線性與對數(shù)模型案例分析

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關(guān)于農(nóng)村居民各種不同類型

的收入對消費(fèi)支出影響

一、試驗(yàn)?zāi)康?/p>

影響農(nóng)村居民收入的因素有多種，主要因素可能有以下4項(xiàng)：農(nóng)業(yè)經(jīng)營收入、工資性收入、財(cái)產(chǎn)性收入及轉(zhuǎn)移性收入。此試驗(yàn)就是研究這四項(xiàng)不同類型收入對消費(fèi)支出是否有影響，又怎樣的影響，建立怎樣的模型比較適合描述農(nóng)村居民收入的變化。

二、模型設(shè)定

以下是全國主要地區(qū)消費(fèi)性支出、工資性收入、家庭經(jīng)營純收入、財(cái)產(chǎn)性收入、轉(zhuǎn)移性收入的數(shù)據(jù)。地區(qū)全國北京天津河北山西內(nèi)蒙古遼寧吉林黑龍江上海江蘇浙江安徽消費(fèi)性支出工資性收入2829.025724.503341.062495.332253.252771.973066.872700.662618.198006.004135.216057.162420.941374.805047.393247.921514.681374.34590.701499.47605.11654.866685.983104.773575.141184.11家庭經(jīng)營純財(cái)產(chǎn)性收入轉(zhuǎn)移性收入收入1930.961957.092707.352039.641622.862406.212210.842556.702521.51767.712271.373084.281617.76100.50678.81126.37107.7274.5184.81141.80187.74145.69558.17178.51311.6052.78180.78592.19146.29139.78109.21260.16238.30291.58230.381126.80258.58363.80114.43福建江西山東河南湖北湖南廣東廣西海南重慶四川貴州云南西藏陜西甘肅青海寧夏新疆3591.402676.603143.802229.282732.463013.323885.972413.932232.192205.212395.041627.072195.642023.242181.001855.492178.952246.972032.361855.531441.341671.541022.741199.161449.652906.15974.32555.721309.911219.51715.49441.81568.39848.26637.37653.30823.09254.072481.621863.502409.782108.262095.151743.391693.641705.752486.941349.571586.541112.811631.601410.511219.331291.851374.361662.072323.01113.5235.13127.6040.3725.9142.49220.8722.4549.4427.2952.8436.9382.19156.0052.5652.56100.6653.3558.69384.09119.57159.4089.6699.13154.09259.1269.96163.43187.07143.50119.3894.85300.06140.04152.27230.05221.63101.51分別設(shè)消費(fèi)性支出、工資性收入、家庭經(jīng)營純收入、財(cái)產(chǎn)性收入、轉(zhuǎn)移性收入為Y、X1、X2、

X3、X4。

1、建立如下線性模型：

Y?A1?A2X1?A3X2?A4X3?A5X4??i

用Eviews得到如下回歸結(jié)果：

DependentVariable:YMethod:LeastSquaresDate:06/16/10Time:22:54Sample:132Includedobservations:32

CoefficienVariabletStd.Errort-Statistic

C483.4083253.13621.909676X10.6271400.0804207.798311X20.4810250.1155234.163869X3-0.2563070.906787-0.282654X42.6781490.6165544.343738R-squared0.951902Meandependentvar

AdjustedR-squared0.944777S.D.dependentvarS.E.ofregression316.4870AkaikeinfocriterionSumsquaredresid2704428.SchwarzcriterionLoglikelihood-226.9207Hannan-Quinncriter.F-statistic133.5893Durbin-WatsonstatProb(F-statistic)0.000000

參數(shù)估計(jì)的結(jié)果為：

^

Prob.0.06690.00000.00030.77960.00022976.8461346.77414.4950414.7240614.570961.735377

Y?483.4083?0.62714X1?0.481025X2?0.256307X3?2.678149X4

Se=（253.1326）（0.080420）（0.115523）（0.906787）（0.616554）t=（1.909676）（7.798311）（4.163869）(-0.282654)(4.343738)p=(0.0669)(0.0000)*(0.0003)(0.7796)(0.0002)

R=0.951902R=0.944777

2、建立如下雙對數(shù)回歸模型

2__2lnY?B1?B2lnX1?B3lnX2?B4lnX3?B5lnX4??

得到如下回歸結(jié)果：

Variable

CLOG(X1)LOG(X2)

Coefficie

ntStd.Errort-StatisticProb.3.2524950.7492294.3411250.00020.2879180.0392307.3391680.00000.1846950.0840192.1982470.0367

LOG(X3)LOG(X4)

R-squared

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

參數(shù)估計(jì)結(jié)果為：

^0.0637840.0552971.1534850.25880.1840940.0774502.3769490.0248

0.879103Meandependentvar7.9292070.861193S.D.dependentvar0.349982

Akaikeinfo

0.130392criterion-1.0939400.459057Schwarzcriterion-0.86491922.50305F-statistic49.082822.076804Prob(F-statistic)0.000000

lnY?3.252495+0.287918lnX1?0.184695lnX2?0.063784lnX3?0.184094lnX4

Se=(0.749229)(0.039230)(0.084019)(0.055297)(0.077450)

t=(4.341125)(7.339168)(2.198247)(1.153485)(2.376949)p=(0.0002)(0.0000)(0.0367)(0.2588)(0.0248)

R=0.879103R=0.861193

三、模型檢驗(yàn)

①線性模型的檢驗(yàn)1、多重共線性檢驗(yàn)

(1)假設(shè)Ri表示變量Xi對于其他變量的回歸結(jié)果的樣本判定系數(shù)。a、做X1對其他變量的回歸

X1=232.2140+0.061979X2+5.661497X3+2.288138X4

^2__22R12=0.749576

建立F檢驗(yàn)：

R12(k?1)F=~F（k-1,n-k）2(1?R1)(n?k)代入數(shù)據(jù)得;

F=

0.749576(4?1)

(1?0.749576)(32?4)=27.93679

原假設(shè)H0：R1=0；H1：R1≠0，在α=0.05的顯著水平下，

22F0.05(3,28)=2.95F=1.394337。說明在95%的置信水平下，不能拒絕原假設(shè):R1=0。即X2與剩余幾項(xiàng)不存在共線性。

c、做X3對其他變量的回歸

222X3=-90