statistical analysis on stock prices

Wednesday, July 23, 2008

BUSINESS STATISTICS I (BA‐205)

A REPORT ON ANALYSIS OF SHARE STOCK PRICES OF FIVE COMPANIES

A Report On-

Analysis of Share Prices Of

Five Companies

Prepared for-

Tania Afroze Assistant Professor

Business Administration Discipline Khulna University

Prepared by- Name ID Abdur Rakib Akon 070305 Md Masrul Mollah 070314 Md Nazmul Huda 070323 Ahmed Ibtehaj 070324 SM Mazharul Islam 070351

Date of Submission: July 23, 2008

BBA Program

Business Administration Discipline Khulna University

Letter of Transmittal July 23, 2008 Tania Afroze Assistant Professor Business Administration Discipline Khulna University Dear Madam, Here is the report on ‘Analysis of Share Prices Of Five Companies’. This is for you asked to make a report on any topic on June 17. As you will see, the statistical calculations we have used a variety of methods and that resulted some conclusions about all the prices. These calculations are made by the formulas and techniques we’ve learned through our course of ‘Business Statistics I’. As a student of BA discipline we enjoyed to prepare this report. We tried our best to make this report best to present. Therefore we hope that our report will fulfill your requirements about share prices of the five companies we’ve observed. Any short comings or mistakes are absolutely our fault and we will be always available at any time to interpret any portion of the report. Sincerely yours, Abdur Rakib Akon (070305) Md Masrul Mollah (070314) Md Nazmul Huda (070323)

Ahmed Ibtehaj (070324) SM Mazharul Islam (070351) 2nd Year, 1st Term BBA Program Business Administration Discipline Khulna University

Acknowledgement First we would like to thank the Almighty Allah for completing the report successfully. And it was also a great pleasure to us to make this report. We wish to express thank to all who helped me a lot during the making of the report. We would like to express my gratitude and regards to our honorable course teacher and instructor Mrs. Tania Afroze, Assistant Professor, Business Administration Discipline, Khulna University. It was very difficult to make such a report of statistical analysis without group work. We are so glad that we have made it to complete this assignment. We have chosen these five companies – Social Investment Bank Ltd., Lanka Bangla Finance Ltd., BD Autocars Ltd., Jamuna Oil Ltd., and Square Pharmaceuticals Ltd. We have collected the prices of the shares from the ‘Daily Prothom-Alo’. Finally we want to thank all who helped us to prepare this report. And again thank you also to assign us such type of job.

V

Table of Contents

Contents Page No.Letter of Transmittal IIIAcknowledgement V Summary of the report 01 Part 1: Introduction 01-05

Origin of the report 03Purpose of the report 03Scopes of the report 03Limitations of making the report 04

Hard to find 04Inaccuracy 04Time Limit & Exam Time 04

Methodology 04Sources of collecting data 04Method of preparing the report 05

Part 2: Statistical Analysis 06-37

Business Statistics Chapter 2: Collection of Data 07Category of data: Secondary data 07

Business Statistics Chapter 3: Presentation of Data 07Type of data class: Geographical classified data 07Frequency Distribution 07Tabulation of Data 07Type of Table 08Diagrams 08

Business Statistics Chapter 4: Measures of Central Tendency 11Arithmetic Mean 11

Direct Method 12Short-cut method 13

Combined arithmetic mean 14Median 15

Quartiles, Deciles, Percentiles 15Mode 16Geometric Mean 16Harmonic Mean 17

Business Statistics Chapter 5: Measures of Variation 19Range 19Inerquartile range or Quartile deviation 19

Average deviation 20Standard deviation 22Combined Standard Deviation 24Coefficient of variation 25

Business Statistics Chapter 7: Correlation Analysis 26Scatter Diagram 26Karl Pearson’s coefficient of correlation 30

Actual mean method 30Assumed mean method 31Probable error of coefficient correlation 32

Rank correlation coefficient 33Business Statistics Chapter 6: Correlation Analysis 34

Regression equation 34Regression equation using arithmetic mean 36

Part 3: Statistical Analysis 38-39Conclusion 39

Appendix 40

Page | 1

Summary of the Report Share market is like flowing river. Every time the prices of the shares are changing. We have prepared a report which shows the statistical analysis of the share prices of five selected companies of first seven working days of May and June. The prices list is given below-

Date Social Investment Bank Ltd.

Lanka Bangla Finance Ltd.

BD Autocars Ltd.

Jamuna Oil Ltd.

Square Pharmaceuticals Ltd.

30 April 2008 341.00 115.60 202.25 265.50 4552.25 01 June 2008 361.75 175.60 190.00 210.00 5397.25 04 May 2008 338.00 121.90 203.00 263.30 4649.00 02 June 2008 357.25 181.10 191.00 206.90 5295.50 05 May 2008 335.75 127.10 196.50 264.40 4679.50 03 June 2008 369.00 182.20 190.00 204.30 5293.25 06 May 2008 336.00 131.80 199.75 263.20 4660.50 04 June 2008 431.00 191.10 191.50 201.30 5292.25 07 May 2008 334.00 135.10 196.00 261.00 4657.25 05 June 2008 414.00 210.90 190.00 204.90 5273.75 08 May 2008 335.25 137.30 203.75 260.60 4660.50 08 June 2008 414.50 205.20 187.75 201.50 5247.50 11 May 2008 330.00 136.70 207.50 256.60 4733.25 10 June 2008 399.25 195.30 181.25 221.80 5164.75 Holidays- May 2008 - 01 (May Day), 02 (Friday), 03 (Saturday), 09 (Friday), 10 (Saturday) June 2008 - 06 (Friday), 07 (Saturday), 09 (Budget Day)

Chapter 1 Introduction

Page | 3

Origin of the Report Mrs. Tania Afroze, the honorable course instructor of ‘Business Statistics I’, assigned us to prepare a report on June 17, 2008 about ‘Statistical Analysis on Five Companies of May and June’ according to the rules we have learned through the course. So this is the report as the result of that action. The date of submission of this report is July 23, 2008. Purpose of the Report We are very much passionate to obtain educational background through practical work besides the theoretical studies. We do not want to study only with the classroom materials; I want to gather some practical knowledge so that it will help me in achieving my personal objectives. The purposes of our report are-

• To make a clear concept through making a relationship between my report writing theoretical knowledge and my practices.

• To gather knowledge about ‘Stock Exchange’.

• To know something about how share market goes on and how a price change can have effect on some other variables.

Scopes of the Report We have collected data from newspaper. We got the needed information from the ‘Daily Prothom-Alo’. But for the excess of holidays we have included a price of April 30. As the report is calculation based we have used the secondary source to collect data. We got no internal data to prepare this report but the secondary data we have collected was sufficient enough to make it done. And we have used our text book ‘Business Statistics – Gupta and Gupta’ as a guide to prepare this report.

Page | 4

Limitations of making the Report We are lucky that we have completed the report successfully within this short time but we had to face some problems in collecting the data and in making the report. We tried our best to overcome the difficulties; Allah knows how much we could do. There were basically 3problems. Hard to Find It was so tough to collect the newspaper cutting of May and June. But it we were so lucky that we got those in collection. Inaccuracy The data we have collected was not so accurate. We have got the rates of the last of those working days. But if we could manage to have the average rate of those days it would be better for us. Time Limit & Exam Time It needs more time to well prepare this kind of report; but we had to prepare it within a very short time. On the other hand now it took much time during preparatory leave for our term final examination. We were so busy with my study. In this busyness we had to give time for this report. This made us so confusing about the report. Methodology

Sources of collecting data Primary Sources

No primary sources found. Secondary Sources

The ‘Daily Prothom-Alo’ (Share prices page)

Page | 5

Method of preparing the report To prepare this report we have collected the data we needed and made the calculations we have learned through our ‘Business Statistics I’. And finally we are submitting this report today.

Chapter 2 Statistical Analysis

Page | 7

Business Statistics Chapter 2: Collection of Data Category of Data: Secondary Data We didn’t get any internal source of data. We have collected data from newspaper. So we have collected data from ‘Secondary Source’.

Business Statistics Chapter 3: Presentation of Data Type of Data Class: Geographical Classified Data Our collected data is in a chronological order. So it can be defined as a ‘Chronological Classified Data’. So this will be a ‘Geographical Classification’ of data type. Frequency Distribution Our collected data can’t be distributed in fixed frequency. Tabulation of Data

Table 2.1: Prices of Shares (in tk.)

Mon

th Date Social

Investment Bank Ltd.

Lanka Bangla Finance Ltd.

BD Autocars Ltd.

Jamuna Oil Ltd.

Square Pharmaceuticals Ltd.

May

30 April 2008 341.00 115.60 202.25 265.50 4552.25 04 May 2008 338.00 121.90 203.00 263.30 4649.00 05 May 2008 335.75 127.10 196.50 264.40 4679.50 06 May 2008 336.00 131.80 199.75 263.20 4660.50 07 May 2008 334.00 135.10 196.00 261.00 4657.25 08 May 2008 335.25 137.30 203.75 260.60 4660.50 11 May 2008 330.00 136.70 207.50 256.60 4733.25

June

01 June 2008 361.75 175.60 190.00 210.00 5397.25 02 June 2008 357.25 181.10 191.00 206.90 5295.50 03 June 2008 369.00 182.20 190.00 204.30 5293.25 04 June 2008 431.00 191.10 191.50 201.30 5292.25 05 June 2008 414.00 210.90 190.00 204.90 5273.75 08 June 2008 414.50 205.20 187.75 201.50 5247.50 10 June 2008 399.25 195.30 181.25 221.80 5164.75

Page | 8

N.B.: May 2008 - 01 (May Day), 02 (Friday), 03 (Saturday), 09 (Friday), 10 (Saturday), June 2008 - 06 (Friday), 07 (Saturday), 09 (Budget Day) were holidays.

Type of Table The table we have presented is a ‘Simple Table’. Diagrams The diagrams of the rates of the shares are given below - N.B.: Here we calculated the prices by first seven working days.

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Page | 11

As the data is not distributed in frequency we have only made ‘Bar Diagrams’. It is not possible to draw ‘Histogram’, ‘Frequency Polygon’, or ‘Cumulative Frequency Curves or Ogives’.

Business Statistics Chapter 4: Measures of Central Tendency To calculate ‘Central Tendency’ of the prices of shares we got our data is not ‘Grouped Data’; this is ‘Ungrouped Data’. So, we followed only rules of ‘Ungrouped Data’ for this chapter. Arithmetic Mean We have calculated the ‘Arithmetic Mean’ in two approaches -

Page | 12

1. Direct Method 2. Indirect Method

Direct Method

Formula: N

X

NXXX

X

N

iN∑==

+++= 1

121 ...

If the subscripts are dropped, the formula becomes:

N

XX ∑=

Here, =X Average =X Observation =N Number of Observations Average of the Prices of Social Investment Bank Ltd. of May:

N

X

NXXX

X

N

iN∑==

+++= 1

121 ...

7

330.00335.25334.00336.00335.75338.00341.00 ++++++=X

335.71=X Averages: Prices of May Social Investment Bank Ltd. = 335.71

Lanka Bangla Finance Ltd. = 129.36

BD Autocars = 201.25

Jamuna Oil = 262.09

Square Pharmaceuticals Ltd. = 4656.04 Prices of June Social Investment Bank Ltd. = 392.3929


Page | 13


Jamuna Oil = 207.2429

Square Pharmaceuticals Ltd. = 5280.6071

Short-cut Method

Formula: N

dAX ∑+=

Here, =X Average =d )( AX − [Here, =A Assumed Mean] =N Number of Observations Average of the prices of Social Investment Bank Ltd. of June: We take, Assumed Mean, =A 400

Calculation of Average Price X

( .Tk ) d

)400( −X 361.75 357.25 369.00 431.00 414.00 414.50 399.25

-38.25 -42.75 -31.00 +31.00 +14.00 +14.50 -00.75

∑ =d -53.25

N

dAX ∑+=

7

25.53400 −+=X

3929.392=X Averages: Averages of May

Page | 14

Social Investment Bank Ltd. = 335.71



Jamuna Oil = 262.09

Square Pharmaceuticals Ltd. = 4656.04 Averages of June Social Investment Bank Ltd. = 392.3929




Square Pharmaceuticals Ltd. = 5280.6071 Combined Arithmetic Mean

Formula: 21

221112 NN

XNXNX++

=

Here, 12X = Combined mean of the two groups. 1X = Arithmetic mean of the first group. 2X = Arithmetic mean of the second group. 1N = Number of the observations in the first group. 2N = Number of the observations of the second group. Combined Average of May and June Prices of Social Investment Bank Ltd.:

21

221112 NN

XNXNX++

=

77

3929.392771.335712 +

×+×=X

0515.36412 =X Averages: Social Investment Bank Ltd. = 364.0515

Page | 15





Median

Formula: Median = Size of 2

1+N th observation

= Size of 2

17 + th observation

= Size of 4th observation Medians: Medians of May Social Investment Bank Ltd. = 336.00



Jamuna Oil = 263.20

Square Pharmaceuticals Ltd. = 4660.50 Medians of June Social Investment Bank Ltd. = 431.00



Jamuna Oil = 201.30

Square Pharmaceuticals Ltd. = 5292.25 Quartiles, Deciles, Percentiles etc. As our data is ungrouped, we didn’t get any formula to calculate Quartiles, Deciles, or Percentiles.

Page | 16

Mode Modes: Modes of May Social Investment Bank Ltd. = No mode

Lanka Bangla Finance Ltd. = No mode

BD Autocars = No mode

Jamuna Oil = No mode

Square Pharmaceuticals Ltd. = No mode Modes of June Social Investment Bank Ltd. = No mode

Lanka Bangla Finance Ltd. = No mode


Jamuna Oil = No mode

Square Pharmaceuticals Ltd. = No mode Mode is calculated by determining the value repeated most. Geometric Mean:

Formula: N

XantiMG ∑=

loglog..

Here, =..MG Geometric Mean X = Observations N = Number of Observation Geometric Mean of Prices Lanka Bangla Finance Ltd. of May:

Log List of Prices Price, X log X 115.60 121.90 127.10

2.0630 2.0860 2.1041

Page | 17

131.80 135.10 137.30 136.70

2.1199 2.1307 2.1377 2.1358

∑ = 7771.14log X

7771.14log.. antiMG =

110.2log.. antiMG = 1269.129.. =MG Geometric Means: Geometric Means of May Social Investment Bank Ltd. = 335.6996




Square Pharmaceuticals Ltd. = 4655.7677 Geometric Means of June Social Investment Bank Ltd. = 391.4397




Square Pharmaceuticals Ltd. = 5280.2190 Harmonic Mean

Formula: ∑ ⎟

⎠⎞

⎜⎝⎛

=

X

NMH1

..

Here, =..MH Harmonic Mean X = Observations N = Number of Observation

Page | 18

Harmonic Mean of Prices of Lanka Bangla Finance Ltd. of June:

X1 list

X, Price X

1

175.6 181.1 182.2 191.1 210.9 205.2 195.3

0.0057 0.0055 0.0055 0.0052 0.0047 0.0049 0.0051

∑ =⎟

⎠⎞

⎜⎝⎛ 0367.01

X

∑ ⎟

⎠⎞

⎜⎝⎛

=

X

NMH1

..

0367.07.. =MH

8755.190.. =MH Harmonic Means: Harmonic Means of May Social Investment Bank Ltd. = 335.6849




Square Pharmaceuticals Ltd. = 4655.4982 Harmonic Means of June Social Investment Bank Ltd. = 390.4852





Page | 19

Business Statistics Chapter 5: Measures of Variation Range Formula: SLRange −= L = Largest Value S = Smallest Value Range of the prices of BD Autocars Ltd. of May: Range = 207.50 – 196.00 = 11.50 Ranges: Ranges of May Social Investment Bank Ltd. = 11.00


BD Autocars = 11.50

Jamuna Oil = 8.90

Square Pharmaceuticals Ltd. = 181.00 Ranges of June Social Investment Bank Ltd. = 73.75


BD Autocars = 10.25

Jamuna Oil = 20.50

Square Pharmaceuticals Ltd. = 232.50 Inerquartile Range or Quartile Deviation Inerquartile Range or Quartile Deviation can’t be determined by ‘Ungrouped Data’.

Page | 20

Average Deviation

Formula: N

MedXDA Med

∑ −=

|.|.. .)(

Coefficient of Median

DADA Med.... .)( =

Here, ..DA = Average Deviation X = Observation .Med = Median N = Number of Observations Average Deviation of the Prices of BD Autocars Ltd. of June: Here,

Median = 191.50

Average Deviation Chart X ,

Price |.| MedX −

190 191 190

191.5 190

187.75 181.25

1.5 0.5 1.5 0

1.5 3.75 10.25

∑ =− 19|.| MedX

N

MedXDA Med

∑ −=

|.|.. .)(

7

19.. .)( =MedDA

7142.2.. .)( =MedDA Average Deviations: Average Deviations of May Social Investment Bank Ltd. = 2.2900



Page | 21

Jamuna Oil = 2.1429

Square Pharmaceuticals Ltd. = 30.6786 Average Deviations of June Social Investment Bank Ltd. = 38.6071



Jamuna Oil = 5.9429

Square Pharmaceuticals Ltd. = 42.8571 Coefficient of Average Deviation of the Prices of Jamuna Oil Ltd. of May: Here, A.D. = 2.1429 Median = 263.20

∴Coefficient of 20.263

1429.2.. .)( =MedDA

0081.0= Coefficients of Average Deviations: Coefficients of Average Deviations of May Social Investment Bank Ltd. = 0.0068



Jamuna Oil = 0.0081

Square Pharmaceuticals Ltd. = 0.0066 Coefficients of Average Deviations of June Social Investment Bank Ltd. = 0.0896



Jamuna Oil = 0.0295


Page | 22

Standard Deviation

Formula: N

XX∑ −=

2)(σ ; (Deviation taken from Actual Mean)

Here, =σ Standard Deviation =X Observation =X Average =N Number of Observations

22

⎟⎟⎠

⎞⎜⎜⎝

⎛−= ∑∑

Nd

Nd

σ ; (Deviation taken from Assumed Mean)

Here, =σ Standard Deviation =d AX − =A Assumed Mean =N Number of Observations Standard deviation taken from Actual Mean of the Prices of Jamuna Oil Ltd. of June: Here,

Average = 207.2429

Standard Deviation Chart X ,

Prices 2)( XX −

210 206.9 204.3 201.3 204.9 201.5 221.8

7.60180.11768.6604

35.31765.4890

32.9804211.9104

∑ =− 0771.302)( 2XX

70771.302

=∴σ

5692.6=σ Standard Deviations:

Page | 23

Standard Deviations of May Social Investment Bank Ltd. = 3.1408



Jamuna Oil = 2.7570

Square Pharmaceuticals Ltd. = 49.8210 Standard Deviations of June Social Investment Bank Ltd. = 27.2943



Jamuna Oil = 6.5692

Square Pharmaceuticals Ltd. = 64.0233 Standard deviation taken from Assumed Mean of the Prices of Square Pharmaceuticals Ltd. of May: Take, Assumed Mean = 4660.50 Assumed Mean Chart

X , Prices

,d AX −

2d

4552.25 4649.00 4679.50 4660.50 4657.25 4660.50 4733.25

-108.25 -11.50 19.00 0.00 -3.25 0.00 72.75

11718.0625 132.25

361 0

10.5625 0

5292.5625

25.31−=∑d ∑ = 4375.175142d

2

725.31

74375.17514

⎟⎠⎞

⎜⎝⎛ −−=∴σ

=σ 49.9760 Standard Deviations Standard Deviations of May

Page | 24

Social Investment Bank Ltd. = 3.1408



Jamuna Oil = 2.7570

Square Pharmaceuticals Ltd. = 49.9760 Standard Deviations of June Social Investment Bank Ltd. = 27.2943



Jamuna Oil = 6.5692

Square Pharmaceuticals Ltd. = 64.0233 Combined Standard Deviation

Formula: 21

222

211

222

211

12 NNdNdNNN

++++

=σσ

σ

Here, 1N = Number of observations of the first group =2N Number of observations of the second group =1σ Standard Deviation of the first group =2σ Standard Deviation of the second group =1d || |121 XX −

=2d || |122 XX −

=1X Average of the first group =2X Average of second group 12X = Combined Average of the two groups Combined Standard Deviation of the Prices of Square Pharmaceuticals Ltd.: Here, 1N = 7 =2N 7 =1σ 49.8210

Page | 25

=2σ 64.0233 12X = 5292.25

=1X 4656.04 =2X 5280.6071 =1d 312.2836 =2d 312.2835

21

222

211

222

211

12 NNdNdNNN

++++

=σσ

σ

=12σ77

2835.31272836.31270233.6478210.497 2222

+×+×+×+×

5084.31712 =σ Combined Standard Deviations Social Investment Bank Ltd. = 34.3607




Square Pharmaceuticals Ltd. = 317.5084 Coefficient of Variation

Formula: 100.. ×=X

VC σ

Here, =..VC Coefficient of Variation σ = Standard Deviation X = Arithmetic Mean of the observations Coefficient of Variation of the prices of Square Pharmaceuticals Ltd. of June: Here,

σ = 64.0233 X = 5280.6071

1006071.5280

0233.64.. ×=∴ VC

2124.1=

Page | 26

Coefficients of Variations Coefficients of Variations of May Social Investment Bank Ltd. = 0.9356



Jamuna Oil = 1.0519

Square Pharmaceuticals Ltd. = 1.0700 Coefficients of Variations of June Social Investment Bank Ltd. = 6.9559



Jamuna Oil = 3.1698

Square Pharmaceuticals Ltd. = 1.2124 Combined Coefficients of Variations (Combined Standard Deviation×100/Combined Arithmetic Mean) Social Investment Bank Ltd. = 9.4384





Business Statistics Chapter 7: Correlation Analysis Scatter Diagram Here the scatter diagrams of the share prices are drawn.

Page | 27

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Page | 29

Page | 30

Karl Pearson’s Coefficient of Correlation Actual Mean Method

Formula: ∑∑

∑−−

−−=

22 )()(

))((

YYXX

YYXXr

The above formula can be written as:

∑ ∑∑=

22 yx

xyr

Where, )( XXx −= and )( YYy −= Here, =X Observation from the first group =X Arithmetic Mean of the first group =Y Observation from the second group =Y Arithmetic Mean of the second group Calculation of Correlation Coefficient of the prices of Social Investment Bank Ltd. (of May and June) Take X as the prices of May and take Y as the prices of June.

Page | 31

Working Day

May Prices,

X xXX ),( −

2x June

Prices, Y y

YY ),( − 2y xy

1 341.0000 +5.2900 27.9841 361.7500 -30.6429 938.9873 -162.1009 2 338.0000 +2.2900 5.2441 357.2500 -35.1429 1235.0234 -80.4772 3 335.7500 +0.0400 0.0016 369.0000 -23.3929 547.2278 -0.9357 4 336.0000 +0.2900 0.0841 431.0000 +38.6071 1490.5082 +11.1961 5 334.0000 -1.7100 2.9241 414.0000 +21.6071 466.8668 -36.9481 6 335.2500 -0.4600 0.2116 414.5000 +22.1071 488.7239 -10.1693 7 330.0000 -5.7100 32.6041 399.2500 +6.8571 47.0198 -39.1540

∑ =X 2350.0000

∑ =x 0.0300

∑ =2x

69.0537 ∑ =Y

2746.7500 ∑ =y -0.0003

∑ =2y 5214.3571

∑ =xy -318.5893

∑ ∑∑=

22 yx

xyr

3571.52140537.69

5893.318×

−=r

5309.0−=r Correlation Coefficients between May and June Prices: Social Investment Bank Ltd. = -0.5309


BD Autocars = -0.6982

Jamuna Oil = -0.5775

Square Pharmaceuticals Ltd. = -0.9390 Assumed Mean Method

Formula: ( ) ( )∑ ∑∑ ∑∑ ∑ ∑

−−

−=

2222yyxx

yxyx

ddNddN

ddddNr

Here, r = Correlation Coefficient N = Number of Observations xd = xAX − X = Observation of the first group xA = Assumed Mean of the first group yd = yAY − Y = Observation of the second group yA = Assumed Mean of the second group

Page | 32

Calculation of Correlation Coefficient of the prices of Lanka Bangla Finance Ltd. (of May and June): Take X as the prices of May and take Y as the prices of June.

Working Day

May Prices,

X xd

X )80.131( −

2xd

June Prices,

Y yd

Y ),10.191( −

2yd yxdd

1 115.60 -16.20 262.44 175.60 -15.50 240.25 -3982.05 2 121.90 -9.90 98.01 181.10 -10.00 100.00 -990.00 3 127.10 -4.70 22.09 182.20 -8.90 79.21 -372.287 4 131.80 0 0 191.10 0 0 0 5 135.10 +3.30 10.89 210.90 +19.80 392.04 +1293.732 6 137.30 +5.50 30.25 205.20 +14.10 198.81 +1093.455 7 136.70 +4.90 24.01 195.30 +4.20 17.64 +86.436

∑ =X 905.50

∑ =xd -17.10

∑ =2xd

447.69

∑ =Y

1341.40

∑ =yd 3.70

∑ =2yd

1027.95 ∑ =yxdd-2780.714

22 )70.3()95.10277(}10.17()69.4477(

)70.310.17()714.27807(−×−−×

×−−−×=∴ r

2949.4−=∴ r Correlation Coefficients between May and June Prices: Social Investment Bank Ltd. = 44.9742

Lanka Bangla Finance Ltd. = -4.2949



Square Pharmaceuticals Ltd. = -0.5551 Probable Error of Coefficient of Correlation

Formula: NrrEP

216745.0.. −=

Here, rEP .. = Probable error of Coefficient of Correlation r = Correlation Coefficient N = Number of observations Probable Error of Coefficient of Correlation of the prices of May and June of BD Autocars Ltd.:

Page | 33

7

)2148.10(16745.0..2−

×=rEP

3457.26.. −=rEP Probable Errors of Correlation Coefficients of the share prices of May and June: Social Investment Bank Ltd. = -515.4008

Lanka Bangla Finance Ltd. = -4.4477

BD Autocars = -26.3457


Square Pharmaceuticals Ltd. = 0.1764 Rank Correlation Coefficient

Formula: NN

Dor

NND

R−

−−

−= ∑∑3

2

2

2 61

)1(6

1

Here, R = Rank Correlation Coefficient D = 21 RR − 1R = Rank of observation of the first group 2R = Rank of observation of the second group N = Number of Observations Rank Correlation Coefficient of the prices of BD Autocars Ltd. of May and June: Take, 1R as the Prices of May and 2R as the Prices of June

Working Days May Prices

Rank for May Prices,

1R June Prices

Rank for June Prices,

2R 2

221 ,)(

D

RR −

1 202.25 4 190.00 1 9 2 203.00 5 191.00 4 1 3 196.50 2 190.00 2 0 4 199.75 3 191.50 5 4 5 196.00 1 190.00 3 4 6 203.75 6 187.75 7 1 7 207.50 7 181.25 6 1

10=N ∑ = 202D

Page | 34

NN

DR

−−=∴ ∑

3

261

77

201 3 −−=∴R

6429.0=∴R Rank Correlation Coefficients: Social Investment Bank Ltd. = -0.5000



Jamuna Oil = 0.0000

Square Pharmaceuticals Ltd. = -0.7500

Business Statistics Chapter 8: Regression Analysis Regression Equation Formula: Regression Equation of X on Y: bYaX += To determine the values of a and b the following two normal equations are

to be solved simultaneously:

∑ ∑∑∑ ∑

+=

+=2YbYaXY

YbNaX

Regression Equation of Y on X:

bXaY += To determine the values of a and b the following two normal equations are

to be solved simultaneously:

∑ ∑∑∑ ∑

+=

+=2XbXaXY

XbNaY

Regression Equation of the prices of Jamuna Oil Ltd.: May Prices, X 2X June Prices, Y 2Y XY

265.50 70490.25 210.00 44100.00 55755.00

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263.30 69326.89 206.90 42807.61 54476.77264.40 69907.36 204.30 41738.49 54016.92263.20 69274.24 201.30 40521.69 52982.16261.00 68121.00 204.90 41984.01 53478.90260.60 67912.36 201.50 40602.25 52510.90256.60 65843.56 221.80 49195.24 56913.88

∑ = 60.1834X ∑ = 66.4808752X 70.1450=∑Y 29.3009492∑ =Y 53.380134=∑ XY

From this, using the formula, we can say that- 1834.60 = 7a + 1450.70b 380134.53 = 1450.70a + 300949.29b From these equations, we get- a = 312.3160 b = -0.2424 Then the regression equation of the prices of May on the prices of June of Jamuna Oil Ltd. is – X = 312.3160 – 0.2424Y Regression equations: Price of May on Price of June Social Investment Bank Ltd. → X = 359.6885 – 0.0611Y

Lanka Bangla Finance Ltd. → X = 23.9350 + 0.5504Y

BD Autocars Ltd. → X = 355.2364 – 0.8157Y

Jamuna Oil Ltd. → X = 312.3160 – 0.2424Y

Square Pharmaceuticals Ltd. → X = 8514.7970 – 0.7307Y Price of June on Price of May Social Investment Bank Ltd. → Y = 1941.1260 – 4.6132X

Lanka Bangla Finance Ltd. → Y = 11.7540 + 1.3905X

BD Autocars Ltd. → Y = 309.0680 – 0.5977X

Jamuna Oil Ltd. → Y = 567.8763 – 1.3760X

Square Pharmaceuticals Ltd. → Y = 10898.4480 – 1.2066X

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Regression Equation using Arithmetic Mean Formula: )( XXbYY yx −=−

)( YYbXX xy −=− Here, X = Observation of the first group Y = Observation of the second group X = Arithmetic Mean of the first group Y = Arithmetic Mean of the second group

∑∑= 2x

xybyx and

∑∑= 2y

xybxy

x = XX − y = YY − Regression Equation of the prices of Square Pharmaceuticals Ltd.:

Working Day

May Prices, X XXx −= 2x

June Prices, Y YYy −= 2y xy

1 4552.25 -103.7860 10771.4745 5397.25 5397.25 13605.56 -12105.9002 4649.00 -7.0357 49.5013 5295.50 5295.50 221.7972 -104.7820 3 4679.50 23.4643 550.5727 5293.25 5293.25 159.8418 296.6556 4 4660.50 4.4643 19.9298 5292.25 5292.75 135.5561 51.9770 5 4657.25 1.2143 1.4745 5273.75 5273.75 47.0204 -8.3265 6 4660.50 4.4643 19.9298 5247.50 5247.50 1096.0830 -147.8000 7 4733.25 77.2143 5962.0459 5164.75 5164.75 28688.7300 -8945.8300

Total 32592.25 0.0000 17374.9300 36964.25 0.0000 28688.73 -20963.96

Here, 25.32592=X and 6071.5280=Y

9300.17374

96.20963−=yxb

2066.1=yxb Then the equation of the price of June on price of May of Square Pharmaceuticals Ltd. is- )6071.5280(2066.1)25.32592( −=− XY Or, Y = 10898.4480 – 1.2066X Regression equations: Price of May on Price of June Social Investment Bank Ltd. → X = 359.6885 – 0.0611Y

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Lanka Bangla Finance Ltd. → X = 23.9350 + 0.5504Y

BD Autocars Ltd. → X = 355.2364 – 0.8157Y

Jamuna Oil Ltd. → X = 312.3160 – 0.2424Y

Square Pharmaceuticals Ltd. → X = 8514.7970 – 0.7307Y Price of June on Price of May Social Investment Bank Ltd. → Y = 1941.1260 – 4.6132X

Lanka Bangla Finance Ltd. → Y = 11.7540 + 1.3905X

BD Autocars Ltd. → Y = 309.0680 – 0.5977X

Jamuna Oil Ltd. → Y = 567.8763 – 1.3760X

Square Pharmaceuticals Ltd. → Y = 10898.4480 – 1.2066X

Chapter 3 Report Ending

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Conclusion It was really a tough job to complete this report without any error. But our group work made this possible to make this without any error. We are thanking again to the Almighty, you who gave us such an assignment and those who helped us and made this report more beautiful and complete in information.

Appendix

We have collected our all the data from newspaper. We have attached the copies of the paper with this report.

statistical analysis on stock prices

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