Statistics and Research Methods for Business Decision Making - HI6007

This document presents a comprehensive solution to a statistics and research methods assignment, likely for a business decision-making course. The assignment covers a range of statistical techniques, including the analysis of Australian export data using column and pie charts to identify trends over time. It explores frequency distributions, histograms, and ogives to analyze umbrella sales data. Time series analysis and scatterplots are used to investigate relationships between retail turnover and final consumption expenditure, including descriptive statistics, correlation coefficients, and regression analysis. Hypothesis testing is performed to assess the significance of regression coefficients, and the model's goodness of fit is evaluated. The solution demonstrates the application of statistical methods to real-world business scenarios, supported by references to relevant academic literature.

Statistics and Research Methods for Business Decision Making
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Question 1
(a) Australia Direction Exports Values (Column chart)
(b) Australia Direction Exports Percentage (Pie chart)
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(c) The above graphical representation (both absolute value and percentage) highlight the
export break up from Australia to different countries (destinations). This representation
has been carried out for two years namely 2004-2005 and 2014-2015. Based on the
graphical representation above, certain key trends can be identified. The first trend relates
to the surge of China as the major export destination for Australian products. This is
apparent from the huge jump in share of exports which stood at only 15% in 2004-2005
but have increased to 40% in 2014-2015. Owing to rising share of China in the overall
exports from Australia, there is a decline in the shares of the other destinations as
exhibited from 2014-2015 graphical illustration. However, there is only one destination
namely UK where there has been a decline in absolute terms as the exports from Australia
to this country in 2014-2015 are lesser than the corresponding figure in 2004-2005. Yet
another interesting trend is the stagnation of exports from Australia to New Zealand
which has not seen any increase during the period under consideration.
Question 2
(a) The requisite frequency distribution for umbrella sold (Number of classes 10)
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(b) The requisite frequency distribution for umbrella sold (Number of classes 10)
(c) The histogram for relative frequency is shown as follows.
(d) The required Ogive
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(e) Let the proportion of umbrella sales lower than 60 is Po
Total number of umbrellas = 40
Number of umbrella sales lower than 60 = 14
Proportion Po = 14 / 40 = 0.35
(f) Let the proportion of umbrella sales greater than 70 is P1
Total number of umbrellas = 40
Number of umbrella sales greater than 70 = 15
Proportion P1 = 15 / 40 = 0.375
Question 3
(a) Time series
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(b) For the purposes of the given scatterplot, “Retail Turnover per capita” has been assumed
to be the independent variable and thereby represented on the x or horizontal axis. “Final
Consumption Expenditure” is the dependent variable which has been represented on the y
or vertical axis. The key reason behind the above choice is that the total expenditure on
consumption is essentially the function of per capita retail turnover.
(c) The relevant descriptive statistics for the given variables are summarised below.
(d) The coefficient of correlation
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The correlation coefficient estimated above has two aspects namely the magnitude and the
sign. For correlation coefficient, the maximum magnitude is one and the given correlation
coefficient seems quite close to the same which implies a very strong linear relationship
between the variables provided. Also, the sign is positive which implies that it would be
reasonable to expect that both variables would move in the same direction (Hastie, Tibshirani
and Friedman, 2014).
(e) The regression output as obtained from Excel is as exhibited below.
Based on the above output, the following is the equation of best fit line.
The relevant coefficients from the above model are interpreted below (Liebermann et. al.,
2015).
 Intercept- The intercept refers to the final consumption expenditure which is expected
when no retail turnover per capita exists. The negative value hints that this value lacks
practical utility.
 Slope– This highlights that a unit dollar alteration in per capita retail turnover would
bring about a change of $ 85.29 million in final consumption expenditure. The
changes for both variables would be in same direction.
(f) From regression output (R Square) = 0.9755
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The above value indicates that the 97.55% of the changes in the dependent variable (“Final
Consumption Expenditure”) in the given regression model can be accounted for by changes
in the independent variable (“Retail Turnover per capita”) (Fehr and Grossman, 2016).
(g) Claim to test: Slope (Retail turnover per capita) is statistically significant or not.
The relevant hypotheses are as highlighted below.
The relevant output from the regression result indicating the test statistic and p value is
shown below.
Significance level= 0.05
Observation: Significance level >> p value
Result: H0 is rejected while H1is accepted
Conclusion: The slope coefficient is significant and thereby cannot be assumed as zero
implying a significant linear relationship.
(h) Based on the regression output, the standard error has come out as 7363.225. For the
given data, this value is quite low which implies that the estimates provided by the
regression model tend to quite close to the actual values thereby minimising the residuals
or errors. Hence, it can be concluded that the given model presents an excellent fit
(Hastie, Tibshirani and Friedman, 2014).
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References
Fehr, F. H. and Grossman, G. (2016). An introduction to sets, probability and hypothesis
testing. 3rd ed. Ohio: Heath, pp. 225,252
Hastie, T., Tibshirani, R. and Friedman, J. (2014) The Elements of Statistical Learning. 4th
ed. New York: Springer Publications, pp. 189
Lieberman, F. J., Nag, B., Hiller, F.S. and Basu, P. (2015) Introduction To Operations
Research. 5th ed.New Delhi: Tata McGraw Hill Publishers, pp. 167, 198
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