students of tax return lodgement method.
b) Dataset 1:
The dataset1 is a secondary data. The data is gathered from internet sources. In dataset1, Gender is a qualitative variable, age_range is
the ordinal variable, Lodgement_method is the nominal variable, Tot_inc_amt and Tot_inc_amt are the numeric variables. Here, gender and
lodgement method is transformed where “Male”=1, “Female” = 0 and “A”=1, “S”=2.
c) Dataset 2:
The dataset2 is primary. The samples of data are gathered by survey method. In dataset2, we took into account only quantitative
dataset that is actually lodgement method. The data is collected by survey method. The target population was 215 students, among which 20
students incurred to respond. The remaining 195 students responded about the questions of questionnaire of survey method. Therefore, the
sample size of the data is 195. The data sampling method is simple random sampling without replacement that is unbiased in nature. However,
we nullified the missing data for getting good outcomes. Therefore, bias could arise. The dataset involves two variables that are “Country_name”
and “Lodgment_method”. Lodgement method has similar levels in dataset2 as was in dataset1 that are “A”=lodgement by agent and
“S”=lodgement by self-preparation.
2. Section 2: Lodgement Method-Dataset 1
A) Part a
Lodgment Frequency Proportion
Agent 721 0.721
Self 279 0.279
Total 1000 1
The above frequency table of dataset1 refers that out of 1000 people 732 people (73.2%) carry out their lodgment by Agents. Only 268
people (26.8%) carry out their lodgment by self-preparation.
Pie Chart of Lodgement Method
agent
self
The pie chart refers the distribution of two types of lodgment methods that are agent (A) and self-preparation (S) in dataset1.
B) Part b
One Sample Proportional Z-test
proportion (p) = 0.721
(1-p) = 0.279
total sample = 1000
standard error = 0.014183053
Level of significance = 5%
confidence limit = 95%
z-value at 0.05 critical region = 1.959963985
Confidence Intervals
upper confidence interval = 0.748798274

3PROBLEM ANALYSIS AND STATISTICS
lower confidence interval = 0.693201726
C) Part c
One sample proportional z-test is used for testing the proportion of lodging method as agent. The exact proportion of lodging method as
agent is 0.721. The lower and upper confidence intervals of proportion of lodging method by agents are 0.693201726 and 0.748798274 at 5%
level of significance. It refers that there is 95% probability of being the proportion of lodging method via agent between these two intervals.
3. Section 3: Lodgement Method-Dataset2
A) Part a
Lodgment Count Proportion
Agent 131 0.671794872
Self 64 0.328205128
Total 195 1
The frequency table in dataset2 indicates that among 195 people, 131 people (67.18%) carry out their lodgment method by Agents. Only
64 people (32.82%) carry out their lodgment method by Self-preparation.
Pie Chart of Lodgment Method
Agent
Self
The pie chart refers the distribution of two types of lodgment methods that are lodgment method via agent and self-preparation in dataset 2.
B) Part b
One sample proportional Z-test
proportion (p) = 0.671794872
(1-p) = 0.328205128
total sample = 195
standard error = 0.033625885
Level of significance = 5%
confidence limit = 95%
z-value at 0.05 critical region = 1.959963985
Confidence Intervals
upper confidence interval = 0.737700394
lower confidence interval = 0.605889349
C) Part c
One sample proportional z-test is carried out for testing the proportion of lodging method as agent in dataset2. The exact proportion of
lodging method as agent is 0.671794872. The calculated confidence intervals of proportion of lodging method via agent are 0.737700394 and
0.605889349. That refers that there is 95% probability of being the proportion of lodging method via agent between these two intervals in
dataset2.
The dataset1 has greater sample than dataset2 (1000>195). In the dataset1, among 1000 people 732 people (73.2%) make their lodging
via agent. Whereas, in the dataset2, among 180 people 131 people (more than 67.18%) make their lodging via agent. The survey outcome
provides lesser percentage of lodging by agent. We execute two samples proportional z-test of examining equality of proportions.
Null hypothesis: The proportions are equal for both the dataset1 and dataset2.
Alternative hypothesis: The proportions are unequal for both the dataset1 and dataset2.
Two sample z-test
dataset 1 total sample 1000
lodging by agent 732
proportion (p1bar) 0.732
dataset 2 total sample 195

4PROBLEM ANALYSIS AND STATISTICS
lodging by agent 131
proportion (p2bar) 0.671794872
total sample 1195
total lodging by agent 863
total proportion (p-bar) 0.722175732
numerator of z-statistic (p1bar - p2bar) 0.060205128
pbar* (1-pbar) 0.200637944
proportion*sample 0.00122955
denominator of z-statistic SQRT(proportion*sample) 0.035064947
z-statistic 1.716960501
p-value 0.15386
Decision-making Null hypothesis accepted
The two samples z-test for testing the equality of means is applied for testing the equality of proportions ( Cleophas, Ton and Aeilko,
2016). The calculated z-statistic is 1.716960501. According to the calculated p-value, we accept the null hypothesis at 95% confidence interval.
Hence, there is 95% probability of being the proportions of lodgment method of two datasets equal. We can say that these two datasets have
equality in proportional values of lodgment methods.
4. Section 4: Lodgement Method and Age group-Dataset1:
A) Part a
Correlation Coefficient
age_range Lodgment_method
age_range 1
Lodgment_method -0.024900721 1
The Pearson correlation coefficient is -0.024900721. Therefore, the correlation coefficient between age range and lodgment method is
insignificant. Hence, we can say that the amount of age range and lodgment method are uncorrelated to each other. For calculating the
correlation coefficient, we transformed “agent” as 1 and “self” as 2 for making qualitative variable quantitative variable.
Lodging Method is Self:
Numerical Summary
age_range
Mean 7.028673835
Standard Error 0.173313376
Median 8
Mode 10
Standard Deviation 2.894904112
Sample Variance 8.380469818
Kurtosis -0.456227604
Skewness -0.675677893
Range 11
Minimum 0
Maximum 11
Sum 1961
Count 279
Largest(1) 11
Smallest(1) 0
Confidence Level(95.0%) 0.341173258
upper control limit 7.368368052
lower control limit 6.688979619
The mean age range of lodging method by “Self-preparation” is 7.028673835. The age range of “Self-preparation” lodging method has
the 95% probability of being within the interval 6.688979619 and 7.368368052.
Table: The frequency distribution table of age group when lodging method is “Self”
age_group frequency cumulative frequency percentage of frequency cumulative percentage of frequency
0 7 7 2.51% 2.51%
1 8 15 2.87% 5.38%
2 11 26 3.94% 9.32%
3 15 41 5.38% 14.70%
4 17 58 6.09% 20.79%
5 22 80 7.89% 28.67%
6 22 102 7.89% 36.56%
7 31 133 11.11% 47.67%

5PROBLEM ANALYSIS AND STATISTICS
8 39 172 13.98% 61.65%
9 40 212 14.34% 75.99%
10 50 262 17.92% 93.91%
11 17 279 6.09% 100.00%
total 279 1
0 1 2 3 4 5 6 7 8 9 10 11
0
10
20
30
40
50
60
Histogram of age wise frequencies
Age group
Frequency
The frequency is maximum for age group number “10” (50) and minimum for age groups “0“(7).
0 1 2 3 4 5 6 7 8 9 10 11
0
50
100
150
200
250
300
Histogram of age wise cumulative frequencies
Age group
cumulative frequencies
0 1 2 3 4 5 6 7 8 9 10 11
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
20.00%
Histogram of age-wise percentage of frequencies
Age group
Percentage frequency
The percentage of frequency is maximum for age group number “10” (17.92%) and minimum for age group “0” (2.51%).
0 1 2 3 4 5 6 7 8 9 10 11
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Histogram of age wise cumulative percentage of frequencies
Age group
cumulative percentage of frequency

6PROBLEM ANALYSIS AND STATISTICS
Lodging Method is Agent:
Numerical Summary
age_range
Mean 5.513176144
Standard Error 0.106084403
Median 6
Mode 7
Standard Deviation 2.84851931
Sample Variance 8.114062259
Kurtosis -0.842582863
Skewness -0.109402233
Range 11
Minimum 0
Maximum 11
Sum 3975
Count 721
Largest(1) 11
Smallest(1) 0
Confidence Level(95.0%) 0.208271712
upper control limit 5.721101574
limit control limit 5.305250715
The mean of the age-range where lodging method is agent is 5.513176144. The age-range of lodging method via agent has the 95%
probability of being in the interval 5.305250715 and 5.721101574.
Table: The frequency distribution table of age group when lodging method is “Agent”
age_group frequency cumulative frequency percentage of frequency cumulative percentage of frequency
0 37 37 5.13% 5.13%
1 28 65 3.88% 9.02%
2 55 120 7.63% 16.64%
3 70 190 9.71% 26.35%
4 80 270 11.10% 37.45%
5 84 354 11.65% 49.10%
6 82 436 11.37% 60.47%
7 86 522 11.93% 72.40%
8 75 597 10.40% 82.80%
9 60 657 8.32% 91.12%
10 51 708 7.07% 98.20%
11 13 721 1.80% 100.00%
total 721 100.000000%
0 1 2 3 4 5 6 7 8 9 10 11
0
10
20
30
40
50
60
70
80
90
100
Histogram of age wise frequencies
Age group
frequencies
The frequency is maximum for age group number “7” (86) and minimum for age group number “11” (13).

7PROBLEM ANALYSIS AND STATISTICS
0 1 2 3 4 5 6 7 8 9 10 11
0
100
200
300
400
500
600
700
800
Histogram of age wise cumulative frequencies
Age group
Cumulative frequency
1 2 3 4 5 6 7 8 9 10 11 12
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
Histogram of percentage of frequencies
Percentage of frequency
The percentage of frequency is maximum for age group number “7” (11.93%) and minimum for age group number “11” (1.8%).
1 2 3 4 5 6 7 8 9 10 11 12
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Histogram of cumulative percentage of frequencies
Age group
cumulative percentage of frequency
B) Part b
95% confidence interval of correlation coefficient
Pearson Correlation Coefficient ( r ) 0.231324379
Z' 0.23558827
Number of samples (N) 1000
Standard Error [1/SQRT(N-3)] 0.031670318
Z(0.05,997) 1.959963985
Confidence intervals of Z'
Lower limit of Z' 0.173515587
Upper limit of Z' 0.297660952
Confidence intervals of r
Lower limit of r 0.171794924
Upper limit of r 0.289170607
The factorized “age group” and “lodging method” has correlation coefficient (0.23558827). The two factors are weakly and positively
correlated at 95% confidence intervals also as the lower and upper limits of correlation coefficients are respectively ( 0.171794924) and
(0.289170607) (Chen, Zhongxue and Nadarajah, 2006). The technique of sampling distribution is utilized for finding the confidence intervals of
correlation coefficient ( r ).
Linear regression method:

8PROBLEM ANALYSIS AND STATISTICS
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.231324379
R Square 0.053510968
Adjusted R Square 0.052562583
Standard Error 0.436779509
Observations 1000
ANOVA
df SS MS F
Significance
F
Regression 1 10.76421289
10.7642
1
56.4232
1 1.29525E-13
Residual 998 190.3947871
0.19077
6
Total 999 201.159
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 1.069404756 0.031134541
34.3478
6 2.7E-171 1.008308083
1.13050142
9
age_range 0.035309172 0.004700658
7.51153
8 1.3E-13 0.026084865
0.04453347
9
The calculated value of multiple R-square is 0.053510968. The calculated F-statistic is 56.42321. These two variables are not highly
related with each other. The p-value 1.29525E-13 less than 0.05 interprets that these age range has insignificant association with lodgment
method at 5% level of significance. Hence, age group and lodging method are not linearly associated.
C) Part c
The calculations of “part-a” and “part-b” of section 4 infer that the age range and Lodgment method of the 1000 people is uncorrelated
in dataset1. However, the histograms and frequency tables indicate that distribution of lodgment method via agent has better normally
distributed curve than the distribution of age group by self-preparation lodgment method.
5. Section 5: Lodgement Method and Total Income Amount-Dataset1:
A) Part a
Lodgment_method Tot_inc_amt
Lodgment_method 1
Tot_inc_amt -0.074065024 1
The calculated Pearson correlation coefficient is (-0.074065024). Hence, the correlation coefficient between amount of total income and
lodgment method is strongly insignificant. The amount of total income and lodgment method are definitely uncorrelated. For calculating the
correlation coefficient, we transformed “agent” as 1 and “self” as 2 for making qualitative variable quantitative variable.
Lodgment Method is Agent:
Numerical Summary
Tot_inc_amt
Mean 67437.6061
Standard Error 6031.099485
Median 49493
Mode 84478
Standard Deviation 161943.725
Sample Variance 26225770078
Kurtosis 426.8326537
Skewness 19.26010917
Range 3842048
Minimum -750
Maximum 3841298
Sum 48622514
Count 721
Largest(1) 3841298
Smallest(1) -750
Confidence Level(95.0%) 11840.6418
Upper confidence limit 79278.24791
Lower confidence limit 55596.9643
For the lodgment method “agent”, the average amount of total amount income is $67437.6061. There exists 95% probability for being
total amount of income ranging between $55596.9643 and $79278.24791 (Bedeian and Arthur, 2014).

9PROBLEM ANALYSIS AND STATISTICS
0 2 4 6 8 10 12
0
2
4
6
8
10
12
Line plot of Total Income Amount
frequency number
Total Income Amount
The line plot indicates Total Income Amount for the people whose lodgment method is via agent.
Lodgment Method is Self:
Numerical Summary
Tot_inc_amt
Mean 44442.66667
Standard Error 2273.983478
Median 39252
Mode 0
Standard Deviation 37983.01251
Sample Variance 1442709239
Kurtosis 11.87000582
Skewness 2.433576055
Range 315737
Minimum -43
Maximum 315694
Sum 12399504
Count 279
Largest(1) 315694
Smallest(1) -43
Confidence Level(95.0%) 4476.413596
Upper confidence limit 48919.08026
Lower confidence limit 39966.25307
For the lodgment method via agent, the average amount of total amount income is $ 44442.66667. There exists 95% probability for total
amount of income ranging between $39966.25307 and $48919.08026.
0 2 4 6 8 10 12
0
2
4
6
8
10
12
Line plot of Total Income Amount
Frequency number
Total Income Amount
The line plot shows Total Income Amount of income for the people whose lodgment method is self-preparation.
95% confidence interval of correlation coefficient
Pearson Correlation Coefficient ( r ) -0.074065024
Z' -0.074200903
Number of samples (N) 1000
Standard Error [1/SQRT(N-3)] 0.031670318
Z(0.05,997) 1.959963985
Confidence intervals of Z'

10PROBLEM ANALYSIS AND STATISTICS
Lower limit of Z' -0.136273585
Upper limit of Z' -0.01212822
Confidence intervals of r
Lower limit of r -0.135436248
Upper limit of r -0.012127626
The Pearson correlation coefficient between total amount of income and lodgment methods is (-0.074065024). Hence, these two factors
are uncorrelated. The upper and lower confidence limits of correlation coefficient are (-0.012127626) and (-0.135436248).
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.074065024
R Square 0.005485628
Adjusted R Square 0.00448912
Standard Error 0.447723608
Observations 1000
ANOVA
df SS MS F
Significance
F
Regression 1 1.103483398
1.10348
3
5.50485
4 0.019158615
Residual 998 200.0555166
0.20045
6
Total 999 201.159
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 1.293557293 0.015458086 83.6816 0 1.263223214
1.32389137
2
Tot_inc_amt -2.38558E-07 1.01677E-07 -2.34624
0.01915
9
-4.38083E-
07
-3.90335E-
08
The value of multiple R-square (0.00516221) indicates that the association of these two factors is not significant. The significant p-value
(0.023077745<0.05) of F-statistic indicates that total amount of income and lodgment method are linearly uncorrelated.
B) Part b
The box plot refers that the distribution of quartiles and spread of total amount of income. Its spread is very high. However, all the
quartiles are below $200000.
Tot_amt_inc via agent
Minimum -750
Maximum 3841298
1st Quartile 26868
2nd Quartile (Median) 49493
3rd Quartile 77689
Bottom 26868
2q Box 22625
3q Box 28196
Whisker- 27618
Whisker+ 3763609
IQR 50821
Upper bound 153920.5
Lower bound -49363.5
The “five point summary” indicates the distribution of amount of total income by the agents. The minimum, first quartile, second
quartile, third quartile and maximum of the amount of income are $(-750), $26868, $49493, $77689 and $3841298 (Tyner, Bryan and Daniel,
2015). Inter-quartile range is lower for total amount of income by agents than self-preparation.
Tot_amt_inc by self preparation
Minimum -43
Maximum 315694
1st Quartile 17602.75
2nd Quartile (Median) 39257
3rd Quartile 62461.75
Bottom 17602.75
2q Box 21654.25
3q Box 23204.75
Whisker- 17645.75

11PROBLEM ANALYSIS AND STATISTICS
Whisker+ 253232.25
IQR 44859
Upper bound 129750.25
Lower bound -49685.75
The “five point summary” indicates the distribution of amount of total income by self-preparation. The minimum, first quartile, second
quartile, third quartile and maximum of the amount of income are $(-43), $17602.75, $39257, $62461.75 and $315694. Inter-quartile range is
higher for total amount of income by self-preparation.
Tot_amt_inc
Minimum -750
Maximum 3841298
1st Quartile 23437.5
2nd Quartile (Median) 45728
3rd Quartile 74112.75
Bottom 23437.5
2q Box 22290.5
3q Box 28384.75
Whisker- 24187.5
Whisker+ 3767185.25
IQR 50675.25
Upper bound 150125.625
Lower bound -52575.375
The “five point summary” indicates the distribution of amount of total income of every type of lodgment method. The minimum, first
quartile, second quartile, third quartile and maximum of the amount of income are $(-750), $23437.5, $45728, $74112.75 and $3841298.
Tot_amt_inc
0
10000
20000
30000
40000
50000
60000
70000
80000
Distribution of Total Income Amount
Lodgment Methods
Total Amount of Income
The box plot of distribution of total amount of income infers that spread is very high from small negative value to high positive value.
However, three quartiles, minimum and maximum values of the distribution lie in the interval $0 to $100000.

12PROBLEM ANALYSIS AND STATISTICS
Tot_amt_inc via agent Tot_amt_inc by self preparation
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
Distribution of total amount of income via agent and self preparation
Lodgement Methods
Total Amount of Income
The grouped box plot of total amount of income of agents and self-preparation indicates that the range and spread is higher for total
amount of income via agent than total amount of income via self-preparation. The quartiles (first, second and third) for total amount of income
via agent are greater than total amount of income by self-preparation (Spitzer and Michaela, 2007). The maximum amount of income is
significantly greater for lodgment method via agent than self-preparation.
The calculated number of Outliers for total income by both the lodging method is 47, the outliers for total income by lodging method via
agent is 36 and the outliers for total income by lodging method via self preparation is 7. The percentages of outliers in all the three cases are
4.7%, 4.9930% and 2.5090% respectively. It is notable that the number of outliers for total income by lodging method via agent is maximum in
percentage.
6. Section 6: Total Income Amount and Deduction Amount-Data set 1:
A) Part a
For both the self and agent lodging method:
Tot_inc_amt Tot_ded_amt
Tot_inc_amt 1
Tot_ded_amt 0.741468594 1
In case of the lodgment method by self-preparation, total income amount and deduction amount are strongly correlated.
Linear Regression between amount of total income and total amount of deduction for the people whose lodging method is agent and self
both:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.741468594
R Square 0.549775676
Adjusted R Square 0.54932455
Standard Error 4455.001408
Observations 1000
ANOVA
df SS MS F Significance F
Regression 1 24187044267 2.42E+10 1218.673 3.9162E-175
Residual 998 19807343468 19847038
Total 999 43994387735
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 470.366301 152.164921 3.091161 0.002049 171.7664114 768.9661905
Tot_inc_amt 0.032515845 0.000931433 34.90949 3.9E-175 0.030688053 0.034343636
According to the value of multiple R-square (0.549775676), the linear association between total deduction amount and total income
amount in case of lodging method via agent are weakly associated. The p-value (0.0<0.05) refers that, we can reject the hypothesis of strong
linear association of these two variables.

13PROBLEM ANALYSIS AND STATISTICS
-1000000 0 1000000 2000000 3000000 4000000 5000000
-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
50000
Tot_inc_amt Residual Plot
Tot_inc_amt
Residuals
The residual scatter plot of total income amount vs. total deduction amount for the both types of lodgment methods
Linear Regression between amount of total income and amount of total deduction for the people whose lodging method is self:
Correlation Coefficient Tot_inc_amt Tot_ded_amt
Tot_inc_amt 1
Tot_ded_amt 0.192430044 1
In case of the lodgment method by self, total income amount and deduction amount are weakly correlated.
Linear Regression
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.192430044
R Square 0.037029322
Adjusted R Square 0.033325588
Standard Error 2931.433206
Observations 262
ANOVA
df SS MS F Significance F
Regression 1 85914417.43 85914417.43 9.997837 0.001753096
Residual 260 2234258167 8593300.642
Total 261 2320172584
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 962.1735152 259.1844136 3.71231241 0.000251 451.8057249 1472.541305
Tot_inc_amt 0.012969791 0.004101852 3.16193561 0.001753 0.004892712 0.021046871
According to the value of multiple R-square (0.037029322), the linear association between total deduction amount and total income
amount in case of self-preparation lodging method are not associated. The p-value (0.001753096<0.05) refers that, we can reject the hypothesis
of linear relevance of these two variables of lodging method by self-preparation.
-50000 0 50000 100000 150000 200000 250000 300000 350000 400000 450000
-10000
-5000
0
5000
10000
15000
20000
25000
30000
Tot_inc_amt Residual Plot
Tot_inc_amt
Residuals
The residual scatter plot of total income amount vs. total deduction amount for the people whose lodgment method is self-preparation
Lodgment method is agent:
Tot_inc_amt Tot_ded_amt

14PROBLEM ANALYSIS AND STATISTICS
Tot_inc_amt 1
Tot_ded_amt 0.762426172 1
In case of the lodgment method by self, total income amount and deduction amount are strongly and positively correlated.
Linear Regression between amount of total income and amount of total deduction for the people of lodging methods Agents:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.762426172
R Square 0.581293667
Adjusted R Square 0.580724773
Standard Error 4851.158768
Observations 738
ANOVA
df SS MS F Significance F
Regression 1 24046665032 2.4E+10 1021.795 2.8083E-141
Residual 736 17320833668 23533741
Total 737 41367498700
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 586.1034102 191.6237716 3.058615 0.002304 209.9090867 962.2977336
Tot_inc_amt 0.032860855 0.001028009 31.96553 2.8E-141 0.030842676 0.034879035
According to the value of multiple R-square (0.581293667), the linear association between total deduction amount and total income
amount in case of both types of lodging method are weakly related. The p-value (2.8083E-141<0.05) indicates that, we can reject the relevance
of these two variables when lodgment method is agent.
-1000000 0 1000000 2000000 3000000 4000000 5000000
-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
50000
Tot_inc_amt Residual Plot
Tot_inc_amt
Residuals
The residual scatter plot is showing total income amount vs. total deduction amount plot for both types of lodgment method of agent
B) Part b
Interpretation of Pearson Correlation Coefficient:
1. Both types of Lodgment method: The Pearson correlation coefficient ( r ) of total income amount and total deduction amount of all
the 1000 samples is 0.741468594. Hence, we conclude that there exists a strong positive correlation between these two factors.
( Puth et al., 2012)
2. Self-lodgment method: The Pearson correlation coefficient between total income amount and total deduction amount for those
people whose lodgment is self-preparation, is calculated as 0.192430044. Hence, we conclude that there exists a weak positive
correlation between these factors for self-preparation lodgment method.
3. Agent lodgment method: The Pearson correlation coefficient between total income amount and total deduction amount for those
people whose lodgment is agent, is calculated as 0.762426172. Hence, we conclude that there exists a strong positive correlation
between these factors for the particular lodgment method.
4. The correlation is highest for lodgment method via agent.
Linear Regression Model:
The linear regression equation of the model is- Y = β0 + β1*X.
1. People whose lodgment method is self-preparation: The linear regression model refers the total deduction amount as response or
dependent variable and amount of total income as single predictor or independent variable.
The linear regression model is, Tot_ded_amount = 962.1735152 + 0.012969791* Tot_inc_amt (Fayers, Peter and Machin, 2013).
The value of multiple R-square (coefficient of determination) is 0.188285136. Hence, only 18.82% variability of house price can be
described by total deduction amount (Faraway 2016). The linear relationship of these two factors is insignificant. The value of F-statistic is
9.997837. The p-value of the linear regression model is 0.001753096 that is less than 0.05. Therefore, we reject the null hypothesis at 5% level of
significance. In accordance to the slope of dependent variable (β1 = 0.012969791), we can conclude that amount of total income is positively
associated with total deduction amount. Hence, we can indicate that amount of total income is greater than amount of total deduction. The
graph indicated that the fitting is not good.

15PROBLEM ANALYSIS AND STATISTICS
2. People whose lodgment method is via agent: The regression model considers the total deduction amount as response or dependent
variable and amount of total income as single predictor or independent variable.
The linear regression model is, Tot_ded_amount = 586.1034102 + 0.032860855 * Tot_inc_amt.
The value of multiple R-square (coefficient of determination) is 0.581293667. Hence, only 58.12% variability of house price can be described
by total deduction amount (Faraway 2016). The linear association of these two factors is insignificant. The value of F-statistic is 1021.795. The p-
value of the model is 0.0. It is less than 0.05. Hence, we reject the null hypothesis at 5% level of significance. According to the slope of
dependent variable (β1 = 0.032860855), we can conclude that amount of total income is positively related with total deduction amount.
Therefore, we can conclude that amount of total income is greater than amount of total deduction. The graph indicated that the fitting is not
good.
3. All people whose lodgment method is via agent and self-preparation: The regression model considers the total deduction amount as
response or dependent variable and amount of total income as single predictor or independent variable.
The linear regression model is, Tot_ded_amount = 470.366301 + 0.032515845 * Tot_inc_amt.
The value of multiple R-square (coefficient of determination) is 0.208855238. Hence, only 20.88% variability of house price can be
described by total deduction amount (Faraway 2016). The linear association of these two factors is insignificant. The value of F-statistic is
1218.673. The calculated p-value is 0.0. It is less than 0.05. Hence, we reject the null hypothesis at 5% level of significance. According to the
slope of dependent variable (β1 = 0.032515845), we can consider that amount of total income is positively associated with total deduction
amount. Therefore, we can say that amount of total income is greater than amount of total deduction. The graph indicated that the fitting is not
also good.
7. Section7: Conclusion
A) Part a
The conclusion that we can draw from the previous results that lodging method is not at all reflected by amount of total income and age
range. Total income amount is insignificantly associated with total deduction amount. The people whose lodgment is carried out by agents are
more in percentage and number. The spread of total income amount is high for lodgment method via agents than self-preparation lodgment.
B) Part b: Further Research
We could add many other factors including qualitative and quantitative variables. The regression models may include more explanatory
variables for estimating. Then the estimation of the model could be more apprehensible. More samples in datase2 could give the exact
outcomes. The logistic model might give further explanation about the dataset. The nature of lodgment method could be derived by gender
distribution and total amount of income.

16PROBLEM ANALYSIS AND STATISTICS
References:
Bedeian, Arthur G. "“More than meets the eye”: A guide to interpreting the descriptive statistics and correlation matrices reported in
management research." Academy of Management Learning & Education 13.1 (2014): 121-135.
Chen, Zhongxue, and Saralees Nadarajah. "On the optimally weighted z-test for combining probabilities from independent
studies." Computational Statistics & Data Analysis 70 (2014): 387-394.
Cleophas, Ton J., and Aeilko H. Zwinderman. "Data Spread: Standard Deviations, One Sample Z-Test, One Sample Binomial Test." Clinical Data
Analysis on a Pocket Calculator. Springer International Publishing, 2016. 201-205.
Faraway, Julian J. Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models. Vol. 124. CRC press,
2016.
Fayers, Peter M., and David Machin. Quality of life: the assessment, analysis and interpretation of patient-reported outcomes. John Wiley & Sons,
2013.
Puth, Marie-Therese, Markus Neuhäuser, and Graeme D. Ruxton. "Effective use of Pearson's product–moment correlation coefficient." Animal
Behaviour 93 (2014): 183-189.
Spitzer, Michaela, et al. "BoxPlotR: a web tool for generation of box plots." Nature methods 11.2 (2014): 121-122.
Tyner, Bryan C., and Daniel M. Fienup. "A comparison of video modeling, text based instruction, and no instruction for creating multiple baseline‐
graphs in Microsoft Excel." Journal of applied behavior analysis 48.3 (2015): 701-706.

17PROBLEM ANALYSIS AND STATISTICS
Appendices:
Dataset 1:
Gender age_range Lodgment_method Tot_inc_amt Tot_ded_amt
0 4 A 136797 1964
1 0 S 1659 0
0 9 S 72761 16473
1 6 A 20218 728
1 7 A 20299 0
0 5 S 34450 1503
1 10 A 35784 859
0 7 A 53184 1552
1 10 S 29688 76
1 4 A 58039 268
1 5 S 66806 879
1 8 S 61008 3100
0 11 A 32673 1311
0 4 A 66932 870
1 4 A 44817 521
1 10 S 5227 0
0 4 A 67525 647
0 9 S 47344 326
0 3 A 102172 303
0 10 S 8893 130
0 7 A 103041 2313
0 5 A 102402 1794
1 8 S 868 0
0 7 A 146831 2804
1 9 A 22937 315
1 6 A 17572 0
0 8 A 58580 649
0 6 A 22239 0
1 9 A 95109 4591
0 2 A 174 897
1 2 A 74423 2564
0 0 A 39271 3919
1 5 A 23358 687
1 8 S 62602 831
0 0 S 3804 0
0 11 S 15616 0
0 2 A 3058 181
0 4 A 88602 3565
1 9 A 29158 1514
1 10 A 27318 288
0 11 S 16242 0
1 1 A 19890 0
0 9 S 45832 3054
0 7 S 85498 707
0 0 A 30817 241
0 9 A 62003 956
0 5 A 13000 0
1 3 A 90854 6116
1 7 S 49025 452
0 7 S 77719 4625
0 7 S 100878 4557
1 5 A 3968 0
0 1 S 47895 40
0 9 A 26293 468
1 10 A 14067 0
0 10 S 25002 2868
0 5 S 16661 3139
0 6 A 106422 580
0 7 A 53069 5575
0 6 A 69426 613
1 11 A 7391 228
0 9 A 52136 1982
0 6 A 78761 3247
1 8 A 49824 1064
0 8 S 58286 727
1 10 S 3308 140

18PROBLEM ANALYSIS AND STATISTICS
1 0 A 33723 206
0 3 A 232878 4158
0 6 A 79450 4334
0 2 A 30538 188
0 10 A 49867 4774
0 8 A 59838 5021
0 7 S 15712 0
1 10 S 19262 107
1 4 A 78603 188
0 2 A 64745 3581
1 4 A 117956 13401
1 10 S 36135 327
0 4 A 50007 152
0 6 S 93416 0
0 5 A 93132 739
1 5 A 84478 193
1 9 A 34577 877
0 5 A 90309 4977
1 7 A 24438 375
0 8 A 48109 552
0 5 A 48480 4615
0 8 S 74714 1334
1 2 A 514 30
0 10 S 3623 0
0 0 A 68346 1940
0 9 A 72944 2839
1 6 A 42732 2203
0 8 A 13864 4436
0 4 S 315694 8458
0 2 A 80125 12475
1 5 A 24374 7212
1 1 A 20320 3441
1 1 S 567 0
1 0 A 12768 341
0 4 A 185939 22814
0 4 A 62577 0
0 4 A 59128 4533
0 9 A 35367 110
1 3 A 18121 776
1 1 A 4442 383
0 3 A 218948 311
1 0 S 27511 0
1 4 A 33360 0
0 6 A 58115 6605
0 8 S 38612 413
1 9 A 5173 116
1 4 A 132687 0
1 4 A 72406 534
0 2 A 93898 1445
1 2 A 54964 0
1 8 A 39449 1459
0 11 A 22351 328
0 5 S 54366 2160
1 2 S 21179 106
0 10 S 7852 0
1 7 A 20134 936
0 5 A 84372 490
1 2 A 16579 484
1 8 A 72077 1243
0 9 A 27107 320
0 6 A 39967 322
1 6 A 138346 0
1 6 A 75055 4193
0 2 A 54071 850
0 3 A 150732 1040
0 9 S 73813 10902
1 6 A 98133 217
0 7 A 85854 6686
0 11 A 16122 0
0 6 S 43643 1360
0 10 S 10642 0

19PROBLEM ANALYSIS AND STATISTICS
0 10 S 15771 0
0 0 A 57357 104
1 7 S 44543 0
0 3 S 10582 0
1 6 A 42715 995
1 8 A 112722 317
1 7 A 28474 2208
0 7 A 22550 601
0 10 S 45384 5855
0 8 A 53332 6457
0 7 A 49114 570
1 9 S 343 51
1 8 S 9721 0
0 6 A 23766 0
0 7 A 45532 184
1 8 A 27778 3628
0 7 A 73286 4864
1 3 A 589 0
0 10 S 43236 0
0 10 A 56299 6524
0 7 A 53144 4103
0 5 A 147358 8900
0 4 A 3841298 33631
1 6 A 12232 141
1 6 S 41243 249
1 8 S 23379 1059
1 7 S 44953 2920
1 5 A -41 0
0 10 A 125041 8363
0 0 A -750 0
0 8 S 41939 263
1 3 A 42681 2409
0 3 S 49359 1113
1 3 A 33831 771
1 10 A 42213 1171
1 9 A 58167 1181
1 5 S 26799 897
1 8 A 77883 385
0 5 A 50591 590
0 9 A 133186 4316
0 9 S 72790 1224
0 9 S 19201 384
0 8 A 81564 1977
1 6 S 100656 2505
0 4 A 300944 45041
1 9 S 56753 3074
1 4 A 157363 585
0 8 A 133408 9048
1 3 A 101681 16167
0 10 S 41379 4820
1 7 S 44333 3743
0 8 A 54841 2606
1 7 A 52020 1488
1 1 S 629 0
1 5 A 66866 18887
0 7 A 129341 12489
1 1 A 23457 252
1 1 A 3214 181
0 10 A 58906 3
1 10 S 23462 348
1 4 A 152008 4703
0 9 S 36879 0
1 3 A 129466 6957
0 7 A 83925 1109
0 8 A 57035 1570
0 11 S 7282 0
0 5 A 310807 1747
0 4 A 151038 7969
0 5 A 80686 2216
1 9 A 14509 0
1 4 S 35154 138

20PROBLEM ANALYSIS AND STATISTICS
0 4 A 63630 815
1 8 S 6626 0
1 2 A 28177 1415
1 4 S 27488 1942
1 8 S 73058 819
0 3 A 54009 2602
0 8 A 106611 657
0 1 A 149 0
0 3 A 53162 817
1 7 A 25549 568
1 7 A 102 0
0 6 S 82920 655
1 5 A 24171 511
1 3 A 14970 1183
0 6 A 156062 2543
0 10 A 27641 108
1 4 A 16944 279
0 6 A 37304 2811
1 1 S 23000 0
0 2 A 59016 0
0 0 A 13873 0
0 9 A 57507 608
1 5 A 61739 4055
1 2 A 78433 203
0 10 S 10943 274
0 2 A 41450 325
1 7 A 24434 140
1 5 A 35958 170
0 5 A 29718 302
0 7 A 97902 1554
0 8 A 155632 28962
0 10 S 32774 1412
0 4 A 77616 3956
0 5 A 79507 391
1 9 A 13594 185
1 4 A 29170 913
0 0 A 39225 1236
0 8 A 47387 796
1 8 S 76074 3285
0 8 A 134812 17778
1 6 S 47273 48
0 7 S 74934 1282
1 10 A 8252 0
1 3 A 7580 178
0 6 A 90413 4766
0 0 A 28513 131
0 1 A 19161 4168
1 1 A 22387 394
1 9 A 28220 1373
0 7 A 69538 4955
1 4 A 28427 498
1 4 S 54236 710
0 2 A 51626 1376
0 9 A 63261 1381
1 5 S 51594 1164
0 3 A 6586 127
0 5 A 166559 3578
1 2 A 183545 1171
1 8 S 34468 305
1 6 A 71103 2662
0 1 A 20919 1363
1 6 A 49502 608
0 8 A 34262 323
1 10 S 63515 752
1 2 A 57151 4407
1 7 A 21242 925
0 9 A 58941 822
0 3 A 111976 149
1 6 A 90663 2213
1 2 A 21063 0
0 9 A 21505 54

21PROBLEM ANALYSIS AND STATISTICS
0 7 A 41868 871
0 2 A 64426 1930
1 6 S 24704 2165
0 10 S 17222 0
1 10 A 24330 275
0 3 A 55818 2574
0 8 A 33219 862
0 10 A 46477 5364
1 0 A 38892 1731
1 6 A 96692 2731
1 5 S 17368 440
1 6 A 39235 2194
1 7 A 63866 3698
0 3 S 26836 0
0 2 A 12327 0
0 7 A 106076 527
0 8 A 87323 6896
0 2 A 207587 37065
0 4 A 79578 2305
0 5 A 52898 1519
0 7 A 76427 647
1 4 A 4370 319
0 10 A 28531 175
1 5 A 34994 1156
0 6 A 7543 0
1 4 A 60931 155
1 7 A 55437 921
0 10 A 48744 1824
0 5 S 0 0
0 7 A 135531 5963
1 8 S 18004 93
1 8 A 47465 2324
0 8 A 9587 0
1 4 A 28671 1791
0 5 A 1761198 12559
0 1 A -136 0
0 10 A 80253 3703
0 9 A 18253 25
0 1 A 16852 1398
0 9 A 59127 5498
0 9 A 124144 2177
1 2 S 27256 1898
0 3 A 283814 36705
1 8 S 36728 406
1 7 A 37034 42
0 9 A 32510 327
0 5 A 63741 1366
1 7 A 86719 3605
1 10 A 39679 755
1 11 S 19022 137
1 8 S 70503 5768
0 3 A 29435 1507
1 3 A 64312 1471
1 0 A 22249 113
1 7 A 43485 0
0 2 S 78001 1767
1 8 S -43 0
0 7 A 29911 0
0 8 A 58939 3199
0 1 A 75681 1103
1 6 S 13691 109
1 3 A 75274 3966
0 3 A 248258 13772
0 8 A 55243 949
1 6 A 43106 0
1 9 A 28322 351
1 6 S 3350 0
0 4 A 34338 807
0 10 S 61641 589
1 5 A 38820 476
1 5 A 43898 538

22PROBLEM ANALYSIS AND STATISTICS
0 0 A 43030 0
0 11 S 9874 12
0 3 A 79213 21348
1 4 A 77563 537
1 8 S 7709 0
1 4 S 33499 794
1 6 A 51852 2157
1 10 A 72482 11028
0 7 S 75951 217
1 6 S 33692 645
1 3 A 42018 2732
0 8 A 47537 3287
0 6 A 188205 1160
1 9 S 65281 269
0 0 A 34526 625
0 3 A 18162 0
1 0 A 15604 47
0 7 A 70401 2473
0 8 A 87220 171
1 8 A 31935 4568
1 5 A 53144 521
0 5 A 64926 4972
1 7 A 1736 208
1 8 A 77313 2793
0 3 A 67579 2625
0 2 S 74078 708
1 7 S 22596 3079
0 9 A 21858 353
0 5 S 44382 275
0 9 S 14167 0
0 10 A 2574 0
0 9 A 34626 0
0 11 S 5133 0
0 3 A 47161 533
0 7 S 40298 0
1 7 S 42869 374
0 7 A 70303 1045
1 4 A 37984 377
0 9 A 77689 7725
1 4 A 60318 1565
1 6 A 15661 331
0 2 A 64729 7581
0 7 A 149123 6032
0 5 A 175908 0
1 4 A 103112 3904
1 1 A 9428 0
0 6 A 73726 3174
0 2 A 218516 15262
1 1 A 27501 0
0 0 S 51005 27
1 3 A 26868 377
0 5 A 18575 0
0 2 A 52866 0
0 8 A 52900 307
0 10 A 17267 0
0 8 A 76801 8882
0 11 S 1932 0
1 3 A 74808 4608
0 10 A 56909 11210
1 6 A 3887 0
1 7 A 58857 484
0 10 A 19920 23
1 4 S 89842 3964
0 5 A 188906 5365
0 10 A 19378 103
1 11 S 16121 0
0 3 A 40404 979
0 3 A 18466 944
1 3 A 20 0
1 7 A 80900 1561
0 4 A 150909 1386

23PROBLEM ANALYSIS AND STATISTICS
0 6 A 154148 13659
1 3 A 31006 0
0 2 A 66226 511
1 9 A 41397 5670
0 4 A 133733 0
1 10 A 7657 0
0 3 S 66547 323
0 3 A 318659 1152
0 2 A 93010 1043
1 4 A 26518 369
1 8 A 45865 312
1 10 S 44178 3503
0 4 A 41051 5717
0 2 A 72686 3174
1 6 S 26137 0
0 10 S 29064 6143
1 10 A 41637 420
1 6 A 46765 392
1 0 A 694 0
1 1 S 16886 247
0 5 A 95210 2506
0 3 A 51176 440
1 11 A 1799 0
1 8 S 38023 0
0 5 A 22140 0
0 5 A 36176 514
1 3 S 6311 0
1 6 A 34918 279
1 6 A 58014 1556
0 0 A 26405 85
1 5 A 111694 6837
1 10 S 14153 0
1 4 A 27233 8218
1 1 A 31607 624
0 8 A 218445 1937
1 4 A 70978 1920
0 8 A 114400 6473
1 6 A 95572 8179
0 10 S 17791 0
1 10 A 22334 0
1 3 A 67615 1962
0 8 S 85428 9772
1 5 A 50817 7711
0 8 A 412 0
1 4 A 121098 1128
1 7 A 41132 1302
1 4 A 16664 1343
0 7 A 140409 3200
0 11 S 1220 0
0 1 A 18775 38
0 5 A 124051 6340
1 8 A 43542 908
1 10 S 45897 1523
0 11 S 8188 894
0 10 S 55831 161
1 2 S 42139 729
0 3 A 32700 420
0 8 A 70403 2501
1 2 A 81637 2091
0 1 A 16236 455
0 4 A 61562 473
1 2 A 1150 0
1 7 A 11699 158
0 9 S 46636 0
0 7 S 61327 638
0 8 A 30883 4557
1 8 A 28785 4231
0 10 S 3592 0
1 4 A 37164 205
0 5 A 91859 4950
0 2 A 17311 24

24PROBLEM ANALYSIS AND STATISTICS
0 9 S 49363 911
0 8 S 154799 3391
1 5 S 66563 568
1 1 A 15199 0
1 5 A 88027 647
0 0 S 15745 0
1 10 S 20969 731
0 6 S 168327 8932
0 9 A 15184 0
1 10 S 33800 1057
1 9 A 25016 6269
1 5 S 33886 0
1 9 A 36547 489
0 6 A 125159 9725
0 7 S 70413 176
0 10 A 31910 419
0 5 A 62518 1658
1 4 A 92177 15251
1 9 S 89160 0
0 9 A 22910 0
0 7 S 47185 341
0 11 A 14745 0
1 3 A 76525 30264
0 10 S 44607 123
1 10 A 49004 358
1 1 S 29846 0
0 11 S 15773 199
0 7 A 61619 10529
1 2 A 34783 1034
1 5 A 182361 1481
0 10 A 7890 0
0 4 A 54231 1098
1 5 A 23373 0
1 8 S 26990 594
0 9 S 49893 3039
0 7 A 53965 0
1 5 A 49493 1383
1 9 S 93422 266
0 10 S 51826 121
0 6 A 87465 2549
0 9 A 32315 290
0 9 A 108322 4565
0 9 S 82542 1166
1 8 A 34580 412
1 1 A 17116 0
1 5 A 5226 171
1 8 A 84045 3680
1 9 S 62486 3797
1 7 S 25283 1496
1 6 A 36818 555
1 8 A 117587 24152
1 6 A 64761 2298
0 8 S 44961 2110
1 2 A 18767 38
1 5 A 3569 0
0 7 A 99081 458
1 6 A 37995 1106
0 8 A 76722 3956
0 7 A 50358 388
0 3 A 131720 6897
0 9 S 70972 1941
1 2 A 57277 4851
0 5 A 50489 444
1 5 S 61814 194
0 7 S 88795 2594
1 2 A 34377 176
1 6 S 97246 1333
1 2 A 38099 1454
1 0 A 78087 1230
1 6 A 55387 6397
1 3 A 519 0

25PROBLEM ANALYSIS AND STATISTICS
0 2 A 108447 1465
1 8 S 39252 640
0 2 A 191993 1294
1 8 A 40633 494
1 2 A 23045 94
0 5 S 93937 957
0 8 A 106222 2081
1 9 S 5970 0
0 3 A 125902 3966
0 5 A 107478 226
1 6 A 21599 0
1 7 A 46474 361
0 7 A 76208 0
1 3 S 50221 381
0 9 A 20364 0
1 10 A 2132 0
0 6 A 123772 569
0 8 A 48343 347
1 6 A 42750 0
1 9 A 20397 493
1 10 A 10733 0
0 6 A 134450 14274
0 6 A 84478 6455
1 11 S 5408 0
1 2 A 70523 1908
1 4 A 380 89
0 2 A 68235 0
0 4 S 54088 1589
0 2 A 78843 1205
0 4 A 71068 370
1 5 S 5659 32
0 8 A 54964 955
1 8 S 106477 1459
1 3 S 27910 0
1 4 A 23987 533
0 4 S 61929 899
0 7 A 98505 18161
1 9 A 26446 2896
1 4 A 17520 0
1 8 S 91508 986
1 10 A 22146 278
0 8 A 70767 870
1 0 S 1359 0
1 5 S 13711 185
1 4 A 27257 5201
0 2 A 103193 81
0 8 A 54209 0
1 9 A 48946 658
0 1 A 31368 3920
0 3 A 74840 3119
0 9 S 97546 4748
0 2 A 43987 2679
1 4 A 228991 15135
0 7 S 21227 0
0 5 A 131172 15877
1 7 A 72071 28
0 4 A 74625 426
0 1 A 288 19
1 4 A 22896 3907
0 0 A 224343 6599
0 0 A 22064 272
0 9 S 28829 440
1 7 S 17540 47
1 10 A 29237 1515
1 2 A 30504 0
1 2 S 51758 473
1 0 A 18080 426
1 3 S 31643 159
1 0 S 2951 0
1 5 S 62389 9277
0 7 A 23698 404

26PROBLEM ANALYSIS AND STATISTICS
0 4 A 92881 1322
0 5 S 153347 17024
0 10 S 19722 331
1 8 S 24029 135
1 3 A 65070 475
1 7 A 58947 5277
0 9 A 47295 0
1 5 A 44270 81
1 10 A 266 338
1 10 A 12375 276
0 0 A 60508 3918
0 1 A 75806 11076
0 6 A 135580 5050
0 7 A 97731 3891
0 0 A 20073 120
1 4 A 68436 1382
1 7 A 25011 650
1 10 S 56024 583
0 10 S 21548 1168
0 3 A 86782 710
0 10 S 62243 6086
1 7 A 38197 1742
0 4 A 74872 0
1 11 S 13353 0
1 6 A 59492 4035
0 3 A 27759 138
1 7 A 26562 429
1 8 A 90739 6030
1 9 S 29049 405
0 7 A 62237 1024
1 6 A 67820 741
1 9 S 547 0
1 5 A 20850 4156
1 1 A 77651 0
1 0 A 22881 1710
1 6 S 82267 1079
0 4 A 76729 3654
0 7 A 119227 1458
1 4 A 38141 5033
0 6 A 204424 2147
0 10 A 30092 859
1 4 A 32928 270
0 10 S 79016 3751
0 5 A 54239 8918
1 10 S 22637 324
0 3 S 18527 182
1 8 A 37314 182
1 3 A 159348 933
0 6 A 44392 1294
1 10 S 28711 227
1 11 A 21047 1142
0 3 A 65573 13533
1 9 A 78938 6313
1 3 A 55571 1795
0 3 S 83956 1539
0 8 A 65392 3580
0 9 A 60855 387
0 4 A 129375 1043
0 7 A 92927 1480
0 2 A 23956 748
1 4 A 46209 142
0 3 A 81522 5653
0 5 A 94492 1951
0 4 A 191689 3012
1 6 A 35322 4530
0 4 A 70885 13902
1 10 A 22135 285
1 4 A 17986 3
1 5 A 42447 449
1 8 S 91969 300
1 8 S 93521 6945

27PROBLEM ANALYSIS AND STATISTICS
1 10 S 11580 0
1 6 A 66250 1063
0 3 S 123585 1794
0 10 A 34774 2096
1 5 A 1677 9
0 9 S 71125 279
0 2 A 36359 642
0 5 A 32912 1057
0 3 A 17735 0
1 4 A 86724 1370
1 8 A 80772 6150
0 9 S 29439 343
1 9 S 9860 0
0 10 A 13697 0
1 3 A 6077 0
0 6 A 82771 748
0 6 A 16938 0
1 8 A 51731 317
1 0 A 119870 36433
0 10 A 160309 324
1 0 A 47550 3318
1 2 A 64503 1859
1 4 S 62569 4768
1 8 A 48335 4444
0 8 S 13614 2061
0 8 A 86524 18703
1 3 A 25765 0
1 8 S 251001 15512
1 6 S 71795 1008
0 4 A 148661 810
1 9 A 7713 0
0 5 A 0 0
0 1 A 179129 2538
1 8 A 28869 433
0 11 A 18551 0
0 11 S 14628 0
1 10 S 19282 2776
1 3 A 47585 4718
0 11 A 12503 0
1 10 S 18568 0
1 1 A 30981 3512
1 0 A 42061 260
0 6 A 90303 3072
0 4 S 21572 3201
1 3 A 49275 3640
1 6 A 48343 1973
0 8 A 43552 1416
1 6 A 44340 3515
0 8 A 24470 580
0 5 A 35779 332
0 8 S 42081 1923
0 4 A 45849 1983
1 6 S 63450 76
0 4 A 65547 268
0 5 A 76684 2846
0 3 A 79478 1825
1 4 A 58556 272
1 6 A 45717 1376
0 7 A 139776 1257
1 6 A 31827 744
1 4 S 10294 0
1 9 S 3828 678
0 5 A 61126 1409
0 9 A 102192 3858
1 4 A 30130 1851
1 9 S 78081 63
0 6 A 23009 3476
0 3 A 53246 646
1 9 A 14430 372
0 9 A 3190 380
0 5 A 138329 9494

28PROBLEM ANALYSIS AND STATISTICS
0 8 A 78712 3632
1 6 A 890 251
1 10 A 24684 499
1 7 A 61562 2531
0 4 S 42081 306
0 4 S 151243 2669
0 7 A 23375 54
1 10 S 34659 283
1 5 S 83403 882
1 10 A 20484 1627
1 3 S 13386 0
1 5 A 334507 0
0 9 A 50751 4485
1 6 S 45819 155
0 8 A 60225 5887
0 8 A 30190 5310
1 6 S 55066 289
0 8 A 46188 1545
1 10 A 7558 143
0 7 S 64659 11036
0 3 A 59703 667
0 6 A 69762 2750
1 9 S 15997 0
1 8 A 53664 1153
0 2 S 20412 0
0 7 A 50249 0
0 5 A 103728 421
1 5 A 25788 374
0 11 S 23585 491
1 9 S 72722 92
1 7 A 29478 7481
1 2 A 75859 1735
1 9 A 96850 2138
1 8 S 25458 460
1 9 A 50295 1716
1 5 A 73679 15609
0 7 A 149730 4478
0 9 S 59624 1739
0 9 A 19730 0
0 6 A 74327 0
0 0 A 19802 0
0 4 A 68877 14979
0 0 A 33698 265
1 5 A 29077 549
1 6 A 43556 1564
1 6 A 21645 0
0 7 S 93975 476
0 5 A 128915 816
0 9 S 18512 0
1 11 A 38649 160
0 8 S 125258 2974
0 9 A 26144 273
1 5 A 37840 1713
0 2 S 45653 301
0 2 A 38943 357
0 7 S 18952 1007
1 3 A 71880 93
1 11 A 27001 530
1 9 S 40486 161
1 7 A 68118 882
0 8 A 81926 1441
0 7 A 158370 5246
1 6 A 47032 1286
0 3 A 19680 0
0 5 S 8605 252
0 8 A 62166 6478
0 10 A 63344 2401
1 3 A 45463 1479
0 10 S 27515 470
1 5 S 45813 873
1 5 A 71266 4837

29PROBLEM ANALYSIS AND STATISTICS
1 2 A 7887 0
0 9 A 47060 434
0 8 S 92147 2247
1 6 A 20795 0
1 8 A 77790 461
0 10 A 20420 531
0 4 A 79781 15690
0 0 A 41642 261
0 9 A 4441 0
0 7 A 50389 2147
0 7 A 221574 226
1 10 S 5487 0
0 7 A 181363 20203
1 0 A 5315 1138
0 7 S 71794 10601
1 6 A 8797 1629
0 10 S 58678 6982
0 0 A -2 0
0 3 A 27628 0
1 7 S 40107 777
0 10 A 61559 608
1 11 S 17536 890
1 8 A 18441 140
0 7 A 51965 995
0 8 A 56584 648
0 6 A 4041 0
0 4 A 75725 0
1 6 A 65632 277
0 4 S 64924 305
1 6 A 29056 1523
1 8 A 10332 0
0 7 A 29747 136
0 9 S 48826 315
0 9 A 50545 2692
1 3 A 34565 2014
0 7 A 113663 9912
1 4 S 68129 1252
0 5 A 122313 6157
1 6 S 62278 4549
1 8 A 44121 202
0 10 A 30534 4931
0 6 S 39262 1697
1 7 A 35333 580
1 2 S 62252 179
0 3 A 80593 387
1 10 S 45464 328
0 4 A 32665 1065
0 3 A 290803 4475
0 2 S 1166 0
0 9 A 26096 278
1 4 S 68515 3382
1 9 A 51208 3465
1 6 A 75149 276
0 2 A 121512 1735
0 9 S 24795 3189
1 5 A 50557 2069
1 7 A 29656 10593
0 10 A 37617 0
1 6 A 53376 491
1 5 A 50655 2946
0 9 A 58176 4350
1 4 A 19275 111
0 9 A 73844 6523
0 6 A 85784 4807
1 3 A 39426 4149
1 7 A 37673 372
0 11 S 25245 259
0 6 A 70477 826
1 9 A 47334 435
1 8 A 27641 9704
0 3 A 85657 14488

30PROBLEM ANALYSIS AND STATISTICS
0 9 S 1032 4174
0 8 A 64731 814
1 8 S 89191 2066
1 3 A 39345 1049
0 1 S 35330 307
0 5 A 52805 708
1 4 S 39326 1468
1 7 A 133327 3071
1 0 A 37811 204
1 7 S 60810 290
0 7 A 80041 964
1 7 A 113341 4478
0 5 A 98670 1162
1 2 A 100931 7022
1 5 A 18171 0
0 10 S 23162 3939
0 6 A 84488 13526
1 1 S 403 0
0 3 S 111231 989
0 5 S 37128 6109
0 6 S 4345 229
1 8 S 14762 5112
1 4 A 26907 1045
0 5 A 110274 6455
0 0 A 22440 0
1 2 A 5383 0
1 10 A 16801 272
0 3 S 150473 0
1 4 A 55657 955
0 5 S 115375 1117
0 4 A 86698 7767
1 8 S 30920 1249
1 0 A 17748 0
1 7 A 931 0
0 10 A 27657 272
1 7 S 44986 1241
0 5 A 31855 0
0 6 S 84855 641
0 6 A 39142 5408
1 9 S 23226 1508
0 1 A 58408 525
1 9 S 18784 0
0 3 S 0 0
1 6 A 44428 741
0 9 A 123991 7289
0 5 A 110338 0
0 10 A 10952 0
1 8 A 51814 147
1 7 S 44026 3943
1 3 A 71714 2765
0 11 A 8483 0
0 10 S 45251 2266
0 7 S 40396 3944
1 5 A 81084 2045
1 7 A 62247 963
0 10 S 8764 0
0 3 A 136579 2696
0 7 A 133101 9797
1 4 A 131799 797
1 7 S 56009 6922
0 8 S 42032 149
1 2 S 35234 447
0 0 A 38413 894
0 10 S 15920 0
1 2 A 3003 119
0 7 A 40199 3064
1 6 A 27659 819
0 7 S 72725 33
0 9 S 38978 163
0 11 A 8529 0
0 5 A 124803 1483

31PROBLEM ANALYSIS AND STATISTICS
1 7 A 101910 6533
1 5 A 37726 971
0 6 A 18392 8
1 1 A 29686 339
0 5 A 74217 727
0 0 A 18502 181
1 10 A 51701 2052
0 1 A 28469 1104
1 7 A 46195 140
0 7 A 45739 8199
0 5 A 12136 92
Dataset 2:
Sample no. Country_name Lodgment_method
1 India A
2 Germany S
3 South Africa A
4 India S
5 Germany S
6 Netherland S
7 USA A
8 USA A
9 India S
10 UK A
11 HongKong S
12 Malaysia A
13 Germany A
14 Malaysia S
15 China A
16 China A
17 USA S
18 UK A
19 HongKong A
20 India S
21 Germany A
22 South Africa A
23 Netherland S
24 Malaysia A
25 Egypt S
26 India A
27 India A
28 India S
29 NewZealand A
30 India A
31 Egypt A
32 HongKong S
33 Egypt A
34 Germany S
35 USA S
36 USA A
37 Germany S
38 India A
39 Japan A
40 South Africa A
41 India A
42 South Africa S
43 Netherland A
44 HongKong S
45 UK A
46 USA A
47 USA S
48 NewZealand A
49 Egypt A
50 UAE S
51 India A
52 UAE S
53 Egypt A
54 HongKong A
55 China A
56 USA A
57 USA S

32PROBLEM ANALYSIS AND STATISTICS
58 China A
59 NewZealand A
60 Egypt A
61 HongKong A
62 India S
63 South Africa A
64 NewZealand A
65 Egypt S
66 China A
67 HongKong A
68 UAE S
69 Germany A
70 Germany A
71 NewZealand A
72 Japan S
73 HongKong A
74 India A
75 USA S
76 India A
77 UK A
78 India A
79 India A
80 USA S
81 UK A
82 HongKong A
83 China S
84 UK A
85 Germany A
86 Egypt A
87 Egypt A
88 UAE S
89 UAE A
90 NewZealand A
91 India S
92 India A
93 UK A
94 HongKong A
95 China S
96 India A
97 China A
98 UK A
99 Germany S
100 HongKong A
101 Germany A
102 China A
103 HongKong S
104 Germany A
105 UK A
106 UAE A
107 UK A
108 UAE A
109 Germany A
110 HongKong S
111 China A
112 Japan S
113 UAE A
114 Malaysia A
115 UK A
116 Malaysia A
117 HongKong S
118 India S
119 HongKong A
120 India A
121 India A
122 HongKong S
123 HongKong A
124 UK S
125 NewZealand A
126 India S
127 UAE A
128 Malaysia S

33PROBLEM ANALYSIS AND STATISTICS
129 China A
130 India S
131 Germany A
132 HongKong S
133 India A
134 NewZealand S
135 Netherland A
136 China S
137 Japan A
138 UAE S
139 Egypt A
140 USA S
141 USA A
142 Japan S
143 China A
144 India S
145 India A
146 USA A
147 Japan A
148 China A
149 UK A
150 Germany S
151 USA S
152 UAE A
153 USA A
154 USA A
155 India A
156 India S
157 NewZealand A
158 Netherland A
159 India A
160 NewZealand S
161 Germany A
162 China S
163 Japan S
164 China A
165 Japan A
166 India A
167 Germany A
168 HongKong A
169 Malaysia S
170 India A
171 India S
172 India A
173 Germany A
174 HongKong A
175 HongKong S
176 India S
177 India A
178 China A
179 India A
180 China A
181 HongKong A
182 Germany A
183 India S
184 Japan S
185 China A
186 NewZealand S
187 USA A
188 USA A
189 HongKong A
190 India A
191 Germany A
192 Netherland A
193 USA S
194 Netherland A
195 India A

34PROBLEM ANALYSIS AND STATISTICS