线性与对数模型案例分析

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关于农村居民各种不同类型

的收入对消费支出影响

一、试验目的

影响农村居民收入的因素有多种，主要因素可能有以下4项：农业经营收入、工资性收入、财产性收入及转移性收入。此试验就是研究这四项不同类型收入对消费支出是否有影响，又怎样的影响，建立怎样的模型比较适合描述农村居民收入的变化。

二、模型设定

以下是全国主要地区消费性支出、工资性收入、家庭经营纯收入、财产性收入、转移性收入的数据。地区全国北京天津河北山西内蒙古辽宁吉林黑龙江上海江苏浙江安徽消费性支出工资性收入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家庭经营纯财产性收入转移性收入收入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福建江西山东河南湖北湖南广东广西海南重庆四川贵州云南西藏陕西甘肃青海宁夏新疆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分别设消费性支出、工资性收入、家庭经营纯收入、财产性收入、转移性收入为Y、X1、X2、

X3、X4。

1、建立如下线性模型：

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

用Eviews得到如下回归结果：

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

参数估计的结果为：

^

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、建立如下双对数回归模型

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

得到如下回归结果：

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

参数估计结果为：

^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、模型检验

①线性模型的检验1、多重共线性检验

(1)假设Ri表示变量Xi对于其他变量的回归结果的样本判定系数。a、做X1对其他变量的回归

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

^2__22R12=0.749576

建立F检验：

R12(k?1)F=~F（k-1,n-k）2(1?R1)(n?k)代入数据得;

F=

0.749576(4?1)

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

原假设H0：R1=0；H1：R1≠0，在α=0.05的显著水平下，

22F0.05(3,28)=2.95F=1.394337。说明在95%的置信水平下，不能拒绝原假设:R1=0。即X2与剩余几项不存在共线性。

c、做X3对其他变量的回归

222X3=-90