线性与对数模型案例分析

线性与对数模型案例分析----关于农村居民各种不同类型的收入对消费支出影响一、实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。此实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宜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全国2829.021374.801930.96100.50180.78北京5724.505047.391957.09678.81592.19天津3341.063247.922707.35126.37146.29河北2495.331514.682039.64107.72139.78山西2253.251374.341622.8674.51109.21内蒙古2771.97590.702406.2184.81260.16辽宁3066.871499.472210.84141.80238.30吉林2700.66605.112556.70187.74291.58黑龙江2618.19654.862521.51145.69230.38上海8006.006685.98767.71558.171126.80江苏4135.213104.772271.37178.51258.58浙江6057.163575.143084.28311.60363.80安徽2420.941184.111617.7652.78114.43福建3591.401855.532481.62113.52384.09江西2676.601441.341863.5035.13119.57山东3143.801671.542409.78127.60159.40河南2229.281022.742108.2640.3789.66湖北2732.461199.162095.1525.9199.13湖南3013.321449.651743.3942.49154.09广东3885.972906.151693.64220.87259.12广西2413.93974.321705.7522.4569.96海南2232.19555.722486.9449.44163.43重庆2205.211309.911349.5727.29187.07四川2395.041219.511586.5452.84143.50贵州1627.07715.491112.8136.93119.38云南2195.64441.811631.6082.1994.85西藏2002.24568.391410.51156.00300.06陕西2181.00848.261219.3352.56140.04甘肃1855.49637.371291.8552.56152.27青海2178.95653.301374.36100.66230.05宁夏2246.97823.091662.0753.35221.63新疆2032.36254.072323.0158.69101.51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、1X、2X、3X、4X。1、建立如下线性模型：iXAXAXAXAAY453423121用Eviews得到如下回归结果：DependentVariable:YMethod:LeastSquaresDate:06/16/10Time:22:54Sample:132Includedobservations:32VariableCoefficientStd.Errort-StatisticProb.C483.4083253.13621.9096760.0669X10.6271400.0804207.7983110.0000X20.4810250.1155234.1638690.0003X3-0.2563070.906787-0.2826540.7796X42.6781490.6165544.3437380.0002R-squared0.951902Meandependentvar2976.846AdjustedR-squared0.944777S.D.dependentvar1346.774S.E.ofregression316.4870Akaikeinfocriterion14.49504Sumsquaredresid2704428.Schwarzcriterion14.72406Loglikelihood-226.9207Hannan-Quinncriter.14.57096F-statistic133.5893Durbin-Watsonstat1.735377Prob(F-statistic)0.000000参数估计的结果为：4321^678149.2256307.0481025.062714.04083.483XXXXY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)2R=0.9519022__R=0.9447772、建立如下双对数回归模型453423121lnlnlnlnlnXBXBXBXBBY得到如下回归结果：VariableCoefficientStd.Errort-StatisticProb.C3.2524950.7492294.3411250.0002LOG(X1)0.2879180.0392307.3391680.0000LOG(X2)0.1846950.0840192.1982470.0367LOG(X3)0.0637840.0552971.1534850.2588LOG(X4)0.1840940.0774502.3769490.0248R-squared0.879103Meandependentvar7.929207AdjustedR-squared0.861193S.D.dependentvar0.349982S.E.ofregression0.130392Akaikeinfocriterion-1.093940Sumsquaredresid0.459057Schwarzcriterion-0.864919Loglikelihood22.50305F-statistic49.08282Durbin-Watsonstat2.076804Prob(F-statistic)0.000000参数估计结果为：^lnY3.252495+0.287918ln4321ln184094.0ln063784.0ln184695.0XXXX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)2R=0.8791032__R=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2iR表示变量iX对于其他变量的回归结果的样本判定系数。a、做1X对其他变量的回归^1X=232.2140+0.0619792X+5.6614973X+2.2881384X21R=0.749576建立F检验：F=)()1()1(2121knRkR~F（k-1,n-k）代入数据得;F=)432()749576.01()14(749576.0=27.93679原假设0H：21R=0；1H：21R≠0，在α=0.05的显著水平下，05.0F(3,28)=2.95F=27.93679。说明在95%的置信水平下，拒绝原假设:21R=0。即1X与剩余几项存在共线性。b、做2X对其他变量的回归^2X=2043.177+0.0300351X+1.9579213X-1.8915504X22R=0.129974建立F检验：F=)()1()1(2222knRkR~F（k-1,n-k）代入数据得;F=)432()129974.01()14(129974.0=1.394337原假设0H：22R=0；1H：22R≠0，在α=0.05的显著水平下，05.0F(3,28)=2.95F=1.394337。说明在95%的置信水平下，不能拒绝原假设:21R=0。即2X与剩余几项不存在共线性。c、做3X对其他变量的回归^3X=-90.55611+0.0445301X+0.0317782X+0.3839404X23R=0.812587建立F检验：F=)()1()1(2323knRkR~F（k-1,n-k）代入数据得;F=)432()812587.01()14(812587.0=40.46755原假设0H：23R=0；1H：23R≠0，在α=0.05的显著水平下，05.0F(3,28)=2.95F=40.46755。说明在95%的置信水平下，拒绝原假设:23R=0。即3X与剩余几项存在共线性。d、做4X对其他变量的回归^4X=-184.9268+0.0389281X-0.0664072X+0.8304853X24R=0.779290建立F检验：F=)()1()1(2424knRkR~F（k-1,n-k）代入数据得;F=)432()779290.01()14(779290.0=32.95443原假设0H：24R=0；1H：24R≠0，在α=0.05的显著水平下，05.0F(3,28)=2.95F=32.95443。说明在95%的置信水平下，拒绝原假设:24R=0。即4X与剩余几项存在共线性。2、异方差检验a、残差的图形检验做2e对Yˆ图形：0200,000400,000600,000800,0001,000,00002,0004,0006,0008,000Y1RESIDEQ1该图清楚地表明了残差平方与消费性支出是系统相关的。散点图表明回归方程中很可能存在异方差问题。b、怀特检验HeteroskedasticityTest:WhiteF-statistic9.576534Prob.F(14,17)0.0000Obs*R-squared28.39906Prob.Chi-Square(14)0.0126ScaledexplainedSS52.82365Prob.Chi-Square(14)0.0000TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/21/10Time:22:21Sample:132Includedobservations:32VariableCoefficientStd.Errort-StatisticProb.C640414.2443785.51.4430720.1672X1-262.1711192.0428-1.3651700.1900X1^20.0438980.0411221.0674980.3007X1*X20.1395130.0670672.0802150.0529X1*X30.7032791.1568900.6079050.5513X1*X4-1.0364070.822200-1.2605280.2245X2-332.3679530.6481-0.6263430.5394X2^20.0458940.1524230.3010930.7670X2*X31.9616091.4322461.3696040.1886X2*X4-0.7401110.784698-0.9431790.3588X3-3185.8422770.232-1.15