文档介绍：Chapter 3 Econometrics
Xi’An Institute of Post & munication
Dept of Economic & Management
Prof. Long
The Simple Linear
Regression
Model
Chapter 3
Population and Samples
population
sample
sample
sample
1. Estimate a relationship among economic variables, such as y = f(x).
2. Forecast or predict the value of one  variable, y, based on the value of   another variable, x.
Purpose of Regression Analysis
Weekly Food Expenditures
y = dollars spent each week on food tems.
x = consumer’s weekly e.
The relationship between x and the expected value of y , given x, might be linear: E(y|x) = b1 + b2 x
f(y|x=480)
f(y|x=480)
y
my|x=480
Figure Probability Distribution f(y|x=480)
of Food Expenditures if given e x=$480.
f(y|x)
f(y|x=480)
f(y|x=800)
y
my|x=480
my|x=800
Figure Probability Distribution of Food
Expenditures if given e x=$480 and x=$800.
PRF (Population Regression Function)
Weekly e X
Weekly consumption Y
80
140
220
149
101
65
PRF
Linear PRF
{
b1
Dx
DE(y|x)
E(y|x)
Average
Expenditure
x (e)
E(y|x)=b1+b2x
b2=
DE(y|x)
Dx
Figure The Economic Model: a linear relationship
between average expenditure on food and e.
.
.
xt
x1=480
x2=800
yt
f(yt)
Figure . The probability density function
for yt at two levels of household e, x t
expenditure
Homoskedastic Case
e