Analyzing Export Markets and Umbrella Sales

This document analyzes the export markets for goods and services in Australia and the sales of umbrellas. It includes comparative analysis, frequency distribution, cumulative frequency distribution, and more.

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Business Decision Making

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Answer 1
(a) A comparative analysis with a clustered bar chart has been presented in Figure 1
(Jelen, 2010). Export market figures of goods and services from Australia to other
countries have been compared between two time periods, 2004-05 and 2014-15.
Export to China is noted to have increased heavily in 2014-15 from 2004-05.
China Japan United
States Republic of
Korea India New
Zealand Singapore United
Kingdom
0
10
20
30
40
50
60
70
80
90
100
A Comparitive Export Market Figure for Goods and Services for
Australia
Exports (AUS $ Billion)
Figure 1: Export Markets for Goods and Services for Australia in 2004-05 and 2014-15
(b) Yet again, a comparative analysis with a clustered bar chart has been presented in
Figure 2 with percentage of exports. Export market figures of goods and services from
Australia to other countries have been compared between two time periods, 2004-05
and 2014-15. Export to China is noted to have increased so heavily in 2014-15 from
2004-05 that it has reduced percentage increase in exports to other 7 countries.

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China Japan United
States Republic of
Korea India New
Zealand Singapore United
Kingdom
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
A Comparitive Figure for Percentage of Exports by Country of
Destination
Percentage (%)
Figure 2: Percentage of Australian Exports of goods and services by Country in 2004-05 and 2014-15
(c) Exports to seven countries, with the exception of exports to the United Kingdom,
increased. Compared to 2004-05, exports to the UK declined in 2014-15. The
distribution of export allocations to the countries shows the real situation with regard to
the relative growth of exports by the countries. The total value of exports increased in
2014-15. Compared to 2004-05, percentage growth in exports to countries increased in
2014-15. However, export growth has declined to other seven countries due to strong
growth in Chinese exports.

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a. Frequency distribution of Umbrella Sales:
Table 1: Frequency distribution of Umbrella Sales of the store
Class Lower Class
Limit
Upper
Class
Limit
Frequency
30-40 30 40 2
40-50 40 50 4
50-60 50 60 8
60-70 60 70 11
70-80 70 80 8
80-90 80 90 5
90-
100 90 100 2
Relative frequency distribution of Umbrella Sales:
Table 2: Relative Frequency distribution of Umbrella Sales of the store
Class Lower Class
Limit
Upper
Class
Limit
Frequency Relative Frequency
30-40 30 40 2 0.05
40-50 40 50 4 0.10
50-60 50 60 8 0.20
60-70 60 70 11 0.28
70-80 70 80 8 0.20
80-90 80 90 5 0.13
90-100 90 100 2 0.05
b. Cumulative frequency distribution of Umbrella Sales:
Table 3: Cumulative Frequency distribution of Umbrella Sales of the store
Class Lower Limit Upper Limit Frequency Cumulative Frequency
30-40 30 40 2 2
40-50 40 50 4 6
50-60 50 60 8 14
60-70 60 70 11 25
70-80 70 80 8 33
80-90 80 90 5 38
90-
100 90 100 2 40

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Cumulative relative frequency distribution of Umbrella Sales:
Table 4: Cumulative Relative Frequency distribution of Umbrella Sales of the store
Class Lower
Limit
Upper
Limit
Frequen
cy
Relative
Frequency
Cumulative Relative
Frequency
30-40 30 40 2 0.05 0.05
40-50 40 50 4 0.10 0.15
50-60 50 60 8 0.20 0.35
60-70 60 70 11 0.28 0.625
70-80 70 80 8 0.20 0.825
80-90 80 90 5 0.13 0.95
90-
100 90 100 2 0.05 1
c. Relative frequency histogram of Umbrella Sales:
30-40 40-50 50-60 60-70 70-80 80-90 90-100
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.05
0.10
0.20
0.28
0.20
0.13
0.05
Relative Frequency Histogram for Umbrella Sales
Umbrella Sales per Day
Relative Frequency
Figure 3: Histogram of Umbrella Sales of the store
d. Less than type Ogive from the cumulative frequency of Umbrella Sales:

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20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
0
5
10
15
20
25
30
35
40
45
Less than type Ogive for Umbrela Sales
Less than Cumulative Frequency
Figure 4: Less than type Ogive for Umbrella Sales of the store
e. From Table 4, it can be identified that in 35% number of day’s umbrella sales was less
than 60 per day. The proportion of umbrella sales less than 60 was 0.35. Hence,
proportion of grades less than 60 is 35% (Remenyi, Onofrei and English, 2011, pp.13-
35).
f. From Table 4, it can be identified that Cumulative Relative Frequency for umbrella sales
less than 70 per day is 0.625. Therefore, the proportion of umbrella sales more than 70
is 0.375. Hence, proportion of grades more than 70 is 37.5%.

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a. An area plot has been used in Figure 5 to describe the trend of Retail Turnover per
Capita ($) from September 1983 to November 2014. A boxplot was drawn in Figure 6
to evaluate the descriptive measure of Retail Turnover per Capita ($).
From the area plot a sharp quarterly increasing trend is noted. Growth in final few
quarters was very high. Boxplot reveals that Median was approximately $ 2200 with a
variation of mid 50% turnover from approximately $ 1650 to $ 2800. Top 25% Retail
Turnover per Capita ($) was noted to be approximately above $ 3000 (Krzywinski and
Altman, 2014, pp.119-120).
Sep-1983
Jan-1985
May-1986
Sep-1987
Jan-1989
May-1990
Sep-1991
Jan-1993
May-1994
Sep-1995
Jan-1997
May-1998
Sep-1999
Jan-2001
May-2002
Sep-2003
Jan-2005
May-2006
Sep-2007
Jan-2009
May-2010
Sep-2011
Jan-2013
May-2014
Sep-2015
1000.0
1500.0
2000.0
2500.0
3000.0
3500.0
Time Series of Retail Turnover per Capita ($)
Time Period (Quarterly)
Retail Turnover per Capita ($)
Figure 5: Area Plot for Retail Turnover per Capita ($)
Retail turnover per capita Boxplot
500.0
1000.0
1500.0
2000.0
2500.0
3000.0
3500.0
Boxplot of Retail Turnover
Retail Turnover per Capita ($)
Figure 6: Boxplot of Retail Turnover per Capita ($)
An area plot has been used in Figure 7 to describe the trend of Final Consumption
Expenditure ($ Millions) from September 1983 to November 2014. A boxplot was

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drawn in Figure 8 to evaluate the descriptive measure of Final Consumption
Expenditure ($ Millions).
From the area plot a sharp quarterly increasing trend is noted. Boxplot reveals that
Median was approximately 140000 ($ Million) with a variation of mid 50%
Consumption Expenditure from approximately 103500 ($ Million) to 193000 ($
Million). Top 25% ($ Million) was noted to be approximately above $ 230000 ($
Million).
Sep-1983
Jan-1985
May-1986
Sep-1987
Jan-1989
May-1990
Sep-1991
Jan-1993
May-1994
Sep-1995
Jan-1997
May-1998
Sep-1999
Jan-2001
May-2002
Sep-2003
Jan-2005
May-2006
Sep-2007
Jan-2009
May-2010
Sep-2011
Jan-2013
May-2014
Sep-2015
50000
70000
90000
110000
130000
150000
170000
190000
210000
230000
250000
Time Series Plot for Final Consumption Expenditure ($ Million)
Time Period (Quarterly)
Final Consumption Expenditure ($ Millions)
Figure 7: Area Plot for Final Consumption Expenditure ($ Millions)
FINAL CONSUMPTION EXPENDITURE Boxplot
50000.0
70000.0
90000.0
110000.0
130000.0
150000.0
170000.0
190000.0
210000.0
230000.0
250000.0
Boxplot of Final Consumption Expenditure
Final Consumption Expenditure ($ Million)
Figure 8: Boxplot of Final Consumption Expenditure ($ Millions)
b. In order to explore the Retail Turnover per Capita towards the impact on Final
Consumption, a two-way scatterplot was created in Figure 9. There was a very high
positive and possibly significant linear relationship between these two factors.
Retail Turnover per Capita was considered as independent (X-axis) and Final
Consumption as the dependent (Y-axis) variables. Retail Turnover per Capita is an

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essential part of consumer spending, and the choice of the predictor was based on
this information (Pesaran and Pesaran, 2009).
1000.0 1500.0 2000.0 2500.0 3000.0 3500.0
5000
55000
105000
155000
205000
255000
Final Consumption Expenditure($ Million)on Retail Turnover per Capita ($)
Retail Turnover per Capita ($)
Final Consumption Expenditure ($ Millions)
Figure 9: Scatter plot for Final Consumption Expenditure ($ Million) on Retail Turnover per Capita ($)
c. Average Retail turnover per capita ($) was calculated as $ 2205.76 with a SD of $
543.19. Retail turnover varied between $ 1455.9 and $ 3014.6. Median of Retail
turnover per capita ($) was $ 2180.2. Highest 25% turnovers per capita were above $
2793.4. Lowest 25% turnovers per capita were below $ 1652.95.
Average Final Consumption Expenditure ($ Millions) was 146019.85 ($ Millions) with a
SD of $ 46904.33 ($ Millions). Final Consumption Expenditure varied between 81889 ($
Millions) and 233148 ($ Millions). Median of Final Consumption Expenditure ($ Millions)

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was 139137 ($ Millions). Highest 25% Final Consumption Expenditure were above
192800.5 ($ Millions). Lowest 25% Final Consumption Expenditure were below
103558.5 ($ Millions).
Table 5: Numerical Summary report tabular form
d. Pearson’s correlation Coefficient between Retail was used to assess the association
between Retail turnover per capita and Final Consumption Expenditure. Almost perfect
positive correlation coefficient ( r2=0 . 99 ) was evaluated between the factors. Final
Consumption Expenditure is noted to increase in same proportion with Retail Turnover
per Capita.
e. A simple linear regression model estimated Final Consumption Expenditure on Retail
Turnover per Capita. Regression equation was evaluated as,
Final Consumption Expenditure=-42102. 53+85 . 29*Retail Turnover per Capita .
Coefficient of regression β=85 . 29 ( t=71. 74 , p<0 . 05 ) for Retail Turnover per Capita was
noted to be statistically significant. Final Consumption Expenditure is expected to
increase by 85.29 million dollars for one dollar increase in Retail Turnover per Capita.
The model was noted to be statistically significant ( F=5146 .13 , p<0 . 05 ) .

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Table 6: Linear Regression for Final Consumption Expenditure on Retail Turnover per Capita
f. Coefficient of determination was R2=0 . 976 , implying Retail Turnover per Capita was
able to explain 97.6% variation of Final Consumption Expenditure. The value of
Coefficient of determination implied that Retail Turnover per Capita was a very strong
predictor of Final Consumption Expenditure (Renaud, and Victoria-Feser, 2010,
pp.1852-1862).
g. A hypothesis test was executed for scrutinizing linearity of Retail Turnover per Capita
had a positive and significant impact on Final Consumption at 5% significance level.
i. H 0: ( β =0 ) : Retail Turnover per Capita had no linear association with Final
Consumption Expenditure.
ii. HA : ( β≥0 ) Retail Turnover per Capita had a positive and significant linear
association with Final Consumption Expenditure.
iii. Significance level: 5%
iv. Test statistic: t=71. 74 with p<0 . 05
v. Decision: Null hypothesis is rejected based on the p-value.
vi. Conclusion: Retail Turnover per Capita had a positive and significant linear
association with Final Consumption Expenditure.
h. Standard error of the estimate was noted as SE=1 .19 .
In this context, the regression model describes a strong linear relationship between the
predictor and the outcome factors.
The intensity of the linear relationship was confirmed by the Coefficient of determination
R2=0 . 976 , where the adjusted R2=0 . 975 .
The ANOVA model proved to be statistically significant ( F=5146 .13 , p<0 . 05 ) .
From the residual plot a heteroscedasticity problem can be noted. Otherwise, we can
conclude that the linear regression model was very strongly fitted (Lee, 2012, pp.329-
340).

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1455.91664.12186.32810.5
0
50000
100000
150000
200000
250000
Line Fit Plot
$ Millions
Predicted $ Millions
Retail Turnover per Capita ($)
$ Millions
Figure 10: Line fit plot from regression output
1000.0 1500.0 2000.0 2500.0 3000.0 3500.0
-20000.00
-10000.00
0.00
10000.00
20000.00
30000.00
Residual Plot
Retail Turnover per Capita ($)
Residuals
Figure 11: Residual plot for Retail Turnover per Capita
References
Jelen, B. (2010). Charts and graphs for Microsoft Excel 2010. 1st ed. Indianapolis, Ind.:
Que.
Krzywinski, M. and Altman, N. (2014). Visualizing samples with box plots. Nature Methods,
11(2), pp.119-120.
Lee, A. (2012). Linear Regression Analysis. 2nd ed. New Jersey: Wiley, pp.329-340.
Pesaran, B. and Pesaran, M. (2009). Time series econometrics. New York, USA: Oxford
University Press.
Remenyi, D., Onofrei, G. and English, J. (2011). An Introduction to Statistics using
Microsoft Excel. 1st ed. UK: Academic Conferences Publishing International, pp.13-35.
Renaud, O. and Victoria-Feser, M.P., 2010. A robust coefficient of determination for
regression. Journal of Statistical Planning and Inference, 140(7), pp.1852-1862.