Tutorial Single Equation Regression Model

7/27/2019 Tutorial Single Equation Regression Model

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Tutorial 1

Econometrics

Two-Variable

Regression Analysis

MEP-DD Muhammad Edhie Purnawan, MA, Ph.D

Prepared by Rafiazka Millanida H.

[email protected]


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Reviewing Methodology of Econometrics

Classical econometric methodology proceeds along thefollowing lines:

1. Statement of theory or hypothesis.

2. Specification of the mathematical model of the theory

3. Specification of the statistical, or econometric, model

4. Obtaining the data

5. Estimation of the parameters of the econometric model

6. Hypothesis testing

7. Forecasting or prediction

8. Using the model for control or policy purposes.

Overview Introduction to EVIEWS

Application Exercise


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Differing Economic Data

Cross sectionaldata

Consists of a

sample ofvariety of unitstaken at a givenpoint in time

Ex: census of

populatioconducted bythe CensusBureau every 10

years

Time series data

Consists of

observations ona variable orseveralvariables overtime.

Ex: stock prices

Panel Data

Data are

elements ofboth time seriesand cross-section data.

Ex: Consumer

Price Index (CPI)for severalcountries for19731997




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Interpreting Regression

Regression analysis is concerned with the study

of the dependence of one variable, the

dependent variable, on one or more other

variables, the explanatory variables, with aview to estimating and/or predicting the

(population) mean or average value of the

former in terms of the known or fixed (inrepeated sampling) values of the latter.




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Contd

Case:

The rate of change of money wages in relation to theunemployment rate. The historical data is an exampleof the celebrated Phillips curve relating changes in the

money wages to the unemployment rate.

Why scattergram?- It may enable the labor economist to

predict the average change in money

wages given a certain unemploymentrate.

- It may be helpful in stating something

about the inflationary

process in an economy, for increases in

money wages are likely to be

reflected in increased prices.




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Determining Regression Statistical Versus Deterministic Relationships

- statistical not functional or deterministic

- random or stochastic (have probability distribution)

- eg: The dependence of crop yield on temperature,rainfall, sunshine, and fertilizer, for example, isstatistical in nature in the sense that the explanatoryvariables, although certainly important, will not enablethe agronomist to predict crop yield exactly because of

errors involved in measuring these variables as well asa host of other factors (variables) that collectivelyaffect the yield but may be difficult to identifyindividually.




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Contd Regression Versus Causation

-A statistical relationship can never establish causalconnection (Kendall and Stuart).

- To ascribe causality, one must appeal to a priori or

theoretical considerations.- eg: There is no statistical reason to assume thatrainfall does not depend on crop yield. The fact that wetreat crop yield as dependent on rainfall (among other

things) is due to non-statistical considerations:Common sense suggests that the relationship cannotbe reversed, for we cannot control rainfall by varyingcrop yield.




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Contd

Regression Versus Correlation

Correlation analysis aims to measure the strength

or degree of linear association between two

variables.

Regression analysis try to estimate or predict the

average value of one variable on the basis of the

fixed values of other variables.




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Selecting Methods of Estimation The three generally used methods of estimation:

1. ordinary least squares (OLS)

2. maximum likelihood (ML)

3. method of moment (MM)

By and large, it is the method of OLS that is usedextensively in regression analysis primarily

because it is intuitively appealing andmathematically much simpler than the ML andMM




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EVIEWS Window

Main Menu

Command Window

Work Area

Status Line

Title Bar




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Workfile1. Creating Workfile

File NewWorkfile

Workfile Structure Type:

- Unstructured/Undated- Dated/Regular Frequency

Annual : 1991 2011Semi-annual : 1995:01 1995:02Quarterly : 1997:03 2007:04Monthly : 2003:05 2011:12Daily : 2005:31 2011:250

- Balanced Panel

2. Saving WorkfileFile Save As ....

3. Opening WorkfileFile Open Workfile




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Data

1. Entering Data:Manual

a. By Command- Make series/variable

series series_nameshow series_name

edit +/-- Enter DataType or paste data from microsoftexcel

b. By option- Make series/variable

ObjectNew ObjectType ofObject: Series Name for Object:series_name

orQuickEmpty Group Series

- Enter dataDouble click to the series/variableedit +/-Type or paste data from microsoftexcel

2. Entering Data:Import Option

a. From Microsoft Excel

File ImportReadFile Type:

ExcelFile Name: file_nameNote: Variables in Excel start at B2.

Excel must be closed before

importing process.

b. From Text

File ImportReadFile Type:

Text-ASCII File Name: file_name




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Contd

3. Opening Data Group

a. By Command

show series1_name series2_name

b. By optionblock series right clickopenas group

or

quickshowobjects:

series1_name series2_name

4. Plotting Data

a. By Commandsingle graph:plot series1_nameseries2_name

multiple graphs:plot(m)series1_name series2_nameb. By optionsingle graph: block series

right clickopen as groupview graphmultiple

series: single graphmultiple graphs: block series right clickopen as groupview graphmultipleseries: multiple graph



O i I d i EVIEWS


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Descriptive Statistics

1. Statistical Value

a. By Command

stats series1_name series2_name

b. By optionblock series right clickopenas group

viewdescriptive stats individual sample

2. Correlation Matrix

a. By Command

cor series1_name series2_name

b. By optionblock series right clickopen

as group

viewcovariance analysis

statistics: correlation



O i I t d ti t EVIEWS


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Equationquick estimates equation specification: series1_name c

series 2_name



block series1_name c series 2_name right clickopen asequation proc series1_name c series 2_name

ls series1_name c series 2_nameObject name name: eq01

equation eq01.ls series1_name c series 2_name

or

or

or



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Step of Regression

1.Hypothesis Testing

If null hypothesis isnt rejected hence independent

variable isnt significant to dependent variable

2.Interpreting Regression Coefficient3.R (R-squared)

4.Residual, Fitted, and Actual Value

5.Test for normality of Residual





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1. Open EVIEWSProgram

2. Open NewWorkfile

3. Quick EmptyGroup (editseries), copy the

data from excel.

Running EVIEWS



Exchange Rate

Gujarati (2003), p.33



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equation eq1.ls france c germany

Compare to value of t-stat table2



Compare to given =5%

O er ie Introd ction to EVIEWS


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Hypothesis Testing

The model:France = o + 1_Germany + u

Ho: 1 = 0

Ha: 1 0

1

Prob. < 0.05: Ho (Null Hypothesis) is notrejected independent variable is

significant to dependent variable.

Prob. > 0.05: Ho (Null Hypothesis) isrejected independent variable is notsignificant to dependent variable.

Prob.

0.0001 < 0.05Ho (Null Hypothesis) is not

rejected.

Independent variable is

significant to dependent

variable.



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t-stat

4,997 > 2.845 or 2.086 or

1.725

4,997 > 2

Ho (Null Hypothesis) is not

rejected.

Independent variable is

significant to dependentvariable.

t-stat > t-table: Ho (Null Hypothesis) is notrejectedindependent variable is

significant to dependent variable.

t-stat < t-table: Ho (Null Hypothesis) isrejectedindependent variable is notsignificant to dependent variable.

t-table

n = 22k = 2df = n-k = 20

= 10% t-table = 1.725= 5% t-table = 2.086

= 1% t-table = 2.845 Note:Since Eviews applies level of significanceis 5% or = 5%, the rule of thumbregarding to t-stats will be for anyregressions with more than n>20 and 0.05level of significant, the critical value is 2.

t-stats > 2: Ho (Null Hypothesis) is

rejected. Independent variable is significant

to dependent variable.

t-stat < 2: Ho (Null Hypothesis) is not

rejected independent variable is not

significant to the dependent variable.



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t-table

Degree of freedom:

n-k

One tail

Two tail

n = number of data

k = number of parameter

Or number of variable





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Interpreting Regression Coefficient

France = 1.618887+ 2.185832Germany

2

If exchange rate of Germany increases by an

average of 1 USD, exchange rate of france

will increase by average of 1.618887 USD,

ceteris paribus.



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R (R-squared) 3

The variance of independent variable (exchange

rate of Germany) can explain 55.53% variance of

the dependent variable (exchange rate of France).



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Residual, Fitted, and Actual Value 4

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

4

5

6

7

8

9

10

78 80 82 84 86 88 90 92 94 96 98

Residual Actual Fitted

Viewactual, fitted, residual

actual, fitted, residual graph

Graph shows the goodness

of fit of the model. Actual

value is close to estimatedvalue or fitted value. The

more closer the two are,

residual is around zero.



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Normality Test 5

JB Test is designed to track departures

from the normal distribution of the OLS

residuals.

viewresidual diagnostics

histogram-normality test

Ho: Disturbance terms are normallydistributed.

Ha: Ho is not true.



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Contd

Prob. > 0.05: Ho (Null Hypothesis) is notrejected Disturbance terms are normallydistributed.

Prob. < 0.05: Ho (Null Hypothesis) isrejected Disturbance terms are notnormally distributed.

JB-stat < c2 table , the model is normallydistributed.

JB-stat > c2 table , the model is notnormally distributed.

JB-stat

4.363461 < 10.8508 ( =

5%; df=22-2=20)

Ho (Null Hypothesis) is not

rejected.

Disturbance terms arenormally distributed.

Prob

0.112846 > 0.05 ( = 5%)

Ho (Null Hypothesis) is notrejected.

Disturbance terms are

normally distributed.



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c2 -tableDegree of freedom:

n-k

n = number of data

k = number of parameter

Or number of variable





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Regress data sales.xls using eviews

as the previous.



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Assignment 1

Journal draft on two-variable regression

analysis

(Abstract, Introduction, Theoretical

Framework, Data&Methodology, Model,

Result, Conclusion, Bibliography)

Due date: 3rd tutorial meeting


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Further Readings

Gujarati, D (2003). Basic Econometrics 4th

edition. New York: Mc Graw-Hill.

Kennedy, P (2003). A Guide to Econometrics

5th edition. Oxford: Blackwell.

Seddighi, Lawler, and Katos (2000).

Econometrics: A Practical Approach. New York:

Routledge.


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For any inquiry regarding to the topics please

text or email me.

Thanks.

Documents

Tutorial Single Equation Regression Model