T1 2019 HI6007 Statistics and Research Methods for Business

This assignment presents a comprehensive solution to a statistics and research methods assignment (HI6007) from Holmes Institute. The solution addresses multiple questions, including an analysis of Australian export values, focusing on destination trends and changes over a ten-year period, visualized using a column chart. It also involves the analysis of umbrella sales using relative and cumulative frequency distributions, histograms, and ogives. Furthermore, the assignment delves into time series analysis, examining the relationship between retail turnover and final consumption expenditure using scatter plots, correlation coefficients, and regression models. The regression analysis includes interpretation of coefficients, the coefficient of determination, and hypothesis testing for the slope's significance. The assignment demonstrates an understanding of statistical techniques and their application in business decision-making, providing detailed interpretations and analyses of the given data.

STATISTICS
STUDENT iD:
[Pick the date]

Question 1
(a) Top 8 Australian export values by destination is presented using a column chart.
(b) Top 8 Australian export percentage
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(c) The biggest change during the ten period for which the graphs indicate export breakup is
the surge in share of China as a preferred destination for Australian exports. China has
managed to increase the exports from Australia manifolds and has emerged as the most
important export destination for Australia. Other countries barring United Kingdom (UK)
have also shown increase in exports from Australia during this period. Exports to New
Zealand however have been retained at the same level as seen in 2004-2005 which may
need to be further analysed.
Question 2
(a) Relative frequency for umbrellas sold
(b) Cumulative frequency distribution for umbrellas sold
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(c) Histogram frequency
(d) Ogive cumulative frequency
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(e) Umbrella sold proportion
(f) Umbrella sold proportion
Question 3
(a) Time series
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(b) Scatter display
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In the above scatter display, there are two variables with the variable on the X axis
(horizontal axis) acting as the independent variable whereas the variable on the Y axis
(vertical axis) acting as the dependent variable. The dependent variable (final consumption
expenditure) is impacted by the independent variable (retail turnover per capita).
(c) Summary table
(d) Correlation
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Interpretation: Correlation coefficient obtained through excel function is indicative of a
strong relationship (as magnitude exceeds 0.6) between the variables whereby it would be
expected that both variables would show movement in the same direction.
(e) Regression model
The two essential coefficients are as follows.
 Intercept –This value is -42102.53. This would denote the expected final consumption
expenditure in case retail turnover drops to zero. However, practical usage is not there
as value is negative.
 Slope- This value represents the rate of change in the final consumption expenditure
with changes in retail turnover per capita.. The change in the independent variable by
only $ 1 would bring corresponding change to the tune of $ 85.29 million in the
dependent variable.
(f) Coefficient of determination
R square = 0.9755
It highlights that the simple regression model is capable of explaining 97.55% of the variation
that is seen in the dependent variable (i.e. final consumption expenditure).
(g) Retail Turnover Per Capita slope significance ought to be tested.
Null Hypothesis: Owing to slope being insignificant, it may be assumed as zero.
Alternative Hypothesis: Owing to slope being significant, it cannot be assumed as zero.
The hypothesis test has been performed based on regression output and a summary of the
same is available in the table indicated below.
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(h) The standard error value is based on the regression output. This is highlighted below.
A low standard error would imply that the residuals value is small and the deviation between
predicted and actual value of dependent variables is less. This indicates a good fitting model
which is the case here as the standard error is small considering the given data.
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