Holmes Institute HI6007 Statistics Assignment: T3 2019

This statistics assignment presents a comprehensive analysis of business data. It begins with a comparison of Australian food and fibre exports across different states for the years 2010 and 2015, utilizing charts to illustrate export values and percentage contributions. The assignment then delves into frequency distributions, constructing tables, histograms, and ogives to analyze data. Furthermore, it explores the relationship between the rate of inflation and the All-Ordinaries Index through descriptive statistics, correlation analysis, and a simple linear regression model. The regression analysis includes hypothesis testing, determination of the coefficient of determination, and an evaluation of the model's fit and significance. The assignment concludes with a discussion of the findings and relevant references.

Running head: STATISTICS FOR BUSINESS DECISIONS
Statistics for Business Decisions
Name of the Student:
Name of the University:
Author note:

1STATISTICS FOR BUSINESS DECISIONS
Answer 1
a)
Victoria Queensland NSW WA SA Tasmania Others
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
7,344
4,872 4,959 4,219 3,391
907 973
11,656
8,179
6,979 6,350
5,255
736
4,278
Australian Food and Fibre exports ($million)
Exports ($million) 2010 Exports ($million) 2015
b)
Victoria Queensland NSW WA SA Tasmania Others
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00% 27.54%
18.27% 18.60%
15.82%
12.72%
3.40% 3.65%
26.84%
18.83%
16.07% 14.62%
12.10%
1.69%
9.85%
Food and Fibre exports ($million, %)
2010 2015

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c) The above two charts show the comparison of Australian food and fibre exports in
million $ and in % for the years 2010 and 2015, broken down by the states. The graphs
show that the performance of food and fibre exports has been considerably good in
Victoria both in 2010 and 2015 in comparison to the other states. The first graph shows
considerable increase in the total value of exports from 2010 to 2015 for all the states.
The export value is highest for Victoria, followed by Queensland, NSW, WA, SA, and
Tasmania. Export value is slightly higher in others compared to Tasmania. The trend is
exactly similar for both the years 2010 and 2015.
The % export values show the contribution of these states in the total value of
exports of the food and fibre for 2010 and 2015. As the total value of exports is different,
hence, the percentage of contribution also differs significantly. This shows that in terms
of percentage value, the states performed better in 2010 than in 2015, as for all the states,
the % export values were higher in 2010 in comparison to the export percentage in 2015.

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Answer 2
(a) and (b)
Classes Frequency Relative
Frequency
Cumulative
Frequency
Cumulative
Relative
Frequency
0 - 4 4 0.1 4 0.100
5 - 9 9 0.225 13 0.325
10 - 14 7 0.175 20 0.500
15 - 19 11 0.275 31 0.775
20 - 24 2 0.05 33 0.825
25 - 29 5 0.125 38 0.950
30 - 34 2 0.05 40 1.000
Total 40 1 40 1
c) Relative frequency histogram

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0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34
0
0.05
0.1
0.15
0.2
0.25
0.3
Relative Frequency
d) Ogive for the data
0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34
0
5
10
15
20
25
30
35
40
45
Cumulative Frequency
e) Proportion of the data is less than 20:

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0.775 (obtained from cumulative relative frequency for data less than 20)
f) Proportion of the data is more than 24:
1 – 0.825 = 0.175 (obtained from cumulative relative frequency for data more than 24)

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Answer 3
a) Rate of inflation trend, 1995 – 2015
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Rate of Inflation (%)
All-Ordinaries Index trend, 1995 – 2015
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
All-Ordinaries index

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b) Plot depicting the relationship between Rate of Inflation (%) and All-Ordinaries Index
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
f(x) = 40.3077051702228 x + 3874.28641228011
R² = 0.00151127464405965
Relationship between Rate of Inflation (%) and All-
Ordinaries index
In this plot, Rate of Inflation (%) is the X variable, that is, independent variable, and All-
Ordinaries Index is the Y variable, that is, dependent variable. The variables are
presented accordingly in the plot. Since, All-Ordinaries Index is influenced by the Rate of
Inflation (%) in the economy, hence, the variables are chosen accordingly.

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c) Descriptive statistics (numerical summary report)
Rate of inflation (%) All-Ordinaries index
Mean 2.69 3982.73
Standard Error 0.26 269.99
Median 2.50 4127.60
Mode 2.4 #N/A
Standard
Deviation 1.19 1237.25
Sample Variance 1.42 1530783.22
Kurtosis 2.04 -1.01
Skewness 0.80 0.18
Range 5.6 4336.8
Minimum 0.3 2000.8
Maximum 5.9 6337.6
Sum 56.5 83637.4
Count 21 21
1st Quartile 2.4 3032
3rd Quartile 2.9 4933.5
d) Coefficient of correlation (r) between RATE OF INFLATION and ALL-ORDINARIES
INDEX
Rate of inflation (%) All-Ordinaries index
Rate of inflation (%) 1
All-Ordinaries index 0.0389 1
The value of the coefficient of correlation (r) between the Rate of Inflation and All-
Ordinaries Index is 0.0389, which is positive. The value of r ranges between -1 to +1.
Values closer to +1 indicate strong positive correlation between the variables, and values
closer to -1 indicate strong negative correlation. Zero indicates no correlation. Values

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closer to zero in either side imply a negligible or insignificant correlation (Akoglu 2018).
In this case, the value is positive, however, closer to zero. Thus, it implies Rate of
Inflation and All-Ordinaries Index are positively correlated, however, the magnitude of
relation is not much strong.
e) Simple linear regression model: Y = mX + C
In this case, Y (Dependent variable) = All-Ordinaries Index
X (Independent variable) = Rate of Inflation
and, C = Constant
The regression hypothesis is:
H0 (null hypothesis): Rate of Inflation does not have significant impact on the All-
Ordinaries Index.
H1 (alternate hypothesis): Rate of has significant impact on the All-Ordinaries Index.
Regression output is as follows:
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.0389
R Square 0.0015
Adjusted R Square -0.0510
Standard Error 1268.4304
Observations 21
ANOVA
df SS MS F
Significance
F
Regression 1 46268.68 46268.68 0.029 0.867
Residual 19 30569395.7 1608915.56

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3
Total 20
30615664.4
1
Coefficients
Standard
Error t Stat P-value
Intercept 3874.29 696.83 5.560 0.000
Rate of inflation (%) 40.31 237.69 0.170 0.867
f) Coefficient of determination (R2) = 0.0015
This determines the best fit of the independent variable to the linear regression model. In
other words, it describes how close the observations are to the fitted regression line
(Zhang 2017) and how best the model can determine variations in the data. In this case
the R2 value is 0.0015, which is very close to zero and as seen from the line plot in the
above figure, it is seen that the data are highly scattered and not much close to the fitted
regression line. The independent variable in this model cannot really much explain the
variance for the dependent variable. Hence, the model is not the best fit for understanding
the relation between the given variables.
g) At 5% level of significance, the value is 0.867. This is greater than the critical significant
value of 0.05. This indicates that the null hypothesis is accepted and the alternative
hypothesis is rejected. In other words, Rate of Inflation does not have significant impact
on the All-Ordinaries Index.
h) Standard error of the estimate (Se): 237.69

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Standard error of the estimate refers to the measure of prediction accuracy. It is the
difference between actual score and predicted score. Lower the value of the standard
error, higher is the precision of the model (Cleophas and Zwinderman 2016). In this case,
the value of standard error is positive and quite high. Thus, the precision of the model is
low, and as the R2 value is 0.0015, the model is not the best fit.