econometric assign1

7/29/2019 Econometric Assign1

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Regression Analysis using STATA

Submitted by

Prashant Jain (547)

Master of Business Economics

Batch of 2013


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Introduction

The basic objective of this work is to get familiar with the statistical tool called stata and

also understand the use of available databases from PROWESS and Capital Line apart from

developing basic understanding of regression.

Regression has been chosen as a subject of this analysis. In this particular study , data for

sales , Profit after tax (PAT) , earnings per share (EPS) has been taken.

Here, PAT will be regressed w.r.t Sales.

We will then try to understand the significance of values of , & R2.

Comparative study is done to understand how similarly or differently regression relationship

between PAT & Sales of two popular FMCG firms vary over the years.

Regression Analysis of Dabur India Ltd.

Data has been taken for past 10 years.

DATA:

Year PAT Sales EPS

2011 471.41 3264.37 2.52

2010 433.33 2855.96 4.65

2009 373.55 2396.16 4.02

2008 316.77 2083.4 3.41

2007 252.08 1600.43 2.72

2006 189.08 1342.79 3.05

2005 148.01 1226.23 4.83

2004 101.2 1082.58 3.28

2003 84.92 1158.93 2.86

2002 65.03 1102.58 2.23

Source : Capital Line database ,www.capitaline.com
http://www.capitaline.com/http://www.capitaline.com/http://www.capitaline.com/http://www.capitaline.com/


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Graphical Interpretation:

For Dabur , relationship between PAT and Sales is more or less linear.

Scatter plot of the estimated values and fitted regression line is not representing a huge

difference.

100

200

300

400

500

PAT

1000 1500 2000 2500 3000 3500

Sales

PAT Fitted values


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Mathematical Interpretation using STATA

Output from Stata for Regression between Sales & PAT:

-------------------------------------------------------------------------------------------------

-----------------------------------

name:

log: C:\Users\Prashant Jain\Desktop\Ecotrix\DaburOutput.log

log type: text

opened on: 1 Feb 2012, 15:56:57

. describe

Contains data from C:\Users\Prashant Jain\Desktop\Ecotrix\DaburProfit.dta

obs: 10

vars: 3 1 Feb 2012 15:56

size: 160 (99.9% of memory free)

-------------------------------------------------------------------------------------------------

-----------------------------------

storage display value

variable name type format label variable label

-------------------------------------------------------------------------------------------------

-----------------------------------

PAT float %8.0g

Sales float %8.0g

EPS float %8.0g

-------------------------------------------------------------------------------------------------

-----------------------------------

Sorted by:


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. summarize

Variable | Obs Mean Std. Dev. Min Max

-------------+--------------------------------------------------------

PAT | 10 243.538 148.9451 65.03 471.41

Sales | 10 1811.343 794.705 1082.58 3264.37

EPS | 10 3.357 .8823964 2.23 4.83

. regress PAT Sales

Source | SS df MS Number of obs = 10

-------------+------------------------------ F( 1, 8) = 153.97

Model | 189800.193 1 189800.193 Prob > F = 0.0000

Residual | 9861.6202 8 1232.70252 R-squared = 0.9506

-------------+------------------------------ Adj R-squared = 0.9444

Total | 199661.813 9 22184.6459 Root MSE = 35.11

------------------------------------------------------------------------------

PAT | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

Sales | .1827347 .0147266 12.41 0.000 .1487752 .2166943

_cons | -87.45728 28.89325 -3.03 0.016 -154.0852 -20.82933

------------------------------------------------------------------------------


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. regress EPS PAT Sales


-------------+------------------------------ F( 2, 7) = 0.74

Model | 1.22758031 2 .613790157 Prob > F = 0.5096

Residual | 5.78002978 7 .82571854 R-squared = 0.1752

-------------+------------------------------ Adj R-squared = -0.0605

Total | 7.0076101 9 .778623344 Root MSE = .90869

------------------------------------------------------------------------------

EPS | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

PAT | .0100804 .0091504 1.10 0.307 -.0115569 .0317178

Sales | -.0016429 .001715 -0.96 0.370 -.0056982 .0024124

_cons | 3.877828 1.095279 3.54 0.009 1.287905 6.46775

------------------------------------------------------------------------------

. twoway (line PAT Sales)

. graph save Graph "C:\Users\Prashant Jain\Desktop\Ecotrix\Graphdabur.gph"

(file C:\Users\Prashant Jain\Desktop\Ecotrix\Graphdabur.gph saved)

. twoway (line PAT Sales) (scatter PAT Sales)

. graph save Graph "C:\Users\Prashant Jain\Desktop\Ecotrix\Graphdab2.gph"

(file C:\Users\Prashant Jain\Desktop\Ecotrix\Graphdab2.gph saved)


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Theoretical Interpretation

The above mentioned regression analysis using STATA was done to recognize the regression pattern

and relationship between PAT of Dabur and Sales of Dabur for past 10 years.

From the data given and also by business logic , we can say Profit after Tax is directly and

almost linearly related to Sales of a firm (in this case Dabur).

If we denote Profit after tax of Dabur by PD

And let Sales of Dabur be denoted by SD

Then according to linear regression model:

PD= S

D

Value of Regression Parameters.

After processing data through STATA, we have following value of regression parameters:

Estimated value of -87.45728

Estimated value of .1827347

Estimated value of R2 = 0.9506

* All values taken at 95% confidence interval.

Analysis of

From PD= S

D

We know PD = -87.45728 + .1827347 SD

This shows us that when the firm will suffer a condition of zero sales, PAT will be non-zero but

a negative quantity . This means the firms will be suffering losses. This is because even when

the firm is having no sales and also production is at halt , it still suffers some amount of

fixed cost of production.

Analysis of

From PD= S

D

Taking a first degree derivative on both sides.

PD/S

D= 0.182

This indicates that 1 unit change in sales can lead to 0.182 change in PAT.

Value of R2 is 0.9506 for this.


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Regression Analysis for Proctor & Gamble

Data has been taken for past 10 years.

DATA:

Year PAT Sales EPS

2011 150.88 1001.91 42.83

2010 179.77 904.45 51.65

2009 178.85 774.22 51.28

2008 131.41 646.01 37.09

2007 89.82 539.64 24.27

2006 139.51 567.59 39.47

2005 124.61 684.71 32.78

2004 92.17 577.24 25.78

2003 68.04 442.39 28.88

2002 77.01 409.42 35.59

Source : Capital Line database ,www.capitaline.com

Just looking at the data of P&G we can say that unlike Dabur India Ltd., Sales & PAT for P&G is

suffering a fluctuation.
http://www.capitaline.com/http://www.capitaline.com/http://www.capitaline.com/http://www.capitaline.com/


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Graphical Interpretation:

For Proctor & Gamble , relationship between PAT and Sales is not exactly linear.

Scatter plot of the estimated values and fitted regression line is representing a huge

difference.

50

100

150

200

400 600 800 1000

Sales

PAT Fitted values

P & G


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Mathematical Interpretation using STATA

-------------------------------------------------------------------------------------------------

-----------------------------------

name:

log: C:\Users\Prashant Jain\Desktop\Ecotrix\P&G.log

log type: text

opened on: 1 Feb 2012, 16:20:05

. describe

Contains data from C:\Users\Prashant Jain\Desktop\Ecotrix\PnG.dta

obs: 10

vars: 3 1 Feb 2012 16:19

size: 160 (99.9% of memory free)

-------------------------------------------------------------------------------------------------

-----------------------------------

storage display value

variable name type format label variable label

------------------------------------------------------------------------------------------------------------------------------------

PAT float %8.0g

Sales float %8.0g

EPS float %8.0g

-------------------------------------------------------------------------------------------------

-----------------------------------

Sorted by:

. summarize

Variable | Obs Mean Std. Dev. Min Max

-------------+--------------------------------------------------------

PAT | 10 123.207 40.34835 68.04 179.77


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Sales | 10 654.758 191.5596 409.42 1001.91

EPS | 10 36.962 9.616517 24.27 51.65

. regress PAT Sales


-------------+------------------------------ F( 1, 8) = 18.72

Model | 10265.3727 1 10265.3727 Prob > F = 0.0025

Residual | 4386.53304 8 548.31663 R-squared = 0.7006

-------------+------------------------------ Adj R-squared = 0.6632

Total | 14651.9058 9 1627.98953 Root MSE = 23.416

------------------------------------------------------------------------------

PAT | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

Sales | .176304 .0407465 4.33 0.003 .0823424 .2702656

_cons | 7.770545 27.68766 0.28 0.786 -56.07732 71.61841

------------------------------------------------------------------------------

. twoway (line PAT Sales)

. twoway (line PAT Sales) (lfit PAT Sales)


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Comparative Analysis of Dabur & P&G:

Dabur P&G

Value of = -87.45728Value of = .1827347

Value of = 7.770545Value of = .176304

R2= .9506 R2 = .7006

Regression Eq.P = -87.45 + 0.182S

Regression Eq.P = 7.77 + 0.176S

Comparing the above data tells us that , In case of Dabur linear regression model is a good fitto represent relationship and pattern between PAT & Sales. Value of 0.9506 of coefficient of

determination is a statistically sufficient to explain a linear relationship between profit and

Sales of Dabur.

In case of P&G , value of coefficient of determination is 0.7 which is relatively far from 1.

So it is difficult to portray linear regression model as goodness of fit in this case

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