MBA 3RD B

Regression Analysis (Manual + Auto)

(Stock Indexes & GDP)

Federal Urdu University of Arts, Science &

Technology, Islamabad

(FUUAST)

Submitted to Mam Sania Nawaz

MANAGERIAL ECONOMICS

Final Project

Submitted by Group A

Muhammad Jawad ul Hassan Hafiz Syed Mehtab Ali Bukhari Muhammad Wajahat Hussain

Noor Ullah Haqani Ali Shan

CONTENTS

MANAGERIAL ECONOMICS ............................................................................................................. 1

INTRODUCTION OF GDP.......................................................................................................................... 1

DEFINITION (GDP) ............................................................................................................................... 1

IMPORTANCE OF GDP ......................................................................................................................... 1

INTRODUCTION OF STOCK INDEXES........................................................................................................ 2

LINK OF STOCK INDEX & GDP .................................................................................................................. 3

RELATIONSHIP DIAGRAM ....................................................................................................................... 3

REGRESSION METHOD ............................................................................................................................ 4

REGRESSION DEFINITION ........................................................................................................................ 4

FORMULA OF REGRESSION ................................................................................................................. 4

IMPORTANCE ...................................................................................................................................... 5

BENEFITS ............................................................................................................................................. 5

ACCURACY OF RESULTS ....................................................................................................................... 5

ASSESSMENT TOOLS ........................................................................................................................... 5

USE OF MULTI-VARIABLES .................................................................................................................. 6

INPUT FOR NEW MANAGEMENT TRENDS ........................................................................................... 6

MANUAL REGRESSION ANALYSIS ............................................................................................................ 6

AUTOMATIC REGRESSION ANALYSIS ...................................................................................................... 7

TEST RESULTS DISCUSSION ..................................................................................................................... 8

MANUAL RESULTS ............................................................................................................................... 8

AUTOMATIC ........................................................................................................................................ 8

SUMMARY OUTPUT ........................................................................................................................ 8

ANOVA ............................................................................................................................................ 8

t-Test: Paired Two Sample for Means ............................................................................................. 9

RESULT INTERPRETATION ....................................................................................................................... 9

CONCLUSION ........................................................................................................................................ 10

SOURCES OF DATA ................................................................................................................................ 10

1

INTRODUCTION OF GDP

Gross Domestic Product is abbreviated as GDP. It is sum of all of the economic goods which are giving benefits to the country in economic or monetary terms. It is important for a country overall because it tells about the present economic status of a country in world. A country with high GDP would be having improved and standard economy while a country with low GDP would be having low standard and poorly developed economy.

The most important measure of economic activity in a country, The Gross Domestic Product is the crossing point of three sides of the economy:

Expenditure

Output,

& Income. As a measure of well-being of a country for international and temporal comparisons, it

provides a good first approximation. Still, it ignores many crucial elements of general well-being, like environment conservation, safety, life expectance, and population literacy. In this respect, one should rather look at the Human Development Index.

DEFINITION (GDP)

Gross Domestic Product is abbreviated as GDP. The monetary value of all the finished goods and services produced within a country's borders in a specific time period, though GDP is usually calculated on an annual basis. It includes all of private and public consumption, government outlays, investments and exports less imports that occur within a defined territory.

GDP = C + G + I + NX

where: "C" is equal to all private consumption, or consumer spending, in a nation's economy "G" is the sum of government spending "I" is the sum of all the country's businesses spending on capital "NX" is the nation's total net exports, calculated as total exports minus total imports. (NX = Exports - Imports)

IMPORTANCE OF GDP

GDP consists of consumer spending, Investment expenditure, government spending and net exports hence it portrays an all inclusive picture of an economy because of which it provides an insight to investors which highlights the trend of the economy by comparing GDP levels as an index

2

GDP is used as an indicator for most governments and economic decision-makers for planning and policy formulation

In case of GDP, each component is given the weight of its relative price. In market economics it clicks as prices reflect both marginal cost of the producer and marginal utility for the consumer, i.e. people sell at a price that others are willing to pay

GDP helps the investors to manage their portfolios by providing them with guidance about the state of the economy

Calculation of GDP provides with the general health of the economy. A negative GDP growth portrays bad signals for the economy. Economists analyze GDP to find out whether the economy is in recession, depression or boom.

INTRODUCTION OF STOCK INDEXES

A statistical measure of change in an economy or a securities market. In the case of financial markets, an index is an imaginary portfolio of securities representing a particular market or a portion of it. Each index has its own calculation methodology and is usually expressed in terms of a change from a base value. Thus, the percentage change is more important than the actual numeric value.

Stock and bond market indexes are used to construct index mutual funds and exchange

traded funds (ETFs) whose portfolios mirror the components of the index. A group of stocks put together in a standardized way to provide a useful window into a

sector or market's performance at a glance. That is, a stock index groups together a certain list of stocks and usually takes an average of their prices so as to provide an idea of how the industry or market represented in the stock index is doing.

A stock index is a method of measuring a group of stocks with a goal to provide a one-number indication of how that group of stocks is performing. Indexes are often used in the same way that averages are used. When it comes to the stock market, there are many indexes. Some indexes, like broad-based indexes, attempt to measure the performance of the entire market. While other indexes, like narrow-based indexes, attempt to measure only a specific sector of the market

A stock market index is a bunch of stocks grouped together to measure a certain sector

(utilities, banks, tech stocks, etc.) of the stock market. Portfolios of individual stocks or mutual funds are often compared to a stock market index to see how well they are performing.

3

LINK OF STOCK INDEX & GDP

We can certainly argue that the economy impacts corporate earnings in terms of

revenues and costs. Stock prices generally reflect investor expectations for future corporate

earnings and consequently for future economic growth. As a result, sound economic forecasts

should help investors make equity market decision. If for example, an economic recovery is

predicted – preferably with some degree of reliability – then this could signal an appropriate

time for investing in stocks.

Scholars say that investors wasting their time with economic analyses and forecasts, since they

believe that the stock market has already priced in expectation for the economy. Those who

invest based on economic forecasts would therefore always be late to the game. Seen from this

perspective, the stock market provides useful information about the future development of the

economy, not the other way around.

So does the economy run ahead of the stock market, or does the stock market anticipate

economic development? Both outcomes are conceivable; the question can only be clarified

empirically based on data and facts. It depends on data how much data affects so change

occurs according to data.

RELATIONSHIP DIAGRAM

Stock

Indexes

GDP (GROSS DOMESTIC

PRODUCT)

Independent Variable Dependent Variable

4

REGRESSION METHOD

REGRESSION DEFINITION

“A statistical measure that attempts to determine the strength of the relationship between one

dependent variable (usually denoted by Y) and a series of other changing variables (known as

independent variables).”

The two basic types of regression are linear regression and multiple regression. Linear

regression uses one independent variable to explain and/or predict the outcome of Y, while

multiple regression uses two or more independent variables to predict the outcome.

The general form of each type of regression is:

Linear Regression: Y = a + bX

Multiple Regression: Y = a + b1X1 +

b2X2 + B3X3 + ... + BtXt

Where:

Y= the variable that we are trying to predict

X= the variable that we are using to predict Y

a= the intercept

b= the slope.

In multiple regression the separate variables are differentiated by using subscripted numbers.

Regression takes a group of random variables, thought to be predicting Y, and tries to find a

mathematical relationship between them. This relationship is typically in the form of a straight

line (linear regression) that best approximates all the individual data points. Regression is

often used to determine how much specific factors such as the price of a commodity, interest

rates, particular industries or sectors influence the price movement of an asset.

FORMULA OF REGRESSION

Regression Equation(y) = a + bx

Slope (b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)

Intercept(a) = (ΣY - b(ΣX)) / N

Where

“x and y are the variables”

5

b = The slope of the regression line

a = The intercept point of the regression line and the y axis.

N = Number of values or elements

X = First Score

Y = Second Score

ΣXY = Sum of the product of first and Second Scores

ΣX = Sum of First Scores

ΣY = Sum of Second Scores

ΣX2 = Sum of square First Scores

IMPORTANCE

Regression analysis can help business to investigate the determinants of key variables such as

their sales. Variations in a company’s sales are likely to be related to variation in product prices,

consumers, incomes, tastes and preference's multiple regression analysis can be used to

investigate the nature of this relationship. Regression can also be used to estimate the trend in

a time series to make forecast.

BENEFITS

Managers need information to evaluate what is going on in the external and the internal

environments of an organization. Regression analysis is one of the quantitative models that

managers use to study the behavior of semi-variable costs and separate the fixed and the

variable elements. Managers prefer the regression analysis technique to other models such as

the high-low and scatter graph methods because of the overall superiority of the results.

ACCURACY OF RESULTS

Regression analysis allows managers to establish objective measures of relationships

between the independent and the dependent variables, rather than purely using

personal judgment. This generally results in accurate information that is more reliable for

decision-making, and other parties can empirically test the results using the same or

separate data without resulting to personal opinions.

ASSESSMENT TOOLS

When the management obtains the results of the regression models electronically, most

of the computers they use have software packages that provide a few statistics, such as

6

the R-square and the student t-value statistics. The two statistics help managers

determine the accuracy of the predictions, and thus the level of reliability of the results

that they have obtained using the regression equations.

USE OF MULTI-VARIABLES

The multiple regression analysis models allow managers to test for several independent

variables that may explain different things about the dependent variable. Though

complex, the manager can test for all the factors that he thinks have an effect on a given

depended variable. This is unlike other inferior models that allow for only one

independent variable. With the use of several variables, the accuracy of prediction is also

improved.

INPUT FOR NEW MANAGEMENT TRENDS

Regression analysis provides needed input for activity-based cost and management

techniques. These techniques are based on knowing what activities or transactions cause

the acquisition and use of resources. The theory of constraints encourages managers to

look at throughput per scarce resource as part of dealing with a dynamic environment of

changing constraints. Regression analysis allows managers to establish objective.

MANUAL REGRESSION ANALYSIS

Manual regression analysis where in which we check the impact and effect of

independent variable on dependent variable manually application of formulas in Ms excel

Following formulas use in the manual regression analysis

Mean of Y

Mean of X

α = Y̅-βX̅

= 𝒀𝒙𝒏=𝟒𝟖 /n

= 𝑿𝒙𝒏=𝟒𝟖 /n

7

T-test = beta/standard deviation

AUTOMATIC REGRESSION ANALYSIS

Over and done with automatic regression analysis we are squared out influence and

consequence of variables just one click. This method is too informal but if user does not

distinguish the manual regression analysis then automatic regression analysis is not helpful for

the user. So for automatic regression analysis it is significant that user must have the knowledge

about the manual regression analysis and interpretation of results.

For the implementation following steps show be kept in mind

In excel open the tab of data.

Search the data analysis tab.

Click on data analysis.

Selection the regression analysis from the given option.

Give in tab rang of Y and X.

Select the test.

Press enter.

Standard Deviation = 𝒀−𝒀 𝟐

(𝒏−𝒌) (𝑿−�̅�)𝟐

8

TEST RESULTS DISCUSSION

MANUAL RESULTS

Regression line =Ῡ=α+βx

b = 864320.61

a = 140418969997.87

Y1 146708293990.47

Y49 146858262259.48

Standard Deviation 269897652008698.00

t-test 2.33278E+20

df 45.00

level of significance 0.05

AUTOMATIC

SUMMARY

OUTPUT

Regression Statistics Column1

Multiple R 0.10

R Square 0.01

Adjusted R Square -0.01

Standard Error 14851157153.28

Observations 47.00

ANOVA

Column1 df SS MS F Significance F

Regression 1.00 100813244814475000000.00 100813244814475000000.00 0.46 0.50

Residual 45.00 9925059095611050000000.00 220556868791357000000.00

Total 46.00 10025872340425500000000.00

9

Column1 Coefficients Standard Error t Stat P-value

Intercept 144118666067.95 9270516040.48 15.55 0.00

7276.61 570943.20 844489.79 0.68 0.50

t-Test: Paired Two Sample for Means

Column1 Column2 Column3

7276.61 120000000000.00

Mean 10673.74 150212765957.45

Variance 6723167.80 217953746530985000000.00

Observations 47.00 47.00

Pearson Correlation 0.10

Hypothesized Mean Difference 0.00

df 46.00

t Stat -69.75

P(T<=t) one-tail 0.00

t Critical one-tail 1.68

P(T<=t) two-tail 0.00

t Critical two-tail 2.01

RESULT INTERPRETATION

We have used two method for the interpretation of regression analysis first is manual

regression analysis and second is automatic regression analysis our results are normally correct

with automatic regression analysis but in minor digits occur due to following differences.

Difference in manual and automatic result results due to following reasons

Exclude the number after point mean we are just take two digits after point.

Human problem due to implementation of different formulas.

Our Hypothesis is rejected…!

10

CONCLUSION

We can certainly argue that the economy impacts corporate earnings in terms of

revenues and costs. Stock prices generally reflect investor expectations for future corporate

earnings and consequently for future economic growth. As a result, sound economic forecasts

should help investors make equity market decision. If for example, an economic recovery is

predicted – preferably with some degree of reliability – then this could signal an appropriate

time for investing in stocks.

So does the economy run ahead of the stock market, or does the stock market anticipate

economic development? Both outcomes are conceivable; the question can only be clarified

empirically based on data and facts. It depends on data how much data affects so change

occurs according to data.

SOURCES OF DATA

www.investopedia.com

www.finance.yahoo.com (Stock Indexes)

www.indexmundi.com (GDP)

www.sbp.com.pk

www.financial-dictionary.thefreedictionary.com

www.cboe.com

www.wikipedia.com

www.statstoolnet.com

www.kse.com

:) THE END :)