Tài liệu Kinh tế ứng dụng_ Lecture 2: Simple Regression Model ppt

Applied Econometrics 1 Simple Linear Regression Model

Applied Econometrics

Lecture 2: Simple Regression Model

‘It does require maturity to realize that models are to be used but not to be believed’

HENRI THEIL, Principles of Econometrics

1) Assumptions of the two-variable linear regression model

The estimation process begins by assuming or hypothesizing that the least squares linear regression

model (drawn from a sample) is valid. The formal two-variable linear regression model is based on

the following assumptions:

(1) The population regression is adequately represented by a straight line: E(Yi) = μ(Xi) = β0 + β1Xi

(2) The error terms have zero mean: E(∈i) = 0

(3) A constant variance (homoscedasticity): V(∈i) = σ

2

(4) Zero covariance (no correlation): E(∈i, ∈j) = 0 for all i ≠ j

(5) X is non-stochastic, implying that E(Xi, ∈i) = 0

2) Least squares estimation

The sample regression model can be written as follows:

Yi = b0 + b1Xi + ei

Its least squared estimators b0 and b1 are obtained by minimizing the sum of squared residual with

respect to b0 and b1

∑ei

2

= ∑(Yi – b0 – b1Xi)

2 → min

The resulting estimators of b0 and b1 are then given by:

( )( )

∑ ⎟⎠

⎞ ⎜

⎝

⎛ −

∑ −−

=

=

=

n

1i

2

n

1i i i

1

Xi X

X X Y Y

b

b0 Y −= b1X

3) Analysis of Variances

The least squared regression splits the variation in the Y variable into two components: the explained

variation due to the variation in Xi and the residual variation

TSS = RSS + ESS

Written by Nguyen Hoang Bao May 20, 2004