HI6007 Statistics and Research Assignment: Analysis and Findings

This assignment analyzes Australian export data from 2004-2015, comparing export destinations and values. It demonstrates statistical techniques by examining sales data, including frequency distributions, histograms, and ogive curves. The report also explores the relationship between retail turnover and final consumption expenditure using scatter plots, correlation coefficients, and linear regression models. Key findings include a strong positive correlation between retail turnover and final consumption, with detailed statistical outputs such as regression statistics, ANOVA, and hypothesis testing to validate the model. The analysis provides a comprehensive understanding of statistical methods and their application in business decision-making.

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STATISTICS AND RESEARCH
by Student’s Name
Code + Name of Course
Professor’s Name
University
City (State)
Date

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Question 1
a. Graphical comparison
b. Comparison by percentage
c. Observation
Australia’s economy just like other countries do depend on exports to advance its
economy and create employment to its citizens. In the period 2004-2005, Japan
was the main export destination for the Australian goods. Japan imported goods
and services worth $28.2 billion from Australia. This value represented around

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27% of all the goods and services moving from Australia to top 8 trading
partners. The graph in (a) gives a visual view of the quantity of goods moving
from Australia to the top 8 trading partners.
From the graph in (b) above, it can be observed that during the period 2014-
2015, China bypassed Japan to become the leading export destination for the
Australian goods and services. From just around 15% in 2004 China increased
its imports from Australia to bypass Japan as the favourite trading partner. The
trading from Australia to Japan moved from just 15% to around 40% of the total
exports to the top 8 trading partners. Also, it can be noted that apart from China
which increased its percentage volume of exports from Australia all the other 7
nations had a drop in the same. The actual value of exports does indicate that
goods moving from Australia to the 8 nations did increase from $ 103.3 billion in
2004 to $223.5 billion by 2015.
Question 2
a. Frequency, relative frequency, Cumulative frequency and relative frequency
distributions
Sales Range Frequency Relative Frequency Cumulative Freq Rel Cumulative Freq
30-40 2 5.00% 2 5.00%
40-50 4 10.00% 6 15.00%
50-60 8 20.00% 14 35.00%
60-70 11 27.50% 25 62.50%
70-80 8 20.00% 33 82.50%
80-90 5 12.50% 38 95.00%
90-100 2 5.00% 40 100.00%
Total 40
b. In the graph above
c. Histogram

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d. Ogive curve
e. Proportion of grades less than 60
Using the cumulative relative column in the table in (a), it can be observed that
35% of the days observed realized sales quantity of less than 60.
f. Proportion greater than 70
62.5% of all the day’s sales recorded were less than 70. This means only 37.5%
of the 40-day recorded sales volume greater than 70.

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Question 3
a. Graphical description of the data
b. Relationship description
So as to describe the relationship between two sets of data, the scatter plot is the
best graphical display. This plot allows for estimation of the line of best fir that
can describe the linear relationship between two data sets. In the graph below
the objective is to predict the values of the final consumption expenditure using
the data for the retail turnover capita.
The capita retain turnover is thus the independent variable (x) and final
consumption expenditure is the dependent variable (y).

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The data in the scatter plot are increasing from left to right. This is interpreted as
a positive correlation which implies that an increase in the retail turnover do have
an increasing impact on the values of the final consumption expenditure.
c. Numerical descriptive
Retail turnover
per capita
FINAL
CONSUMPTION
EXPENDITURE ($
million)
Mean 2205.762 Mean 146019.9
1st Quartile 1652.95 1st Quartile 103558.5
Median 2180.2 Median 139137
Mode 2852.8 Mode #N/A
Standard
Deviation 543.1939
Standard
Deviation 46904.33
Sample Variance 295059.6 Sample Variance 2.2E+09
3rd Quartile 192800.5 3rd Quartile 192800.5
Skewness 0.074658 Skewness 0.306831
Range 1558.7 Range 151259
Minimum 1455.9 Minimum 81889
Maximum 3014.6 Maximum 233148
Sum 288954.8 Sum 19128601
Count 131 Count 131
Largest(1) 3014.6 Largest(1) 233148
Smallest(1) 1455.9 Smallest(1) 81889
d. Coefficient of correlation

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The coefficient of correlation r between the retail turnover capita and the final
consumption expenditure is 0.987697. This value is interpreted as a strong
positive association. It can thus be explained that an increase in the values of the
retail expenditure do lead to an increase in the values of the final consumption.
The finding is similar to the scenario depicted by the scatter plot above.
e. Simple linear model
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.98769713
R Square 0.975545621
Adjusted R Square 0.975356052
Standard Error 7363.225229
Observations 131
ANOVA
df SS MS F Significance F
Regression 1 2.79008E+11 2.79E+11 5146.128864 7.9451E-106
Residual 129 6994004064 54217086
Total 130 2.86002E+11
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0%Upper 95.0%
Intercept -42102.53337 2700.165041 -15.5926 1.819E-31 -47444.87604 -36760.2 -47444.9 -36760.2
Retail turnover per capita85.28680912 1.188889626 71.73652 7.9451E-106 82.93456188 87.63906 82.93456 87.63906
From the simple linear model described by the figure below the equation
y=−42102.53+85.28 x best describes the relationship between the two variables.
The coefficient of x is 85.28 which means that an increase in the value of the
retail turnover by a single unit do lead to an increase in the final consumption by
$ 85 million.
f. R squared
The value of R squared for the two data sets is 0.9755. this value means that the
changes in the retail turnover capita are responsible for up to 97.55% of the
changes in the final consumption. It is a farther proof that the two variables have
a strong positive correlation.
g. Hypothesis testing
To test whether the coefficient of retail turnover value is significant, we use the
coefficient p_value at a 95% level of significance. The test is one sided as the
research is only interested on the values greater than zero. Since the p_value is
less than 0.025, the conclusion is that the final consumption does increase
significantly should the values of retail turnover go up.
h. The value of the standard error of estimate is read from the regression model as
1.1889. To check the fitness of the model we apply the value of the significance
F. Being that the value is less than 0.05, the conclusion is that the regression
model is significant in predicting the final consumption given the retail turnover.

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References
BIBLIOGRAPHY Montgomery, D., 2009. Design and analysis of experiments. , Hoboken, N.J.: Wiley.
Rencher, A. C. & Christensen, W. F., 2012. Methods of Multivariate Analysis; Wiley
Series in Probability and Statistics. 3rd ed. s.l.:John Wiley & Sons.