Business Statistics: Data Collection and Business Report Analysis

This report presents a comprehensive data analysis of two Australian companies, Iluka Resources Limited (ILU) and Boral Limited (BLD), using historical stock data. The analysis includes calculating weekly rates of return, descriptive statistics (mean, standard deviation, skewness, kurtosis), and graphical ...Read More

DATA COLLECTION AND
BUSINESS REPORT

Table of Contents
INTRODUCTION...........................................................................................................................3
MAIN BODY..................................................................................................................................3
PART- A..........................................................................................................................................3
Question: 1 - Statement of Investment goal................................................................................3
Question: 2 – Calculations for weekly rate of return for the two companies..............................3
Question: 3 - Descriptive statistics of two company’s weekly rate of return..............................5
Question: 4 – Interpretation of statistics......................................................................................6
Question: 5 – Graphical representation of company’s weekly returns........................................7
Question: 6 – creating a box and whisker plot............................................................................8
Question:8 – interpretation of confidence interval......................................................................8
Part – B............................................................................................................................................8
Question: 1...................................................................................................................................8
Question: 2 – correlation analysis................................................................................................9
Question: 3 – regression analysis of ILU..................................................................................10
Question: 4 – regression analysis of BLD.................................................................................12
Question: 5 - Trends and conclusions........................................................................................13
REFERENCES..............................................................................................................................15

INTRODUCTION
Data collection and business report here includes the stock analysis of two companies on the
basis of historical closing prices of two companies based in Australia and listed on Australian
stock market (Ranganathan, Pramesh and Aggarwal, 2017). The companies chosen for this report
are Iluka Resources limited and Boral limited. Iluka is an Australian company specialized in
exploring mineral sands, project development, marketing and operations. On the other hand,
Boral limited is a MNC established manufacturer and supplier of building and construction
materials. The stocks of these two companies are among best performers of Australian Securities
Exchange’s index of top 200 shares. In this report, various statistical tools and techniques will be
applied to analyze and suggest which stock is better among the two.
MAIN BODY
PART- A
Question: 1 - Statement of Investment goal
 Planning for expenditure post retirement in order to meet old age expenses in an easier
way.
 Accumulation of wealth for achieving short terms goals such as buying a car within two
years and going on a vacation post marriage (Fagerland, Lydersen and Laake, 2017).
 For meeting any emergency expenses where immediate liquidity is necessary and the
same can be possible and facilitated through investment in stock market as stocks can be
easily liquidated at any point of time an investor wishes to do so.
 To build a corpus in order to meet increasing cost of higher education of children as stock
is considered as an inflation beating instrument suitable for meeting expenses that are
increasing continuously (Xia and Sun, 2017).
 Buying a dream house within five to ten years.
Question: 2 – Calculations for weekly rate of return for the two companies
Date Weekly rate of
return on ILU
weekly rate of return
on BLD stocks

stocks
1/1/2020 - -
1/8/2020 3.02 4.74
1/15/2020 0.31 2.67
1/22/2020 -6.88 0.00
1/29/2020 4.14 -2.40
2/5/2020 3.66 -2.67
2/12/2020 -47.71 1.27
2/19/2020 -2.34 -0.83
2/26/2020 -9.38 -6.93
3/4/2020 -3.49 -12.87
3/11/2020 -6.23 -26.94
3/18/2020 -9.31 -36.70
3/25/2020 2.35 14.85
4/1/2020 3.30 13.66
4/8/2020 7.35 15.02
4/15/2020 -5.17 -4.10
4/22/2020 -0.82 3.89
4/29/2020 1.65 1.50
5/6/2020 0.00 0.37
5/13/2020 7.30 -5.15
5/20/2020 4.66 12.02
5/27/2020 3.37 22.15
6/3/2020 8.03 8.22
6/10/2020 -4.96 -2.88
6/17/2020 -3.06 2.70
6/24/2020 -0.12 -0.52
7/1/2020 3.86 -1.32
7/8/2020 -0.68 0.00
7/15/2020 4.65 2.41
7/22/2020 1.63 2.09
7/29/2020 0.64 -5.63
8/5/2020 2.55 2.44
8/12/2020 2.17 -0.53
8/19/2020 2.13 0.80
8/26/2020 -1.88 1.85
9/2/2020 0.00 6.48
9/9/2020 -0.61 0.24
9/16/2020 -4.57 0.73
9/23/2020 -1.17 10.12
9/30/2020 -1.40 3.72
10/7/2020 5.03 3.59
10/14/202 1.04 -3.26

0
10/21/202
0
-0.06 -0.21
10/28/202
0
-3.84 2.95
11/4/2020 3.79 4.10
11/11/202
0
-0.96 0.98
11/18/202
0
4.66 0.39
11/25/202
0
-0.74 -4.27
12/2/2020 7.48 -1.22
12/9/2020 0.17 -1.85
12/16/202
0
7.47 0.42
12/23/202
0
1.29 0.63
12/30/202
0
5.58 0.21
1/6/2021 -0.30 0.83
1/13/2021 2.88 3.89
1/20/2021 3.68 -0.79
1/27/2021 -7.95 3.38
2/3/2021 4.17 -3.65
2/10/2021 5.93 1.00
2/17/2021 4.20 1.19
Question: 3 - Descriptive statistics of two company’s weekly rate of return
Weekly rate of return on ILU stocks
Mean 0.008644
068
Standard Error 0.988292
172
Median 1.04
Mode 0
Standard Deviation 7.591216
217
Sample Variance 57.62656
365
Kurtosis 26.96926

162
Skewness -
4.419429
219
Range 55.74
Minimum -47.71
Maximum 8.03
Sum 0.51
Count 59
Weekly rate of return on BLD stocks
Mean 0.555593
22
Standard Error 1.088606
133
Median 0.73
Mode 0
Standard Deviation 8.361742
367
Sample Variance 69.91873
542
Kurtosis 8.188939
532
Skewness -
1.666726
236
Range 58.85
Minimum -36.7
Maximum 22.15
Sum 32.78
Count 59
Question: 4 – Interpretation of statistics
a) Central tendency: It refers to the mean, mode and median in the above two tables indicating
the statistics of two companies on the basis of its closing price of its stocks in the previous year.
It is a single value meant for describing a data set by identifying an average value (Little and
Rubin, 2019). In case of two companies, that is ILU and BLD, the central tendency can be
described through the mean value indicating average weekly return from the investment in these
company’s share. The average rate of weekly return of ILU is lower than BLD stocks, where the

former has just 0.0086 while the latter has comparatively higher rate that is 0.55 and this
indicates higher return from the stocks.
b) Variability: In the above table three statistical measures of variability has been included that is
range, variance and standard deviation. In case of ILU, range value is lower than BLD’s range
value which indicates less dispersion among the values in a data set (Nisar and Yeung, 2018).
So, there is low variability and high variability for ILU and BLD respectively. Also, variance of
ILU is lower than BLD which means that there the data points in case of ILU is comparatively
closer to the mean than in case of BLD where the value of variance is quite high. And standard
deviation of BLD is higher than ILU that is 8.36 and 7.59 which means the returns generally
deviates more from the mean returns.
c) Shape of the distribution: In the above table skewness and kurtosis are the two statistical
measures that has been included to indicate the shape of distribution for the weekly rate of
returns of the two companies that is ILU and BLD. lower value of Skewness less than –1 means
that there are higher skewness among the weekly rate of return and the returns are left tailed
(Nabipour and et. al., 2020). Also, the value of kurtosis in both the table is greater than 1 which
means that the returns are heavily tailed due to the presence of many outliers in the data set and
accordingly the distribution is very much peaked. Between the two companies, ILU has more
peak distribution than BLD.
Question: 5 – Graphical representation of company’s weekly returns
-47.71
-42.71
-7.71
-2.71
1
1
2.29
3
5
7.29
8
12.29
19
23
More
0
5
10
15
20
Weekly returns of ILU
Frequency
Weekly returns
Frequency

-
47.71 -
42.71 -7.71 -2.71 1 1 2.29 3 5 7.29 8 12.29 19 23 More
0
2
4
6
8
10
12
14
16
18
Frequency polygon of weekly returns of ILU
The returns of ILU are right tailed with greater than 1 kurtosis as is seen in the above diagram
which indicates peak points in the weekly returns distribution.
-36.7
-26.7
-11.7
-1.7
1
1
1
2
3.3
9
13.3
23.3
More
0
5
10
15
Weekly returns of BLD
Frequency
weekly returns
Frequency
-36.7
-31.7
-26.7
-16.7
-11.7
-6.7
-1.7
0
1
1
1
1
1
1
2
3
3.3
8.3
9
10
13.3
18.3
23.3
30
More
0
2
4
6
8
10
12
Frequency polygon of BLD's weekly returns

Question: 6 – creating a box and whisker plot
The shape of the box and whiskers indicate that there is a normal distribution exists in the data
set of weekly rates of returns of both the two companies. Yes, there are many evidences found
for the outliers in the above plot. The list of identified outliers in case of both companies are as
follows:
In case of ILU, outliers are
 -9.38
 -47.71

In case of BLD, outliers are
 22.15
 15.02
 13.66
 12.02
 -12.87
 -26.94
 -36.7
Question:8 – interpretation of confidence interval
Confidence interval at 95% of ILU = 1.99 and -1.97
Confidence interval at 95% of BDL = 2.73 and -1.62
This indicates that we are 95% confident that the range of values stated above contains the true
mean of the population or weekly returns of the two companies.
Yes, it has been assumed that the there is a normal distribution exists among the data set of
weekly returns and the variance of the sample is independent of the mean and therefore the
obtained confidence interval is considered as a normal approximation.
Part – B
Question: 1
Weekly rate of return on ILU stocks weekly rate of return on BLD stocks
Mean 0.008644068 0.55559322
Known Variance 57.62 69.91
Observations 59 59
Hypothesized Mean Difference 0
z -0.372020421
P(Z<=z) one-tail 0.354938823
z Critical one-tail 1.644853627
P(Z<=z) two-tail 0.709877645
z Critical two-tail 1.959963985
Step: 1
H0: There is no significant difference between company’s return and weekly returns of the
benchmark.
H1: The Company’s return are significantly different from the mean returns of the benchmark.
Step: 2- test statistics

As standard deviation of both company’s weekly returns are known, that is 7.59 and 8.36
respectively for ILU and BLD, so z – test will be applied.
Step: 3 – critical value
Z critical value is 1.64.
Step: 4 – decision to accept or reject null hypothesis.
If Zcal < Zcrit or Zcal > Zcrit, then reject the null hypothesis.
But in this case, -0.37 > -1.64 (one tail critical value) and also -0.37 < 1.64, then we can’t reject
the null hypothesis which says that there is no significant difference between company’s returns
and mean returns of the benchmark.
Question: 2 – correlation analysis
Closing price of
ILU.AX
Closing price of
BLD.AX
Closing price of
ILU.AX
1 0.647625884
Closing price of
BLD.AX
0.647625884 1
The resulting degree of correlation coefficient that is 0.64 indicates that there is a moderate direct
relationship exists between the prices of two companies, where increase and decrease in price of
one company causes an increase or decrease in the price of another company’s stock
respectively.
No, combining two stocks would not result in reduction of investment risks due to the presence
of positive relationship between the prices of stock of both the companies where the direction of
change is quite likely to be the same for both the companies and reduction in price of stock of
company will not be likely to supplement by the corresponding rise in the price of stock of
another company.
Question: 3 – regression analysis of ILU
Regression Statistics
Multiple R 0.003105
151
R Square 9.64196E
-06
Adjusted R Square -
0.017231

571
Standard Error 1.568135
523
Observations 60
ANOV
A
df SS MS F Signific
ance F
Regres
sion
1 0.00137
5197
0.00137
5197
0.00055
9239
0.98121
4365
Residu
al
58 142.624
8431
2.45904
9018
Total 59 142.626
2183
Coeffici
ents
Standar
d Error
t Stat P-value Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Interce
pt
5.58101
3446
0.41000
5465
13.6120
465
1.04034
E-19
4.76029
8339
6.40172
8553
4.76029
8339
6.40172
8553
Time
or
week
-
0.00027
6444
0.01168
9816
-
0.02364
8242
0.98121
4365
-
0.02367
6152
0.02312
3265
-
0.02367
6152
0.02312
3265
b) Linear regression equation
Y = a + bx
a= intercept
b = coefficient of time
y = 5.58 -0.00027x
c) On testing the significance at 5% between time and stock price by looking at the p- value
(0.98) which is greater than 0.05 which means that there is no statistical significance found
between time and stock price.
d) for estimating the stock price at the end of May,2021, firstly it is necessary to determine the
number of week from 1 January 2020, which comes out to be 74th week on 26th May, 2021.
Therefore the forecast of stock price will be as follows:
y = a + bx
a = 5.58
b = -0.00027

x = 74
y = stock price =?
Y = 5.58 + (-0.00027*74)
Y = 5.56
e) Time series plot
12/1/2019 3/10/2020 6/18/2020 9/26/2020 1/4/2021 4/14/2021
0
2
4
6
8
10
12
closing price of ILU
Time
closing price
f) The trend in the above time series plot indicate that there is quite stability in the closing price
of stock ILU, but from past few weeks it is going in an upward direction, so the forecast that has
been made above regarding the closing price of stock at the end of May, 2021 can be adjusted in
a manner by adding constant proportion by which it is increasing to give a more optimistic value
(Huy, Dat and Anh, 2020).
Question: 4 – regression analysis of BLD
Regression Statistics
Multiple R 0.4983308
42
R Square 0.2483336
28
Adjusted R Square 0.2353738
63
Standard Error 0.8052667
1
Observations 60

ANOV
A
df SS MS F Significa
nce F
Regres
sion
1 12.4256
1511
12.4256
1511
19.1618
928
5.07974
Residu
al
58 37.6103
5947
0.64845
4474
Total 59 50.0359
7458
Coeffici
ents
Standar
d Error
t Stat P-value Lower
95%
Upper
95%
Lowe
r
95.0
%
Uppe
r
95.0
%
Interce
pt
3.33612
1469
0.21054
5419
15.8451
3916
9.76462 2.91466
9022
3.75757
3916
2.914
669
3.757
574
week 0.02627
7438
0.00600
2937
4.37742
9931
5.07974 0.01426
1253
0.03829
3623
0.014
261
0.038
294
b) Setting up a linear regression equation
y = a + bx
a = 3.34
b = 0.026
y= 3.34 + 0.026x
c) Testing significance at 5% between stock price and time by considering the p-value (5.079) as
obtained from the regression analysis which is higher than 0.05, it can be said that there is no
statistical significance exists between time and stock price of BLD.
d) Forecasting stock price for May 2021
y = a + bx
y= stock price =?
a = 3.34, b = 0.026, x = 74th week from 1 January, 2020
y = 3.34+ (0.026*74)
y = 5.26

e) Time series plot
12/1/2019 3/10/2020 6/18/2020 9/26/2020 1/4/2021 4/14/2021
0
1
2
3
4
5
6
Closing price of BLD.AX
Time
closing price
f) Yes, in the above time series plot, the trend line is going in an upward direction indicating a
price rise of the stock of BLD. Also, regarding the adjustment in the forecasting made above,
there is less likely to have a need of adjustment because the forecasted price is already indicating
a rise in the price of stock (Shah, Isah and Zulkernine, 2019).
Question: 5 - Trends and conclusions
In part A and B of this report, various statistical techniques has been applied to analyze
both the stocks that is ILU and BLD. Where in Part A weekly returns are calculated on the basis
of closing price of the stock and then descriptive statistics has been obtained for these weekly
return, where it has been found out that BLD’s mean returns are higher than ILU making it more
attractive avenue for investment. Also, it has been found that probability of loss in case of ILU is
higher than BLD that is 41% and 36% respectively. The confidence interval so estimated for ILU
and BLD is also indicating that BLD’s return are more skewed towards positive side as
compared to ILU’s return which is skewed towards negative side (Sahoo, 2020). And at last, in
analyzing regression statistics of two companies, it has been identified that BLD’s stock price is
indicating rising trends as compared to ILU’s stock price which is indicating stable trends and
therefore there is more probability of capital growth by investing in BLD’s stock. Accordingly, it
can be said that among the two alternative investment opportunities available BLD should be
selected for making investment.

REFERENCES
Sahoo, A. P., 2020. A REVIEW ON THE PRACTICABILITY OF FINANCIAL REPORTING
AND STOCK MARKETS WITH REFERENCE TO STATISTICS.
Huy, D. T. N., Dat, P. M. and Anh, P. T., 2020. BUILDING AN ECONOMETRIC MODEL OF
SELECTED FACTORS’IMPACT ON STOCK PRICE: A CASE STUDY. Journal of
Security & Sustainability Issues, 9.
Ranganathan, P., Pramesh, C. S. and Aggarwal, R., 2017. Common pitfalls in statistical analysis:
logistic regression. Perspectives in clinical research, 8(3), p.148.
Fagerland, M., Lydersen, S. and Laake, P., 2017. Statistical analysis of contingency tables. CRC
press.
Xia, Y. and Sun, J., 2017. Hypothesis testing and statistical analysis of microbiome. Genes &
diseases, 4(3), pp.138-148.
Little, R. J. and Rubin, D. B., 2019. Statistical analysis with missing data (Vol. 793). John Wiley
& Sons.
Nisar, T. M. and Yeung, M., 2018. Twitter as a tool for forecasting stock market movements: A
short-window event study. The journal of finance and data science, 4(2), pp.101-119.
Nabipour, M., and et. al., 2020. Deep learning for stock market prediction. Entropy, 22(8), p.840.
Shah, D., Isah, H. and Zulkernine, F., 2019. Stock market analysis: A review and taxonomy of
prediction techniques. International Journal of Financial Studies, 7(2), p.26.