Applied Econometrics

Applied EconometricsSecond edition

Dimitrios Asteriou and Stephen G. Hall

Applied Econometrics

SIMPLE REGRESSION

Applied Econometrics

1. Introduction to the Classical Linear Regression Model

2. The OLS Method of Estimation3. The Overall Goodness of Fit4. Hypothesis Testing5. How to Estimate a Simple Regression in

Eviews6. Applications and Examples

Applied Econometrics

• Compute the equation of a simple regression line from a sample of data, and interpret the slope and intercept of the equation.

• A full understanding of the simple OLS method of estimation and discussion of the properties of estimated coefficients.

• Computation of a standard error of the estimate and interpretation of its meaning and its use in Hypothesis Testing.

• Understanding and interpretation of the R2

Learning Objectives

Applied Econometrics

Introduction

• Regression analysis is the process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable.

• Key issue here is direction of causation of the two variables, or which variable depends on the other.

• Therefore we have two cases of variables

dependent variables (usually denoted by Y)

independent or explanatory (usually denoted by X)

Applied Econometrics

The Scatter Plot

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50

100

150

200

250

300

X

X

Applied Econometrics

Four Ways of Fitting a Line in the Data

• By eye• Connecting the first with the last observation• Take the average of the first two and the

average of the two last and connect• Apply Ordinary Least Squares

Applied Econometrics

Regression Models

Deterministic Regression Model:

Y=0+1XProbabilistic Regression Model:

Y=0+1X+u

0 and 1 are population parameters

0 and 1 are estimated by sample statistics b0 and b1

Applied Econometrics

Equation of the Regression Line

YY

b

bwhere

XbbY

of valuepredicted the= ˆ

slope sample the=

intercept sample the= :

ˆ

1

0

10

Applied Econometrics

Slope and Intercept of the Regression Line

1 2 2 2

22b

X X X X X XX X Y Y XY nXY

n

XYX Y

n

n

0 1 1b b bY XY

n

X

n

Applied Econometrics

Least Squares Analysis

SS X X Y Y XYX Y

n

SSn

SS

SS

XY

XX

XY

XX

X X X X

b

2 2

2

1

0 1 1b b bY XY

n

X

n

Applied EconometricsExample: The Keynesian

Consumption Function

Applied Econometrics

Example: The Keynesian Consumption Function

C2=B2*A2D2=B2*B2

A22=SUM(A2:A21)B22=SUM(B2:B21)

and so on!

Applied EconometricsExcel Calculations

b0=(C22-(A22*B22)/20)/(D22-((B22ˆ2)/20))=0.601888903

b1=AVERAGE(A2:A21)-G2*AVERAGE(B2:B21)=15.116408

Applied Econometrics

Excel Calculations (the easy way!)• Step 1: go to the menu Tools/Data Analysis and choose the command

regression. • Step 2: We are then asked to specify the Input Range, Output Range,

and a choice of including or not labels in the first row.• Step 3: The Input Range is the columns that contain the data for Y and X (i.e. we enter ‘$A$1:$B$21’ or simply select this area using the mouse). • Step 4: The Output Range can be either a different sheet (not

recommended) or any empty cell in the current sheet (i.e. we might specify cell F5).

• Step 5: Since we have chosen the labels in our selection we tick the box.• Step 6: By clicking <OK> we obtain the display shown in Table 4.4.

Applied Econometrics

Excel Results

Applied Econometrics: A Modern Approach using Eviews and

Microfit © Dr D Asteriou

15

Applied Econometrics

The Regression Line

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100

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300X

X

Linear (X)

Applied Econometrics

The Coefficient of Determination

17

The proportion of variability of the dependent variable accounted for or explained by the independent variable in a regression model.

It is called R2 and it takes values from 0-1.

Applied EconometricsHypothesis Tests for the Slope

of the Regression Model

H

H

01

11

0

0

:

:

H

H

01

11

0

0

:

:

H

H

01

11

0

0

:

:

t

whereSS

SSE

n

SSn

df n

bS

S S

S

XX

b

be

XX

e

XX

1 1

2

2

1

2

2

:

the hypothesized slope

Applied Econometrics

Regression in Eviews (1) (1)

Step 1 Open EViews.

Step 2 Choose File/New/Workfile in order to create a new file.

Step 3 Choose Undated or Irregular and specify the number of observations (in this case 20). A new window appears which automatically contains a constant (c) and a residual (resid) series.

Applied Econometrics

Regression in EViews (2)Step 4 In the command line type:

genr x=0 (press enter)genr y=0 (press enter)

which creates two new series named x and y that contain zeros for every observation.Open x and y as a group by selecting them and double clicking with the mouse.

Step 5 Either type the data in EViews or copy/paste the data from Excel®. To edit the series press the edit +/− button. After finishing with editing the series press the edit +/− button again to lock or secure the data.