In this coursework, Johnson & A ; Johnson dataset between the old ages 1980 to 2009 utilizing a monthly time-series is used for this analysis. The Microfit Software is used in order to finish the series being used for the OLS calculators. First, the nominal stock returns and the growing rate of industrial production of the dataset are generated by utilizing their logarithms. Second, the belongingss of the dataset are described utilizing graphs, descriptive statistics ( COR NSR, GIND, and FED ) . Third, the relationship and reading of the two variables are examined. Fourthly, utilizing the assurance interval attack a remark is made to find whether to reject or make non reject the void hypothesis and t-test attack is used as a verification of the consequences. Fifthly, the OLS was re-estimated to find what happened during the fiscal crisis in Sept 2007.The relationship between the stock returns and involvement rate was explained utilizing Muradoglu as verification of the consequences obtained. Last, a comparing was made between theoretical account 1 and model 2 ( where another variable was added to the arrested development ) and a joint hypothesis was found utilizing F-statistics attack.

1. Generate THE SERIES

( I ) In order to general the nominal stock return of Johnson & A ; Johnson ( S ) utilizing Microfit package we need to happen the Log of the stock monetary value.

Measure one: Finding the log of S

LS = Log ( S )

Measure two: DLS ( Nominal Stock Return )

DLS=NSR=LS-LS ( -1 )

( two ) Using Microfit we can cipher the growing rate of industrial production ( IP )

Measure one: Finding log of IP

LIP = Log ( IP )

Measure two: DLIP = FIND = LIP- LIP ( -1 )

2. Describing the belongingss of the dataset.

COR NSR GIND FED

Statisticss

NSR

GIND

Federal

Mean

1.02

0.16

6.02

Standard Error

0.25

0.04

0.20

Median

1.43

0.21

5.50

Standard Deviation

4.84

0.70

3.79

Sample Variance

23.39

0.50

14.35

Kurtosis

0.36

4.24

1.62

Lopsidedness

-0.30

-0.93

1.07

Scope

29.74

6.13

18.98

Minimum

-13.49

-4.00

0.12

Maximum

16.24

2.12

19.10

Sum

368.88

55.99

2167.85

Count

360

360

360

Correlation matrix

DLS DLIP

DLS 1.0000 -.081060

DLIP -.081060 1.0000

The correlativity of the nominal stock returns is absolutely correlated with itself. The correlativity coefficient of NSR and GIND is -0.081060 there is a negative correlativity between these.

The figure above shows the descriptive statistics for Nominal stock returns, federal financess and logarithm of US production index.

Mean: The mean return for the nominal stock return for 1980 Feb to 2009 Dec falls on 1.02 % , this showed an expected return value for the stock of Johnson & A ; Johnson for the period under reappraisal. The scope for the monthly nominal returns was 29.74 % , exposing a minimal negative return of 13.49 % ( in Feb 2000 ) and a maximal positive return of 16.24 % ( Apr 1986 ) . The pecuniary enterprises of the FED for the period was on a monthly norm of 6.02 % for the period under reappraisal, with a minimal rate of 0.12 % ( the bead below 1 % started from the month of Oct 2008 boulder clay it recorded a floor of 0.12 % in Oct 2009 ) in promotion of the FED ‘s expansionary policy to revive the planetary economic crisis eminent at that clip. However, the maximal figure of 19.10 % was recorded in Jun 1981.

Variance & A ; Standard Deviation: Both measures the grade of scattering of our informations set from its expected value. This besides gives us an penetration into the degree of discrepancy or volatility of our given informations. The discrepancies for the NSR, GIND and FED are 23.39, 0.50, and 14.35 severally. The standard divergence on the other manus, could be derived by happening the square root of the discrepancy. The standard divergence of Johnson & A ; Johnson is higher than federal financess.

Lopsidedness and Kurtosis: This besides measures the volatility of the information set around the average value, and which could be described from the form or the degree of lopsidedness of the normal distribution of each parametric quantity. The kurtosis on the other manus, measures the peakedness of our distribution. For a normal distribution the kurtosis is 3 our distribution our value for NSR is 0.36 GIND 4.24 FED 1.62

## Histogram and Normal curve for variable DLS

Frequency

Deciliter

0

2

4

6

8

10

-0.1848

-0.1449

-0.105

-0.06507

-0.02514

0.01478

0.0547

0.09462

0.1345

0.1745

## Histogram for the Nominal Stock Returns Data

The above diagram shows the histogram and normal distribution for the Nominal Stock Returns of Johnson & A ; Johnson for the sample period chosen. This showed that the average figure of 1.02 % fell within the Centre of the bell-shaped curve which is neither skewed to the right nor skewed to the left.

Second

Federal

Calendar months

0

20

40

60

80

1980M1

1983M5

1986M9

1990M1

1993M5

1996M9

2000M1

2003M5

2006M9

2009M12

The diagram above shows the graph nominal stock monetary value of Johnson & A ; Johnson from 1980-2009. The stock monetary value shows a tendency and variableness over the old ages proposing that stock monetary values are non stationary. The graph shows a gradual addition in stock monetary values until 1993 where there was an underperformance. In mid 1994 there was another gradual addition until a fast bead in 2000 due to the dividing it does 2 for 1 split on its returns. After this period it kept fluctuating and had a monolithic autumn in 2008 due to the fiscal crises of the universe impacting all companies.

Deciliter

DLIP

Calendar months

-0.05

-0.10

-0.15

0.00

0.05

0.10

0.15

0.20

1980M1

1983M5

1986M9

1990M1

1993M5

1996M9

2000M1

2003M5

2006M9

The diagram above shows the secret plan of Nominal Stock return against Growth Rate of Industrial Production. The Nominal Stock Return shows a fluctuating line it goes up and down and this could be due to the factors that affect Johnson & A ; Johnson stock during the old ages ( factors such as Risk, Beta etc ) . Using the figures below it could be seen that the line goes from positive to negative depending on the twelvemonth of the stock.

hypertext transfer protocol: //www.1stock1.com/1stock1_235.htm

Johnson & A ; Johnson ( JNJ ) Annually Tax returns

A A A A Year

A Beginning Price

A Ending Price

A Gain or Loss

A Percent Gain or Loss

1975

80.875

89.75

8.875

10.97 %

1976

89.75

78.00

-11.75

-13.09 %

1977

78.00

76.75

-1.25

-1.60 %

1978

76.75

73.75

-3.00

-3.91 %

1979

73.75

79.25

5.50

7.46 %

1980

79.25

99.75

20.50

25.87 %

1981

99.75

111.375*

11.625

11.65 %

1982

37.125

49.625

12.50

33.67 %

1983

49.625

40.875

-8.75

-17.63 %

1984

40.875

36.125

-4.75

-11.62 %

1985

36.125

52.625

16.50

45.67 %

1986

52.625

65.625

13.00

24.70 %

1987

65.625

74.875

9.25

14.10 %

1988

74.875

85.125

10.25

13.69 %

1989

85.125

118.75*

33.625

39.50 %

1990

59.375

71.75

12.375

20.84 %

1991

71.75

114.50

42.75

59.58 %

1992

114.50

101.00*

-13.50

-11.79 %

1993

50.50

44.875

-5.625

-11.14 %

1994

44.875

54.75

9.875

22.01 %

1995

54.75

85.50

30.75

56.16 %

1996

85.50

99.50*

14.00

16.37 %

1997

49.75

65.875

16.125

32.41 %

1998

65.875

83.875

18.00

27.32 %

1999

83.875

93.25

9.375

11.18 %

2000

93.25

105.0625

11.8125

12.67 %

2001

105.0625

118.20*

13.1375

12.50 %

2002

59.10

53.71

-5.39

-9.12 %

2003

53.71

51.66

-2.05

-3.82 %

2004

51.66

63.42

11.76

22.76 %

2005

63.42

60.10

-3.32

-5.23 %

2006

60.10

66.02

5.92

9.85 %

2007

66.02

66.70

0.68

1.03 %

2008

66.70

59.83

-6.87

-10.30 %

2009

59.83

64.41

4.58

7.66 %

3.OLS Calculators

NSRt= 0.0052061+ 0.8457A-10 -3 FEDt+ Aµ

I. )

Ordinary Least Squares Estimation

## ******************************************************************************

Dependent variable is DLS

359 observations used for appraisal from 1980M2 to 2009M12

## ******************************************************************************

Regressor Coefficient Standard Error ( s.e ) T-Ratio [ Prob ]

CON.0052061.0048031 1.0839 [ .279 ]

FED.8457E-3.6780E-3 1.2473 [ .213 ]

R-Squared.0043389 R-Bar-Squared.0015499

S.E. of Regression.048382 F-stat. F ( 1, 357 ) 1.5557 [ .213 ]

Mean of Dependent Variable.010280 S.D. of Dependent Variable.048419

Residual Sum of Squares.83566 Equation Log-likelihood 578.8838

Akaike Info. Criterion 576.8838 Schwarz Bayesian Criterion 573.0004

DW-statistic 1.5755

## SLOPE AND INTERCEPT

The value of the intercept between NSR and FED in this arrested development is positive bespeaking an addition in NSR will besides take to an addition in the intercept ( I± ) . The relationship between NSR and FED ( I? incline ) is besides positive ( 0.0008457 ) bespeaking an addition in Federal financess in a state it will increase nominal stock return of Johnson & A ; Johnson.

If FED increases by 1 % we expect NSR to increase by 0.8457*10-3 all other things being equal ( Gurajati 2003 pp 169-173 ) .

## STANDARD ERROR

The s.e measures how confident one is in the coefficient estimation obtained. The value of the s.e is little for I± and I? demoing that the value of these coefficients is likely to be precise on norm for this peculiar set of sample. The smaller the value of s.e ( 0.048382 ) the closer the existent NSR is to its estimated value from the arrested development theoretical account.

## T_RATIO AND P-VALUE

The t-ratio/value is the ratios of the estimated coefficients to their standard mistakes whilst the p-value is defined as the lowest important degree at which a void hypothesis can be rejected. ( Gujarati 2008 ) . The value of t-ratio for I± is 1.0839 I? 1.2473 whilst the p-value for I± is 0.279 and I? is 0.213. The p-value and the t-value can non be important unless tested against the void hypothesis of the arrested development.

## SUM OF SQUARED RESIDUALS

In this arrested development, the R2 value is 0.0043389 which informs us that 0.484 % of the fluctuation in nominal stock returns is explained by the fluctuation in growing rate of industrial production. The R2 value is low for this arrested development.

two ) Exploitation CONFIDENCE INTERVAL APPROACH

No of observations = 359

K = 2

I? = 0.0008457

df ( grade of freedom ) ( n-k ) = ( 359 – 2 ) = 357

E‘ = 5 % significance degree

Assurance Interval ( C.I ) = ( 1-E‘ ) *100

= 95 %

C.I = I? A± C A- s.e ( I? )

T ( n-k ) , ( E‘/2 ) = T ( 357,0.05/2 ) = 1.960

0.0008457 A± 1.960*0.0006780

( -4.8318A-10-3, 2.17458A-10-3 )

Using the computed value of C.I 0.00021745 & lt ; 1.960, we do non reject H0: I? = 0. The value lies within the assurance interval. I’ is significantly different from nothing at the 5 % degree of significance.

## Using the T-test attack

Using Ho: I? = 0

I? -I?* = T

s.e ( I? )

t = 0.0008457-0 = 1.2473

0.0006780

Since 1.2473 & lt ; 1.960, we do non reject H0: I? = 0. The value lies within non-rejection part. The consequence significance obtained of the assurance interval and the t-test attack is the same. The H0: I?0 is non rejected.

three. ) OLS ESTIMATOR 1980 M2 to 2007M7

NSRt= 0.0068996 + 0.6526 A- 10 -3 FEDt + Aµ

Ordinary Least Squares Estimation

## *******************************************************************************

Dependent variable is DLS

330 observations used for appraisal from 1980M2 to 2007M7

## *******************************************************************************

Regressor Coefficient Standard Error T-Ratio [ Prob ]

CON.0068996.0054122 1.2748 [ .203 ]

FED.6526E-3.7359E-3.88677 [ .376 ]

## *******************************************************************************

R-Squared.0023917 R-Bar-Squared -.6498E-3

S.E. of Regression.048897 F-stat. F ( 1, 328 ) .78636 [ .376 ]

Mean of Dependent Variable.011063 S.D. of Dependent Variable.048881

Residual Sum of Squares.78422 Equation Log-likelihood 528.7062

Akaike Info. Criterion 526.7062 Schwarz Bayesian Criterion 522.9071

DW-statistic 1.5972

## ******************************************************************************

## SLOPE AND INTERCEPT

The value of the intercept between NSR and FED in this arrested development is positive bespeaking an addition in NSR will besides take to an addition in the intercept ( I± ) . The relationship between NSR and FED ( I? incline ) is besides positive ( 0.0008457 ) bespeaking an addition in Federal financess in a state it will increase nominal stock return of Johnson & A ; Johnson.

If FED increases by 1 % we expect NSR to increase by 0.6526*10-3 all other things being equal Gurajati 2003 pp 169-173.

## STANDARD ERROR

The s.e measures how confident one is in the coefficient estimation obtained. The value of the s.e is little for I± and I? demoing that the value of these coefficients is likely to be precise on norm for this peculiar set of sample. The smaller the value of s.e ( 0.048382 ) the closer the existent NSR is to its estimated value from the arrested development theoretical account.

## T-RATIO AND P-VALUE

The t-ratio/value is the ratios of the estimated coefficients to their standard mistakes whilst the p-value is defined as the lowest important degree at which a void hypothesis can be rejected. ( Gujarati 2008 ) . The value of t-ratio for I± is 1.2748 I? 0.88677 whilst the p-value for I± is 0.203 and I? is 0.376. The p-value and the t-value can non be important unless tested against the void hypothesis of the arrested development.

## SUM OF SQUARED RESIDUAL

In this arrested development, the R2 value is 0.0023917 which informs us that 0.23917 % of the fluctuation in nominal stock returns is explained by the fluctuation in growing rate of industrial production. The R2 value is low for this arrested development.

( iiib ) OLS ESTIMATOR 2007 M8

NSRt= -0.0026692 + 0.0024138FEDt + Aµ

Ordinary Least Squares Estimation

## *******************************************************************************

Dependent variable is DLS

29 observations used for appraisal from 2007M8 to 2009M12

## *******************************************************************************

Regressor Coefficient Standard Error T-Ratio [ Prob ]

CON -.0026692.011150 -.23939 [ .813 ]

FED.0024138.0046390.52032 [ .607 ]

R-Squared.0099277 R-Bar-Squared -.026742

S.E. of Regression.043115 F-stat. F ( 1, 27 ) .27074 [ .607 ]

Mean of Dependent Variable.0013685 S.D. of Dependent Variable.042550

Residual Sum of Squares.050191 Equation Log-likelihood 51.0593

Akaike Info. Criterion 49.0593 Schwarz Bayesian Criterion 47.6920

DW-statistic 1.2722

## SLOPE AND INTERCEPT

The value of the intercept between NSR and FED in this arrested development is negative bespeaking a lessening in NSR will besides take to a lessening in the intercept ( I± ) . The relationship between NSR and FED ( I? incline ) is besides positive ( 0.0024138 ) bespeaking an addition in Federal financess in a state it will increase nominal stock return of Johnson & A ; Johnson.

If Federal financess additions by 1 % we expect nominal stock return to increase by 0.24138 % all other things being equal and fixed.

## STANDARD ERROR

The s.e measures how confident one is in the coefficient estimation obtained. The value of the s.e is little for I± and I? demoing that the value of these coefficients is likely to be precise on norm for this peculiar set of sample. The smaller the value of s.e ( 0.043115 ) the closer the existent NSR is to its estimated value from the arrested development theoretical account.

## T-RATIO AND P-VALUE

The t-ratio/value is the ratios of the estimated coefficients to their standard mistakes whilst the p-value is defined as the lowest important degree at which a void hypothesis can be rejected. ( Gujarati 2008 ) . The value of t-ratio for I± is -0.23939 I? 0.52032 whilst the p-value for I± is 0.813 and I? is 0.607. The p-value and the t-value can non be important unless tested against the void hypothesis of the arrested development.

## SUM OF SQUARED RESIDUALS

In this arrested development, the R2 value is 0.0099277 which informs us that 0.99277 % of the fluctuation in nominal stock returns is explained by the fluctuation in growing rate of industrial production. The R2 value is low for this arrested development.

## RELATIONSHIP BETWEEN STOCK RETURNS AND INTEREST Rate

The recent fiscal crisis has affected the stock returns and involvement rates there is a negative relationship during this period. During this period, none of the variables seem to hold important coefficients. Before the crisis, there is positive relationship between the two variables before the fiscal crisis afterwards the relationship is negative. After the crisis, largely there is largely a positive relationship between stock return and involvement rates.

This is supported by Muradoglu et Al ( 2001 ) which reports that the influence of involvement rates on stock returns disappears over clip. And this can be due to alterations in monetary values of rising prices with clip or the hazard values over a period of clip.

4. OLS ESTIMATOR ADDING GIND

NSRt = 0.0065184 + 0.0076526FEDt – 0.51292GINDt + Aµ

Ordinary Least Squares Estimation

## ******************************************************************************

Dependent variable is DLS

359 observations used for appraisal from 1980M2 to 2009M12

## ******************************************************************************

Regressor Coefficient Standard Error T-Ratio [ Prob ]

CON.0065184.0048823 1.3351 [ .183 ]

FED.7626E-3.6795E-3 1.1224 [ .262 ]

DLIP -.52192.36343 -1.4361 [ .152 ]

R-Squared.010074 R-Bar-Squared.0045123

S.E. of Regression.048310 F-stat. F ( 2, 356 ) 1.8114 [ .165 ]

Mean of Dependent Variable.010280 S.D. of Dependent Variable.048419

Residual Sum of Squares.83085 Equation Log-likelihood 579.9206

Akaike Info. Criterion 576.9206 Schwarz Bayesian Criterion 571.0956

DW-statistic 1.5669

## SLOPE AND INTERCEPT

The value of the intercept between NSR and FED in this arrested development is positive bespeaking an addition in NSR will besides take to an addition in the intercept ( I± ) . The relationship between NSR and FED ( I? incline ) is besides positive ( 0.76526 A- 10-3 ) bespeaking an addition in Federal financess in a state it will increase nominal stock return of Johnson & A ; Johnson. The relationship between NSR and GIND ( I?1 ) is negative ( -0.51292 ) bespeaking a lessening in GIND will diminish the nominal stock return. This could be due to cut down grosss and net incomes

If FED increases by 1 % we expect NSR to increase by 0.7626*10-3 all other things being equal ( Gurajati 2003 pp 169-173 ) .

## STANDARD ERROR

The s.e measures how confident one is in the coefficient estimation obtained. The value of the s.e is little for I± , I? and I?1 demoing that the value of these coefficients is likely to be precise on norm for this peculiar set of sample. The smaller the value of s.e ( 0.048310 ) the closer the existent Nominal stock return is to its estimated value from the arrested development theoretical account.

## T-RATIO AND P-VALUE

The t-ratio/value is the ratios of the estimated coefficients to their standard mistakes whilst the p-value is defined as the lowest important degree at which a void hypothesis can be rejected. ( Gujarati 2008 ) . The value of t-ratio for I± is 1.3351 I? 1.1224 I?1 -1.4361 whilst the p-value for I± is 0.183, I? is 0.262 and I?1 is 0.152. The p-value and the t-value can non be important unless tested against the void hypothesis of the arrested development.

## SUM OF SQUARED RESIDUALS

In this arrested development, the R2 value is 0.010074 which informs us that 1.0074 % of the fluctuation in nominal stock returns is explained by the fluctuation in growing rate of industrial production. The R2 value is low for this arrested development.

## Comparison MODEL 1 AND MODEL 2

When another independent variable ( DLIP ) is added to the arrested development the s.e is merely decreased by 1.50A-10-5. This is because the amount of squared remainders must fall when another explanatory variable is added to a arrested development. Adding another variable, the FED has decreased thereby diminishing the s.e of the arrested development. The value of R2 has besides increased from theoretical account 1 and model 2, the t-ratio for the FED has besides decreased.

## USING F-STATISTICS

In order to prove the joint hypothesis we use F-statistics

F = Rn – Ro/No of new regressors

( 1-Rn ) / ( N-no of parametric quantities )

F= ( 0.010074 – 0.0043389 ) /1

( 1-0.010074 ) / ( 359-3 )

F = 0.0057351 =2.0625

0.0027807

Rn is the R2 of new variable being added to the arrested development

Ro is the R2 of old variables for original arrested development

Holmium: I?=I?1= 0

Using the F value statistics in tabular array of F-distribution at 5 % significance degree value is 3.84. The computed value of F is smaller than 3.84 the chance of obtaining the value of F value lower than 2.0625 is really little. We do non reject the Ho:

## Decision

The Microfit has been used to analyze the dataset of Johnson & A ; Johnson where a nominal stock return and the growing rate of industrial production was calculated. The description was made utilizing aforethought graphs and the correlativity of NSR, GIND and FED. The OLS calculator was obtained and the reading of values obtained. The assurance interval and t-test attack were used to find the degree of significance of the OLS estimates where the Null Hypothesis was non rejected. The comparing was made between theoretical account 1 and model 2 and F-statistics was used to prove the joint hypothesis.