### Thirlwall

```Applied Econometrics
Applied Econometrics
Second edition
Dimitrios Asteriou and Stephen G. Hall
Applied
Econometrics
Applied Econometrics
SIMPLE REGRESSION
1. Introduction to the Classical Linear Regression
Model
2. The OLS Method of Estimation
3. The Overall Goodness of Fit
4. Hypothesis Testing
5. How to Estimate a Simple Regression in Eviews
6. Applications and Examples
Applied Econometrics
•
•
•
•
Learning Objectives
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
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
X
300
250
200
150
X
100
50
0
0
20
40
60
80
100
120
140
160
180
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+1X
Probabilistic 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
Yˆ  b 0  b1 X
where : b 0 = the sample intercept
b1 = the sample slope
Yˆ = the predicted
value of Y
Applied Econometrics
Slope and Intercept of the
Regression Line
b
1

 X
 X
 Y
Y
X  X 
b
0
Y 

2
b
1

 XY  nXY
 X n X
X 
2
Y
n

b
2

XY 
 X

1

n
X
  X   Y 
n
2


X
n
2
Applied Econometrics
Least Squares Analysis
S S XY 
 X
S S XX 
X  X
b
b
0
1

 X
 Y

Y
2


 X
XY 
2


S S XY
S S XX
 Y  b1 X 
Y
n
 b1

n
X
  X   Y 
n
X
n
2
Applied Econometrics
Example: The Keynesian
Consumption Function
Applied Econometrics
Example: The Keynesian
Consumption Function
C2=B2*A2
D2=B2*B2
A22=SUM(A2:A21)
B22=SUM(B2:B21)
and so on!
ExcelEconometrics
Calculations
Applied
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
15
Applied Econometrics
The Regression Line
X
300
250
200
150
X
Linear (X)
100
50
0
0
20
40
60
80
100
120
140
160
180
Applied Econometrics
The Coefficient of Determination
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.
17
Applied Econometrics
Hypothesis Tests for the Slope
of the Regression Model
H 0:   0
t 
1
H 1:   0
1
H 0:   0
1
H 1:   0
w h ere :
S
S
b
e


b
1


S
S
b
e
S S XX
SSE
n2
1
H 0:   0
1
H 1:   0
1
S S XX 

1
1
 X
2
 X 

2
n
 th e h yp o th esiz ed slo p e
df  n  2
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.
```