The Assignment on Statistics For Business Decisions

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

1STATISTICS FOR BUSINESS DECISIONS
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................4
Answer 3..........................................................................................................................................6
References......................................................................................................................................13

2STATISTICS 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 by state ($million),
2010 and 2015
Exports ($million) 2015 Exports ($million) 2010
Figure 1: Australian Food and Fibre Exports ($million), 2010, 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%
Australia Food and fibre exports (%), 2010 and 2015
Export ($million, %), 2015 Export ($million, %), 2010

3STATISTICS FOR BUSINESS DECISIONS
Figure 2: Australian Food and Fibre Exports ($million, %), 2010, 2015
c) Figure 1 and 2 compares the total export value of the Australian Food and Fibre in
$million and in percentage values for 2010 and 2015 for each state of Australia and other
regions of Australia. Both bar graphs display that among all the Australian states,
Victoria has provided the maximum in the total export value in $million and in
percentage values as well. It is found from the Figure 1 that the total export value of food
and fibre for each of the states has increased substantially in 2015 than in 2010. The
growth in the value of export in $million has been consistent for all the Australian states
for both the years. All the states show export growth from 2010 to 2015. The regions
under ‘Others’ category have contributed higher than Tasmania.
Figure 2 displays shows the percentage contribution of all the Australian states in
the food and fibre exports for 2010 and 2015. In 2015, the total value of export was much
higher for all the states from that in 2010 and that has influenced the percentage value of
the contribution made by the states in the food and fibre exports. The bar graph displays
that, the percentage contribution of all the states was higher in 2010 than in 2015. As the
total export value has increased quite significantly in 2015, the proportion of the
contribution of the states has changed too. The percentage contribution of the states were
higher in 2010 than in 2015 except for Queensland due to the difference in total value.

4STATISTICS FOR BUSINESS DECISIONS
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
Table 1: Weekly Sales Data: Frequency and class distribution
d) Relative frequency histogram

5STATISTICS FOR BUSINESS DECISIONS
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 Histogram
Figure 3: Relative frequency histogram
e) 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
4
13
20
31 33
38 40
Cumulative Frequency
Figure 4: Ogive

6STATISTICS FOR BUSINESS DECISIONS
e) Proportion of data less than 20 = 0.775 (gained from the cumulative relative frequency of
data less than 20)
f) Proportion of data more than 24 = 1 – 0.825 = 0.175 (gained from the cumulative relative
frequency of data more than 24)

7STATISTICS FOR BUSINESS DECISIONS
Answer 3
a) Rate of inflation (%) in Australia, 1995 – 2015
199 5
199 6
199 7
199 8
199 9
200 0
200 1
200 2
200 3
200 4
200 5
200 6
200 7
200 8
200 9
201 0
201 1
201 2
201 3
201 4
201 5
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
1.9
4.6
2.6
0.3
1.3
2.4
5.9
2.9 3.0
2.4 2.4
2.9 2.5
4.3
2.4
2.9 3.3
1.6
2.5 2.9
1.5
Rate of Infl ati on (%)
Figure 5: Rate of Inflation (%), 1995-2015
All-Ordinaries Index in Australia, 1995 – 2015
Figure 6: All-Ordinaries Index, 1995-2015

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b) Scatter Plot for the connection 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
All-Ordinaries index
Figure 7: Scatter plot for Rate of Inflation (%) and All-Ordinaries Index
Figure 7 represents the relationship between Rate of Inflation (%) and All-Ordinaries
Index. As All-Ordinaries Index is affected by the Rate of Inflation (%), hence the first
one is the dependent or response variable and the latter one is the independent or
predictor variable. Thus, Rate of Inflation (%) is denoted by X and All-Ordinaries Index
is denoted by Y. These variables are represented accordingly in the scatter plot. It is seen
that the observations in the response variables are highly scattered from the fitted line.

9STATISTICS FOR BUSINESS DECISIONS
c) Numerical summary report, that is, Descriptive statistics: Rate of Inflation (%) and All-
Ordinaries Index
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
Table 2: Descriptive statistics: Rate of Inflation (%) and All-Ordinaries Index
d) Correlation analysis and value of Correlation Coefficient (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
Table 3: Correlation analysis between Rate of Inflation (%) and All-Ordinaries Index

10STATISTICS FOR BUSINESS DECISIONS
Correlation analysis is a statistical method of evaluation of the strength of the
relationship between two or more than two, numerically measured and continuous
variables. This analysis is conducted when the possible connection between two or more
than two variables is examined (Aneiros et al. 2019). The measure of the strength of the
relationship is represented by the correlation coefficient (r). Correlation can be positive
or negative. The value of r denotes the level of association between the variables. Value
of the correlation coefficient ranges from +1 to -1. Zero indicates no correlation. The
positive correlation is stronger when r’s value is positive and closer to +1 and the
negative correlation is stronger when the value of r is closer to -1. Values that are
clustered around 0 indicates a weak positive or negative correlation between the variables
(Mirkin 2019). Here the value of the coefficient of correlation between the two variables
is 0.0389. This value is positive and quite closer to zero. Thus, it can be derived that the
variables, Rate of Inflation (%) and All-Ordinaries Index are positively correlated but the
association is not strong and much impactful.
e) Simple linear regression model can be presented through the following equation:
Y =mX +C
where, Y represents the Dependent or response variable, that is, All-Ordinaries Index
X represents the Independent or predictor variable, that is, Rate of Inflation (%)
and, C represents vertical intercept or Constant.
The hypothesis that needs to be examined is:
H0 (Null hypothesis): Rate of Inflation (%) does not affect the All-Ordinaries Index
significantly.

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H1 (Alternate hypothesis): Rate of Inflation (%) affects All-Ordinaries Index
significantly.
Regression outcome:
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 30569395.73 1608915.56
Total 20 30615664.41
Coefficient
s
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
Table 4: Simple linear regression model
f) R2 (Coefficient of determination) = 0.0015.
R2, that is, Coefficient of determination describes the percentage of variations in the
dependent or response variable, which can be predicted by the independent or predictor
variable. According to Murphy and Katz (2019), the level of variations in the dependent
variable that can be produced by the independent variable is defined by R2. The best fit of
the response variable to the fitted line of linear regression is also presented through the

12STATISTICS FOR BUSINESS DECISIONS
coefficient of determination. Here, the values of R2 is obtained as 0.0015, that is, the
predictor variable (Rate of Inflation (%)) can explain only 0.15% of the deviation in the
response variable (All-Ordinaries Index), and this is quite insignificant. The scatter and
line plot in Figure 7 displays that the observations of the response variable are quite
scattered and not much adjacent to the fitted regression line. Hence, the predictor variable
cannot explain much of the deviations in the response variable. Thus, it can be said that
the linear regression model chosen here is not the best fit to elucidate the variance in
response variable (Beyer 2019).
g) The regression analysis between Rate of Inflation (%) and All-Ordinaries Index has
generated 0.867 as the p-value or the significance value at 5% significance level. The rule
of thumb of hypothesis testing says that the null hypothesis should be rejected and the
alternative hypothesis should be accepted when the significance value is smaller than the
critical value of 0.05 (Larson and Farber 2019). Here, as the significance value is found
to be 0.867, which is larger than 0.05, the null hypothesis should be accepted. Hence,
Rate of Inflation (%) does not affect the All-Ordinaries Index significantly.
h) From the regression analysis, the value of Standard error of the estimate (Se) is found to
be 237.69. According to Howarth (2017), standard error of the estimate (Se) is described
as the measure of prediction accurateness. The value of the standard error of the estimate
(Se) pronounces the variation between the actual model fitness score and the predicted
model fitness score. The model accurateness is greater when the value of the standard
error estimate is lower (Ishwaran and Lu 2019). In the given case, value of the standard

13STATISTICS FOR BUSINESS DECISIONS
error of the estimate is 237.69, and this is positive as well as quite high. Hence, the
precision of the model is low. Moreover, R2 describes that the linear regression model
can predict only 0.15% of the variation in the response variable. Thus, the model does not
indicate a best fit.

14STATISTICS FOR BUSINESS DECISIONS
References
Aneiros, G., Cao, R., Fraiman, R., Genest, C. and Vieu, P., 2019. Recent advances in functional
data analysis and high-dimensional statistics. Journal of Multivariate Analysis, 170, pp.3-9.
Beyer, W.H., 2019. Handbook of tables for probability and statistics. CRC Press.
Howarth, R.J., 2017. r2 (r-squared, R-squared, coefficient of determination) The square of the
product-moment correlation coefficient; a measure of the goodness-of-fit of a regression.
Ishwaran, H. and Lu, M., 2019. Standard errors and confidence intervals for variable importance
in random forest regression, classification, and survival. Statistics in medicine, 38(4), pp.558-
582.
Larson, R. and Farber, B., 2019. Elementary statistics. Pearson Education Canada.
Mirkin, B., 2019. Core Data Analysis: Summarization, Correlation, and Visualization. Cham:
Springer International Publishing.
Murphy, A. and Katz, R.W., 2019. Probability, statistics, and decision making in the
atmospheric sciences. CRC Press.
.