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非线性回归分析 PowerPoint PPT Presentation


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非线性回归分析. 基本概念 非线性模型及其线性化方法. 在社会与自然科学中, y 关于 x 的数量关系多数都不是简单的线性关系,而是各种各样的非线性关系,于是我们常会遇到非线性回归模型,在非线性回归模型中,一种类型是可以通过变量变换化为线性模型,然后按线性模型加以解决;另一种类型的非线性模型是用任何变量变换办法都不能或不方便直接化为线性模型求得参数的估计值。. 在实际经济活动中,经济变量的关系是复杂的,直接表现为线性关系的情况并不多见。.

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非线性回归分析

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yx


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(Engle curves)Pillips cuves


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1

s = a + b r + c r2 c<0

s r

X1 = rX2 = r2

s = a + b X1 + c X2 c<0


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2

Cobb-Dauglas

Q = AKL

QKL

ln Q = ln A + ln K + ln L


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3

CES

(1+2=1)

Q:KL

12

ln(1K- + 2L-)=0,

012


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    • lny= ln + x

    • y' = lnyy'= ln + x


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=-1

= 1

1

<-1

0< < 1

-1< <0

    • lg y = lg + lg x

    • y' = lgyx'= lg xy'= lg + x'


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< 0

> 0

    • y' = 1/yx'= 1/x, y'= + x'


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0

<0

    • x'= lgx , y'= + x'


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  • S

    • y' = 1/yx'= e-x, y'= + x'


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SPSS Curve Estimation


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  • Y=0+ 1x + 2x2+ + pxp

  • i=xi

  • :

    Y= 0+ 1 1 + 2 2+ + p p

  • y=x1 1 x2 2 xp p

    lny=ln + 1ln x1++ pln xp

    z= lny, 0= ln ,i= ln xi

    z= 0 + 1 1 + 2 2+ + p p


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  • y=ae ixi

    y=a+ 1x1 + 2x2+ + pxp

    z= y, 0= a,

    z= 0 + 1x1 + 2x2+ + pxp

  • y=a+ 1x1 + 2x2++ pxp

    i= xi,

    y=a+ 1 1 + 2 2 ++ p p


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  • y=aexp{ixi} xibi

    y=a+ 1x1 + 2x2+ + pxp

    +b1x1 +b2x2+ +bpxp

    z= y, 0= a,i= xi

    z= 0 + 1x1 + 2x2+ + pxp +b1 1 +b2 2+ +bp p


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  • 7 15xy,yx,x2x3.(spssex/7)


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  • ,y,

  • ,


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  • 8 1985-1993,.(spssex/8)

MODEL: MOD_2.

Independent: x

Dependent Mth Rsq d.f. F Sigf b0 b1 b2

y QUA 1.000 6 202698 .000 178.095 5.2238 3.8810


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  • 9 ,,.,,.,.(spssex/9)


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  • Analyze->regression->curve estimation

  • Linear: y=b0+b1x

  • Quadratic: y= b0+b1x+b2x2

  • Compound: y=b0b1x

  • Growth: y=e(b0+b1x)

  • Logarithmic: y= b0+b1lnx

  • Cubic: y= b0+b1x+b2x2+b3x3


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  • S: y=e(b0+b1/x)

  • Exponential: y=b0eb1x

  • Inverse: y=b0+b1/x

  • Power: y=b0xb1

  • Logistic: y=1/(1/u+b0b1x))


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Curve Estimation


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Dependent

Independent


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: %XY

%

1 57.1

2 76.0

3 90.9

4 93.0

5 96.7

6 95.6

7 96.2


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  • Analyze==>Regression==>Curve estimation

  • Dependant

  • Independant

  • ModelsQuadraticCurbeLogarithmaticLiner

  • OK


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447


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255000


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7.430


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Curve Estimation

Curve Estimation


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  • Models

  • LinearLinear

  • QuadraticY = b0+b1X+b2X2

  • CompoundY = b0b1X

  • GrowthY = e(b0+b1X)

  • LogarithmicY = b0+b1lnX

  • CubicY = b0+b1X+b2X2+b3X3

  • SSY = e(b0+b1/X)

  • ExponentialY = b0 eb1X

  • InverseY = b0+b1/X

  • PowerY = b0X b1

  • LogisticLogisticY = 1/1/u + b0b1X


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Include constant in equation

Plot models

save

SAVE

Display ANOVA table


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Keynes

Consumptionb1b2incomee0< b2<1


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