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第二章 经典线性回归模型: 双变量线性回归模型 PowerPoint PPT Presentation


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第二章 经典线性回归模型: 双变量线性回归模型. 回归分析概述 双变量线性回归模型的参数估计 双变量线性回归模型的假设检验 双变量线性回归模型的预测 实例. §2.1 回归分析概述. 一、 变量间的关系及回归分析的基本概念 二、 总体回归函数( PRF ) 三、 随机扰动项 四、 样本回归函数( SRF ). 一、变量间的关系及回归分析的基本概念. 1. 变量间的关系 ( 1 ) 确定性关系 或 函数关系 : 研究的是确定现象非随机变量间的关系。. ( 2 )统计依赖 或 相关关系: 研究的是非确定现象随机变量间的关系。.

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第二章 经典线性回归模型: 双变量线性回归模型

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2.1

PRF

SRF


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1.

1

2


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  • (correlation analysis)(regression analysis)


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  • /


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2.

  • (regression analysis)

  • Explained VariableDependent Variable

  • Explanatory VariableIndependent Variable


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    • 1

    • 2

    • 3


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  • 2.1100YX

    10010


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  • X

  • XYXYConditional distributionP(Y=561|X=800=1/4


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  • XXiYconditional meanconditional expectationE(Y|X=Xi)

  • E(Y | X=800)=605

  • Y


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3500

3000

2500

2000

1500

Y

1000

500

0

500

1000

1500

2000

2500

3000

3500

4000

X


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  • XiYipopulation regression linepopulation regression curve

population regression function, PRF


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  • PRFYX

  • 2.1:

01regression coefficients


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  • Xi

  • deviationstochastic disturbancestochastic error


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  • 2.1Xi ,1E(Y|Xi)systematicdeterministic)2nonsystematic)i


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  • PRF


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SRF

  • 2.22.1PRF


Scatter diagram

scatter diagram)

  • sample regression lines


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sample regression functionSRF


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  • /

sample regression model


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SRFPRF


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PRF


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2.2

OLS


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i=1,2,,n

YX01


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  • SRFPRF

  • ordinary least squares, OLS


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---P99-100-105

1. X

2.

E(i)=0 i=1,2, ,n

Var (i)=2 i=1,2, ,n

Cov(i, j)=0 ij i,j= 1,2, ,n


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Y

Y

X

X


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Y

Y

X

X


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3. X

Cov(Xi, i)=0 i=1,2, ,n

4.

i~N(0, 2 ) i=1,2, ,n


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  • 123;

  • 42

GaussClassical Linear Regression Model, CLRM


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OLS

Xi, Yii=1,2,n.

Ordinary least squares, OLS


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OLSdeviation form

ordinary least squares estimators


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2.2.1-2.2.1


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  • SAS,SPSS,ET,ESP,GAUSS,MATLAB,MICROTSP,STATA,

    MINITAB,SYSTAT,SHAZAM,EViews,DATA-FIT

  • EViews

  • EViewsEViewsWindows


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1


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2

3

  • best liner unbiased estimator, BLUE


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4

5

6


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  • OLSOLS


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(Gauss-Markov theorem)


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2. 2

2


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iiei

2

2


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2.3


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Yi=i


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,


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Total Sum of Squares

Explained Sum of Squares

Residual Sum of Squares

TSS=ESS+RSS


Y total variation ess rss

Y(total variation)(ESS)(RSS)

  • TSS

  • ESSTSS

  • ESS/YTSS


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2R2

R2 /coefficient of determination)

[01]

R21


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2.1.1


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R2


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  • 0.90.5


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XY

XY


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1


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2


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1

H0 1=0 H110

2H0t

3tt /2(n-2)


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(4)

|t|> t /2(n-2)H0H1

|t| t /2(n-2)H1H0

0t


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2


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t

=0.05t

t 0.05/2(8)=2.306

|t1|>2.3060.05

|t0|<2.306,0.05


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confidence interval1-confidence coefficientlevel of significanceconfidence limitcritical values


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1

80

  • 80

    P(1 < < 2 )= 1-

    P(75 < <85 )=95%=1-5%


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1-

/2

/2


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i (i=12:

1-(n-2)t(-t/2, t/2)(1- )


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:(1-), i

-=0.01

10

0.6345,0.9195)

-433.32,226.98


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    • 1nnt


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2


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2.4

0E(Y|X=X0)Y0

--------


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X00E(Y|X=X0)Y0

:

1

2


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1


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1-E(Y|X0)


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2

Y0=0+1X0+:

:

1- Y0


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:

X0=1000

0 = 103.172+0.7771000=673.84


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E(Y|X=1000)95%

673.84-2.30661.05< E(Y|X=1000) <673.84+2.30661.05

533.05, 814.62

YX=100095%

673.84 - 2.30661.05<Yx=1000 <673.84 + 2.30661.05

(372.03, 975.65)


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  • confidence band------P120


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YE(Y|X):

1n

2XX


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2.5

GDP


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2.5.1

GDPP1990

CONSP1990=100


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19782000time series data

cross-sectional data

1.

Eviews


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(13.51) (53.47)

R2=0.9927 F=2859.23 DW-d=0.5503

2.

R2=0.9927

TC13.51 GDPP53.47

: t0.05/2(21)=2.08

0<0.3862<1


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3.

2001GDPP=4033.11990

CONSP2001= 201.107 + 0.38624033.1

= 1758.7

2001CONSP1990:1782.2

: -1.32%


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2001

GDP

E(GDPP) =1823.5

Var(GDPP) = 982.042=964410.4

95%E(CONSP2001)

=1758.740.13

1718.6,1798.8


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95%CONSP2001

=1758.786.57

1672.1, 1845.3


2 5 2 gdp

2.5.2 GDP

  • 1980~1998(2000)

I


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  • (OLS)


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    • b1145


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-

  • 99.29%


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-t

  • =5%

    b1


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-F

  • =5%

    b1t223622367F


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  • 199929854.7


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