Analysis Of Tax Return Lodgement Method In Australia

Dataset 1

In Australia, many people require to lodge a tax return after the end of the financial year. Australians could prepare and lodge a own tax return or pay a registered tax agent to do it for themselves. By utilising a subset of the sample-file from the Australian Taxation Office (ATO), we are summarising and analysing several hidden facts of lodgement method.

The report is constructed by elaboration of two datasets. The first dataset has five variables that are Gender, age_range, Lodgement_method, Tot_inc_amt and Tot_ded_amt. We are eager to know the proportion of people who lodge a tax return utilizing a tax agent. We are also eager to see the difference among the age groups according to their lodging group. We are investigating whether there is an association between total income and lodgement method or not. Lastly, we are testing whether there is a relationship between total income and deduction amount or not.

A tax agent to lodge a tax return in the future structures the second dataset.  The dataset 2 is a collection of preference of international students of tax return lodgement method.

The samples of dataset1 are secondary in nature. We collected the data from internet sources. In dataset1, Gender is a factorised qualitative data, age_range is the ordinal variable, Lodgement_method is the nominal variable, Tot_inc_amt and Tot_inc_amt are the numeric variables.

The samples of dataset2 are primary in nature. We gather the data by survey method.  In dataset2, we took into account only quantitative dataset that is actually lodgement method. The data is collected by survey method. Our target population was 200 students, among which 30 students incurred to respond. The remaining 170 students responded about the question of sample survey method. The data sampling method is simple random sampling without replacement that is unbiased. However, we eliminated missing data. Therefore, bias may arise. The dataset contains two variables that are country_name and Lodgment_method. Lodgement method is nominal data necessary for this analysis.

Lodgment	Frequency	Proportion
Agent	732	0.732
Self	268	0.268
Total	1000	1

The frequency table in dataset 1 indicates that among 1000 people 732 people (73.2%) make their lodgment by Agents. Only 268 people (26.8%) make their lodgment by self-preparation.

The pie chart indicates the share of two types of lodgment methods that are agent and self in dataset 1.

One sample proportional Z-test
proportion (p) =		0.732
(1-p) =		0.268
total sample =		1000
standard error =		0.014006
confidence limit =		95%
z-value at 0.05 critical region =		1.96
Confidence Intervals
upper confidence interval =		0.759452
lower confidence interval =		0.704548

We apply one sample proportional z-test for testing the proportion of lodging method as agent. The actual proportion of lodging method as agent is 0.732. The calculated confidence intervals of proportion of lodging method as agent are 0.704548 and 0.759452 at 95% confidence limit. That means, there is 95% probability of being the proportion of lodging method via agent between these two intervals.

Lodgment	Frequency	Proportion
Agent	118	0.694117647
Self	52	0.305882353
Total	170	1

Dataset 2

The frequency table in dataset 1 indicates that among 170 people 118 people (69.4%) make their lodgment by Agents. Only 52 people (30.6%) make their lodgment by self-preparation.

The pie chart indicates the share of two types of lodgment methods that are agent and self in dataset 2.

One sample proportional Z-test
proportion (p) =		0.694117647
(1-p) =		0.305882353
total sample =		170
standard error =		0.035340224
confidence limit =		95%
z-value at 0.05 critical region =		1.959963985
Confidence Intervals
upper confidence interval =		0.763383213
lower confidence interval =		0.624852081

We apply one sample proportional z-test for testing the proportion of lodging method as agent in dataset 2. The actual proportion of lodging method as agent is 0.694117647. The calculated confidence intervals of proportion of lodging method as agent are 0.624852081 and 0.763383213. That means there is 95% probability of being the proportion of lodging method via agent between these two intervals in dataset 2.

The first dataset has greater sample that surveyed dataset (1000>170). In the first dataset, among 1000 people 732 people (73.2%) make their lodging by agent. Whereas, in the second dataset, among 170 people 118 people (more than 69.4%) make their lodging by agent. The survey result gives lesser percentage of lodging. We apply two samples proportional z-test of equality of proportions.

Null hypothesis:	The proportions are equal for both the datasets.
Alternative hypothesis:	The proportions are unequal for both the datasets.
	Two sample z-test
dataset 1	total sample	1000
	lodging by agent	732
	proportion (p1bar)	0.732
dataset 2	total sample	170
	lodging by agent	118
	proportion (p2bar)	0.694117647
	total sample	1170
	total lodging by agent	850
	total proprtion (p-bar)	0.726495726
numerator of z-statistic	(p1bar – p2bar)	0.037882353
	pbar* (1-pbar)	0.198699686
	propotion*sample	0.001367521
denominator of z-statistic	SQRT(proprtion*sample)	0.036980013
z-statistic		1.024400745
p-value		0.15386
Decision-making		Null hypothesis accepted

We apply two samples z-test for testing the equality of means. The calculated z-statistic is 1.024400745. According to the calculated p-value, we accept the null hypothesis at 95% confidence interval. Therefore, there is 95% probability of being the proportions of two datasets equal.

Correlation Coefficient

	age_range	Lodgment_method
age_range	1
Lodgment_method	0.108090763	1

The Pearson correlation coefficient is 0.108090763. Therefore, the correlation coefficient between age range and lodgment method is insignificant and ignorable. The amount of age range and lodgment method is uncorrelated to each other. For calculating the correlation coefficient, we leveled “agent” as 1 and “self” as 2 for making qualitative variable quantitative variable.

Lodging Method is Self:

Numerical Summary

age_range
Mean	6.395522388
Standard Error	0.21041402
Median	7
Mode	9
Standard Deviation	3.444625965
Sample Variance	11.86544804
Kurtosis	-1.00656719
Skewness	-0.490030757
Range	11
Minimum	0
Maximum	11
Sum	1714
Count	268
Largest	11
Smallest	0
Confidence Level (95.0%)	0.414281758
upper control limit	6.807933867
lower control limit	5.983110909

The age range of “Self” lodging method has the 95% probability of being in the interval 6.807933867 and 5.983110909.

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	24	24	8.96%	8.96%
1	9	33	3.36%	12.31%
2	16	49	5.97%	18.28%
3	18	67	6.72%	25.00%
4	13	80	4.85%	29.85%
5	16	96	5.97%	35.82%
6	26	122	9.70%	45.52%
7	18	140	6.72%	52.24%
8	26	166	9.70%	61.94%
9	44	210	16.42%	78.36%
10	37	247	13.81%	92.16%
11	21	268	7.84%	100.00%
total	268		1

The frequency is maximum for age group number “9” and minimum for age group number “1”.

The percentage of frequency is maximum for age group number “9” and minimum for age group number “1”.

Lodging Method is Agent:

Numerical Summary

age_range
Mean	5.640710383
Standard Error	0.108390312
Median	6
Mode	7
Standard Deviation	2.932553929
Sample Variance	8.599872545
Kurtosis	-0.923068312
Skewness	-0.150394186
Range	11
Minimum	0
Maximum	11
Sum	4129
Count	732
Largest	11
Smallest	0
Confidence Level (95.0%)	0.212793429
upper control limit	5.853155394
limit control limit	5.428265371

The age range of “agent” lodging method has the 95% probability of being in the interval 5.853155394 and 5.428265371.

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	38	38	5.19%	5.19%
1	31	69	4.23%	9.43%
2	49	118	6.69%	16.12%
3	77	195	10.52%	26.64%
4	76	271	10.38%	37.02%
5	74	345	10.11%	47.13%
6	75	420	10.25%	57.38%
7	88	508	12.02%	69.40%
8	78	586	10.66%	80.05%
9	71	657	9.70%	89.75%
10	59	716	8.06%	97.81%
11	16	732	2.19%	100.00%
total	732		100.000000%

The frequency is maximum for age group number “7” and minimum for age group number “11”.

Lodgement Method-Dataset 1

The percentage of frequency is maximum for age group number “7” and minimum for age group number “11”.

	95% confidence interval of correlation coefficient
Pearson Correlation Coefficient ( r )	0.108090763
Z’	0.108514702
Number of samples (N)	1000
Standard Error [1/SQRT(N-3)]	0.031670318
Z(0.05,997)	1.96
Confidence intervals
Lower limit of Z’	0.046440879
Upper limit of Z’	0.170588525
Lower limit of r	0.046407521
Upper limit of r	0.168952828

The leveled age group and lodging method has correlation coefficient (0.108090763). The two factors are uncorrelated at 95% confidence intervals also as the lower and upper limits of correlation coefficients are respectively (0.046407521) and (0.168952828).

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.108090763
R Square	0.011683613
Adjusted R Square	0.010693316
Standard Error	0.440763543
Observations	1000
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.292044456	2.292044	11.79809	0.000617314
Residual	998	193.8839555	0.194273
Total	999	196.176
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.177557148	0.029792573	39.52519	2.2E-206	1.119093878	1.236020418
age_range	0.015478838	0.004506429	3.434835	0.000617	0.006635676	0.024322001

The value of multiple R-square is 0.011683613. Calculated F-statistic is 11.79809. These two variables are not highly associated with each other. The p-value 0.000617314 less than 0.05 interprets that these age range has insignificant relationship with lodgment method at 95% confidence interval.

The calculations of “part-a” and “part-b” indicate that the age range and Lodgment method of the 1000 people is uncorrelated. However, the histograms and frequency tables infer that agent more normally distributes the distribution of age group by self-preparation lodgment method than the distribution of age group.

	Lodgment_ method	Tot_inc_amt
Lodgment_method	1
Tot_inc_amt	-0.071848524	1

The Pearson correlation coefficient is (-0.071848524). Therefore, the correlation coefficient between amount of total income and lodgment method is insignificant and ignorable. The amount of total income and lodgment method are uncorrelated. For calculating the correlation coefficient, we leveled “agent” as 1 and “self” as 2 for making qualitative variable quantitative variable.

Tot_inc_amt
Mean	66423.89
Standard Error	4119.671
Median	48222.5
Mode	0
Standard Deviation	111459.8
Sample Variance	1.24E+10
Kurtosis	114.1994
Skewness	9.494428
Range	1693122
Minimum	-37
Maximum	1693085
Sum	48622288
Count	732
Largest	1693085
Smallest	-37
Confidence Level (95.0%)	8087.799
Upper confidence limit	74498.45
Lower confidence limit	58349.33

For the lodgment method “agent”, the average amount of total amount income is $66423.89. The 95% confidence limit for total amount of income is ranges between $74498.45 and $58349.33.

The line plot of Total Income Amount of income for the people whose lodgment method is agent

Tot_inc_amt
Mean	49783.85448
Standard Error	4402.27677
Median	35804
Mode	0
Standard Deviation	72068.37673
Sample Variance	5193850924
Kurtosis	83.48626709
Skewness	7.591961655
Range	924342
Minimum	0
Maximum	924342
Sum	13342073
Count	268
Largest	924342
Smallest	0
Confidence Level (95.0%)	8667.592386
Upper confidence limit	58412.31695
Lower confidence limit	41155.39201

For the lodgment method “agent”, the average amount of total amount income is $49783.85448. The 95% confidence limit for total amount of income is ranges between $58412.31695 and $41155.39201.

The line plot of Total Income Amount of income for the people whose lodgment method is self

	95% confidence interval of correlation coefficient
Pearson Correlation Coefficient ( r )	-0.071848524
Z’	-0.071972541
Number of samples (N)	1000
Standard Error [1/SQRT(N-3)]	0.031670318
Z(0.05,997)	1.96
Confidence intervals
Lower limit of Z’	-0.134046363
Upper limit of Z’	-0.009898718
Lower limit of r	-0.133249225
Upper limit of r	-0.009898394

The Pearson correlation coefficient between total amount of income and lodgment methods is (-0.071848524). Therefore, these two factors are uncorrelated.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.071848524
R Square	0.00516221
Adjusted R Square	0.004165379
Standard Error	0.44221534
Observations	1000
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.012701781	1.012702	5.178619	0.023077745
Residual	998	195.1632982	0.195554
Total	999	196.176
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.287223099	0.016337405	78.78994	0	1.255163494	1.319282704
Tot_inc_amt	-3.10228E-07	1.36325E-07	-2.27566	0.023078	-5.77744E-07	-4.27124E-08

The value of multiple R-square (0.00516221) indicates that the association of these two factors is insignificant.

The box plot indicates the distribution of total amount of income. Its spread is very high. However, the quartiles are below $200000.

Tot_amt_inc via agent
Minimum	-37
Maximum	1693085
1st Quartile	26618.25
2nd Quartile (Median)	48222.5
3rd Quartile	76060.75
Bottom	26618.25
2q Box	21604.25
3q Box	27838.25
Whisker-	26655.25
Whisker+	1617024.25
IQR	49442.5
Upper bound	150224.5
Lower bound	-47545.5

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 $(-37), $26618.25, $4822.5, $76060.75 and $1693085.

Tot_amt_inc by self preparation
Minimum	0
Maximum	924342
1st Quartile	15774
2nd Quartile (Median)	35804
3rd Quartile	65176.5
Bottom	15774
2q Box	20030
3q Box	29372.5
Whisker-	15774
Whisker+	859165.5
IQR	49402.5
Upper bound	139280.25
Lower bound	-58329.75

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 $0, $15774, $35804, $65176.5 and $924342. Inter-quartile range is higher for total amount of income by self-preparation.

Tot_amt_inc
Minimum	-37
Maximum	1693085
1st Quartile	23521.75
2nd Quartile (Median)	45840
3rd Quartile	74404
Bottom	23521.75
2q Box	22318.25
3q Box	28564
Whisker-	23558.75
Whisker+	1618681
IQR	50882.25
Upper bound	150727.375
Lower bound	-52801.625

Lodgement Method-Dataset2

The “five point summary” indicates the distribution of amount of total income. The minimum, first quartile, second quartile, third quartile and maximum of the amount of income are $(-37), $23521.75, $45840, $74404 and $1693085.

The box plot of distribution of total amount of income indicates 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 $200000.  

The grouped box plot of total amount of income refers 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. The maximum amount of income is significantly greater in case of agent than self-preparation.

The calculated number of Outliers for total income by both the lodging method is 49, the outliers for total income by lodging method via agent is 39 and the outliers for total income by lodging method via self preparation is 12. The percentages of outliers in all the three cases are 4.9%, 5.32787% and 4.4776%. The number of outliers for total income by lodging method via agent is maximum in percentage.

For both the self and agent lodging method:

	Tot_inc_amt	Tot_ded_amt
Tot_inc_amt	1
Tot_ded_amt	0.433918351	1

Linear Regression between amount of total income and amount of total deduction for the people whose lodging method is agent:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.433918351
R Square	0.188285136
Adjusted R Square	0.187471794
Standard Error	7680.455019
Observations	1000
ANOVA
	df	SS	MS	F	Significance F
Regression	1	13655794661	1.37E+10	231.4958	3.59212E-47
Residual	998	58871410515	58989389
Total	999	72527205176
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	415.2418564	283.7502247	1.463406	0.143671	-141.5736382	972.057351
Tot_inc_amt	0.036024597	0.002367705	15.21499	3.59E-47	0.031378346	0.040670848

The residual scatter plot of total income amount vs. total deduction amount for the people whose lodgment method is agent

Correlation Coefficient
	Tot_inc_amt	Tot_ded_amt
Tot_inc_amt	1
Tot_ded_amt	0.428452411	1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.428452411
R Square	0.183571469
Adjusted R Square	0.180502188
Standard Error	9173.929557
Observations	268
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5033608656	5033608656	59.80929	2.16458E-13
Residual	266	22386821614	84160983.51
Total	267	27420430271
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1240.313957	681.5035713	-1.819966922	0.069888	-2582.141512	101.5135984
Tot_inc_amt	0.060247545	0.007790315	7.733646607	2.16E-13	0.04490902	0.07558607

The residual scatter plot of total income amount vs. total deduction amount for the people whose lodgment method is self

Correlation Coefficient
	Tot_inc_amt	Tot_ded_amt
Tot_inc_amt	1
Tot_ded_amt	0.457006824	1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.457006824
R Square	0.208855238
Adjusted R Square	0.207771478
Standard Error	6969.341502
Observations	732
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9360429247	9.36E+09	192.7136	4.6926E-39
Residual	730	35457356312	48571721
Total	731	44817785560
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	840.2284205	299.9216382	2.801493	0.005221	251.416582	1429.040259
Tot_inc_amt	0.032104882	0.002312677	13.88213	4.69E-39	0.02756459	0.036645172The residual scatter plot of total income amount vs. total deduction amount for both kind of lodgment method

1. All people: The Pearson correlation coefficient ( r ) of total income amount and total deduction amount of all the 1000 samples is 0.433918351. Therefore, we can tell that there exists a moderate positive correlation between these two factors.
2. Self-lodgmaent method: The Pearson correlation coefficient between total income amount and total deduction amount for those people whose lodgment is self, is calculated as 0.428452411. We can say that there exists a moderate positive correlation between these factors for the particular lodgment.
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 457006824. We can say that there exists a moderate positive correlation between these factors for the particular lodgment. The correlation is highest for lodgment method via agent.

1. People whose lodgment method is 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 equation of the model is- Y = β₀ + β₁ * X.

We can write, Tot_ded_amount = 415.2418564 – 0.036024597* Tot_inc_amt.

The value of multiple R-square (coefficient of determination) is 0.188285136. Therefore, only 18.82% variability of house price is described by total deduction amount (Faraway 2016). The linear association of these two factors is not significant. The value of F-statistic is 231.4958. The p-value of the model is 3.59212E-47. It is less than 0.05. Therefore, we reject the null hypothesis at 95% confidence interval. According to the slope of predictor (β₁ = 0.036024597), we can state that amount of total income is positively associated with total deduction amount. Therefore, we can conclude that amount of total income is greater than amount of total deduction. The graph showed that the fitting is not also good.

1. People whose lodgment method is 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.

Two Sample Proportional Z-Test

The linear regression equation of the model is- Y = β₀ + β₁ * X.

We can write, Tot_ded_amount = -1240.313957- 0.060247545* Tot_inc_amt.

The value of multiple R-square (coefficient of determination) is 0.183571469. Therefore, only 18.35% variability of house price is described by total deduction amount (Faraway 2016). The linear association of these two factors is not significant. The value of F-statistic is 59.80929. The p-value of the model is 2.16458E-13. It is less than 0.05. Therefore, we reject the null hypothesis at 95% confidence interval. According to the slope of predictor (β₁ = 0.060247545), we can state that amount of total income is positively associated with total deduction amount. Therefore, we can conclude that amount of total income is greater than amount of total deduction. The graph showed that the fitting is not also good.

1. All people: 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 equation of the model is- Y = β₀ + β₁ * X.

We can write, Tot_ded_amount = 840.2284205 – 0.032104882* Tot_inc_amt.

The value of multiple R-square (coefficient of determination) is 0.208855238. Therefore, only 20.88% variability of house price is described by total deduction amount (Faraway 2016). The linear association of these two factors is insignificant. The value of F-statistic is 192.7136. The p-value of the model is 4.6926E-39. It is less than 0.05. Therefore, we reject the null hypothesis at 95% confidence interval. According to the slope of predictor (β₁ = 0.032104882), we can state that amount of total income is positively associated with total deduction amount. Therefore, we can conclude that amount of total income is greater than amount of total deduction. The graph showed that the fitting is not also good.

Conclusion

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 not also significantly associated and related with total deduction amount. The people whose lodgment is done by agents are more in count. They have higher maximum price and quartile prices. The spread of total income amount is high in case of agents than self-preparation lodgment.

We can add many other factors including qualitative and quantitative variables. The regression models might involve more predictors for the response. The model prediction would be more apprehensible. More samples could give the accurate result. The logistic model may provide further explanation about the dataset. The behavior of lodgment method can be described by gender distribution and total amount of income.

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