Regression Analysis of Stock Market Returns: S&P/ASX 200 and ANZ

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Statistical report on regression analysis

TABLE OF CONTENTS
1. Introduction and business background........................................................................................1
Introduction..................................................................................................................................1
Purpose of the Study....................................................................................................................1
2. Data distribution of four new variables.......................................................................................1
Descriptive Statistics for four new variables...............................................................................3
3. Test the predictive power of PWR on CWR..............................................................................3
3.1 Predictive Power of weekly returns of open prices for the company S&P/ASX 200 on
Weekly returns of closed prices for the company ANZ...............................................................4
Analyze Sample Data...................................................................................................................8
3.2 Predictive Power of PWR – ANZ on CWR – S&P 200........................................................9
Analyze Sample Data.................................................................................................................12
4. Summary and recommendations................................................................................................13
References......................................................................................................................................15

LIST OF TABLES
Table 1: Data distribution................................................................................................................1
Table 2: Descriptive statistics of four variables..............................................................................3
Table 3: Variable and their meaning...............................................................................................4
Table 4: Given data..........................................................................................................................4
Table 5: Summary of key output.....................................................................................................8
Table 6: Summery of Anova output................................................................................................8
Table 7: Predictive power................................................................................................................9
Table 8: Summary of output..........................................................................................................12
Table 9: Summary of Anova..........................................................................................................13

LIST OF FIGURES
Figure 1: Scatter Plot Graph............................................................................................................6
Figure 2: Residual plot.....................................................................................................................7
Figure 3: Scatter Plot (PWR- ANZ vs. CWR - S&P200)..............................................................11
Figure 4: PWR-ANZ Residual Plot...............................................................................................11

1. Introduction and business background
Introduction
Stock market is the aggregation of the sellers and buyers so business ownership can be claimed.
Every country has own stock market which act as the equity performance benchmark. S&P/ASX
200 (XJO) is such a stock market of Australia which has two hundred largest ASX stock
businesses. The third largest banking sector of the Australia is Australia and New Zealand
Banking Group Limited which is also known as ANZ. The bank has most of the operations in
Australia including the expansions in retailing and commercial banking services. The first and
second position is occupied by Commonwealth and Westpac Banking Corporation respectively
(About ANZ, 2019). The presented report has study of the regression for the organization in
which predictive power of PWR on CWR will be calculated. Also, it has detailed integration the
dependent and independent variables to achieve the outcome. On the basis of conclusion of the
analysis, several recommendations are provided.
Purpose of the Study
The goal of this project is to find out the linear relationship between weekly returns of open &
closed prises of two companies ASX 200 and ANZ, also finding out the predictive power and
proportion for weekly returns of one company when we already know the Weekly returns of
another company. Statistical evaluations are required to understand the strengths and capabilities
in the business. For example, regression analysis is also used with correlation analysis which is a
measure for the relationship between two variables such as continuous and numerical variables
(Little and Rubin, 2019). It is required to understand the data and ensure high precision in the
probability of the variables.
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2. Data distribution of four new variables
Table 1: Data distribution
PWR -
S&P200
CWR -
S&P200 CWR - ANZ PWR - ANZ
0.009430958 -0.00852616 0.004523347 -0.008
-0.00852616 -0.010592954 -0.006581261 0.001402489
-0.010592954 0.007359585 -0.003138075 0.003151296
0.007359585 0.011801637 0.004547009 0.016055881
0.011801637 -0.046296584 -0.000696309 -0.041910064
-0.046296584 0.011305242 -0.032752647 -0.00143417
0.011373741 0.016226254 0.003242075 0.021184955
0.016157426 -0.011817045 0.026929982 0.004570991
-0.017467217 0.005785271 0.001748252 -0.004900245
0.012943139 -0.002314243 0.002443246 -0.01406961
-0.003667527 -0.021632385 -0.020891296 -0.0117731
-0.021632385 -0.010531429 -0.02347091 -0.030324909
-0.010531429 0.005087386 -0.021849892 -0.000372338
0.005087386 0.006979097 -0.002233879 -0.00521419
0.006979097 0.006810606 0 0.000374392
0.006810606 0.014449342 -0.00746265 -0.003368264
0.014449342 0.018358607 -0.002255602 0.034547504
0.018409046 0.008791221 0.042953992 0.021778621
0.008741258 -0.004708854 -0.011921965 0.00071048
-0.004708854 -0.008969363 0.029250457 -0.010649592
-0.008969363 -0.00702823 -0.018472504 -0.038392607
-0.00702823 0.009148019 -0.024610859 -0.005223843
0.009148019 0.008072488 -0.010760705 0.000750188
0.008072488 0.021529405 0.004501163 0.073838081
0.021611453 -0.00491552 0.076176211 -0.014310646
-0.004995438 0.012543135 -0.016308119 0.026558074
0.012543135 -0.000621766 0.02292769 0.000689893
2

-0.00074928 0.002791781 0.001034517 0.01206484
0.002919747 0.002274979 0.009300654 0.004087159
0.001765873 -0.010380684 0 -0.028493928
-0.009877751 0.006993023 -0.015699625 0.023393856
0.006944937 0.009684043 0.013522885 0.033094576
0.009604785 -0.014497159 0.038316798 -0.058784707
-0.014341143 0.011557024 -0.058319605 0.035087719
0.01152461 -0.027802863 0.033240063 -0.037288136
-0.027802863 0.003499463 -0.043345782 -0.008802817
0.003499463 0.004752452 -0.005309735 0.011012398
0.004752452 0.002098602 0.014234875 -0.009838335
0.002098602 -0.003560168 -0.024561439 -0.016323669
-0.004865036 -0.046851476 -0.011870504 -0.065295782
-0.045601663 0.00742911 -0.063705863 0.005017406
0.00742911 -0.046182306 0.010497706 -0.043394814
-0.046182306 0.032478993 -0.037322047 0.024889643
0.032478993 0.012411887 0.021183014 0.062671286
0.012411887 -0.032287432 0.029354209 -0.065241359
-0.032287432 -0.002512809 -0.038022815 0.038643492
-0.002512809 -0.008572128 0.039525693 0.017463895
-0.008572128 0.002523257 0.024334678 -0.040671643
0.002523257 -0.013992784 -0.05976247 -0.035394789
-0.013992784 -0.023991414 -0.030003948 -0.060483873
-0.023991414 0.034146555 -0.063899064 0.044635238
0.034146555 -0.00139715 0.063043522 0.004930115
Descriptive Statistics for four new variables
Table 2: Descriptive statistics of four variables
3

PWR -
S&P200
CWR -
S&P200
CWR -
ANZ
PWR -
ANZ
Mean -
0.001195657 Mean -
0.001405662 Mean -
0.002661491 Mean -0.00264
Standard
Error 0.002429557 Standard
Error 0.002405826 Standard
Error 0.004162118 Standard
Error 0.004244
Median 0.002721502 Median 0.002399118 Median -
0.001465094 Median 1.03E-06
Standard
Deviatio
n
0.017519782 Standard
Deviation 0.017348661
Standard
Deviatio
n
0.030013461 Standard
Deviation 0.030607
Sample
Variance 0.000306943 Sample
Variance 0.000300976 Sample
Variance 0.000900808 Sample
Variance 0.000937
Kurtosis 0.993626446 Kurtosis 1.20031489 Kurtosis 0.34708325 Kurtosis 0.162213
Skewnes
s
-
0.827826062 Skewness -
0.847625967
Skewnes
s 0.108481565 Skewness -0.03344
Range 0.080443138 Range 0.080998031 Range 0.140075275 Range 0.139134
Minimu
m
-
0.046296584 Minimum -
0.046851476
Minimu
m
-
0.063899064 Min. -0.0653
Maximu
m
0.034146555 Maximum 0.034146555 Max. 0.076176211 Max. 0.07383808
1
Sum -
0.062174158
Sum -
0.073094438
Sum -0.13839753 Sum -0.13735296
Count 52 Count 52 Count 52 Count 52
We have generated Summary Statistics for 4 variables as above. Also, we made a comment on
the relevant measure
4

 Mean: it can be defined as the arithmetic mean of the collected data. Therefore, the
observations are summed up and then divided by total number of the observations. Here
negative data is our data.
 Standard Deviation: It shows the deviation from the standard value which is considered
according to the records. It can be defined as the square root of the variation. In most of
the cases, the standard deviation is within the range but for large deviation, it might go
outside the values in observations.
 Skewness: It is used to measure direction and degree of asymmetry whereas skewness
for noral distribution is zero. In our example, one value excepting one column CWR-
ANZ, all are having negative skewness, which means more data are skewed towards the
left side of the distribution
 Kurtosis: tail extremity reflecting can be measured through Kurtosis measure to
understand if distribution has outliers (Blanca et al., 2013).
 Minimum: It presents the smallest value or measure related to a list of variables.
 Maximum: It presents the largest value or measure related to a list of variables.
 Count: It shows the total of observations those are non-missing in a sample.
3. Test the predictive power of PWR on CWR
Before we are going through the Regression analysis and Hypothesis testing we understand the
actual meaning of four variables which are given in the problem.
Table 3: Variable and their meaning
S. No. Name of variable Actual Meaning of Variable Dependent/
independent
1 PWR-S&P200(X) Weekly returns of open prices for the
company S&P/ASX 200 Independent
2 CWR - ANZ(Y) Weekly returns of closed prices for the
company ANZ Dependent
3 PWR - ANZ(X2) Weekly returns of open prices for the
company ANZ Independent
5

4 CWR -
S&P200(Y2)
Weekly returns of closed prices for the
company SP/ASX 200 Dependent
3.1 Predictive Power of weekly returns of open prices for the company S&P/ASX 200 on
Weekly returns of closed prices for the company ANZ
Given Data is
Table 4: Given data
S. No. PWR -
S&P200(X)
CWR -
ANZ(Y)
1 0.009430958 0.004523347
2 -0.00852616 -0.006581261
3 -0.010592954 -0.003138075
4 0.007359585 0.004547009
5 0.011801637 -0.000696309
6 -0.046296584 -0.032752647
7 0.011373741 0.003242075
8 0.016157426 0.026929982
9 -0.017467217 0.001748252
10 0.012943139 0.002443246
11 -0.003667527 -0.020891296
12 -0.021632385 -0.02347091
13 -0.010531429 -0.021849892
14 0.005087386 -0.002233879
15 0.006979097 0
16 0.006810606 -0.00746265
17 0.014449342 -0.002255602
18 0.018409046 0.042953992
19 0.008741258 -0.011921965
20 -0.004708854 0.029250457
6

21 -0.008969363 -0.018472504
22 -0.00702823 -0.024610859
23 0.009148019 -0.010760705
24 0.008072488 0.004501163
25 0.021611453 0.076176211
26 -0.004995438 -0.016308119
27 0.012543135 0.02292769
28 -0.00074928 0.001034517
29 0.002919747 0.009300654
30 0.001765873 0
31 -0.009877751 -0.015699625
32 0.006944937 0.013522885
33 0.009604785 0.038316798
34 -0.014341143 -0.058319605
35 0.01152461 0.033240063
36 -0.027802863 -0.043345782
37 0.003499463 -0.005309735
38 0.004752452 0.014234875
39 0.002098602 -0.024561439
40 -0.004865036 -0.011870504
41 -0.045601663 -0.063705863
42 0.00742911 0.010497706
43 -0.046182306 -0.037322047
44 0.032478993 0.021183014
45 0.012411887 0.029354209
46 -0.032287432 -0.038022815
47 -0.002512809 0.039525693
48 -0.008572128 0.024334678
49 0.002523257 -0.05976247
50 -0.013992784 -0.030003948
51 -0.023991414 -0.063899064
7

52 0.034146555 0.063043522
Hypothesis test of Regression Slope
The presented regression line slop is Y= B0+B1X and the test has main focus on the measurement
of the slop line.
Here B0 shows intercept or constant and B1 shows the slop. X shows other independent variable
in the calculations. The difference from zero of the regression line of the slope can be used to
conclude that dependent and independent variables has significant relationship.
Test Requirement
There is linear relationship between Y (dependent variable) and X (independent variable
i.e. for each value of Weekly returns of open prices for the company S&P/ASX 200(PWR-
S&P200) there is increase or decrease in the slope value of dependent variable CWR- ANZ
For this test requirement, we will make one scatterplot by taking dependent variable in the Y
axis and an independent variable in X-axis with the help of excel.
-0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
f(x) = 0.0238805280010662 ln(x) + 0.124173746618797
R² = 0.46057884911231
f(x) = 1.23280243874382 x − 0.00118748224754331
R² = 0.517859799261504
Scatter plot(PWR-S&P 200 Vs CWR- ANZ)
Figure 1: Scatter Plot Graph
8