某地区某农产品收购量与

某地区某农产品收购量与年份YX196935.5819.6919557.965.33197031.0321.13195615.346.82197114.3332.34195713.558.17197213.8819.57195810.949.48197314.6616.3919596.398.03197419.3717.9619601.943.58197535.4718.3919610.061.17197635.4918.8319620.660.92197732.7721.1519636.041.63197832.219.8196415.417.73197938.534.86196515.39.46198053.7222.96196619.3213.97198151.317.45196735.7617.32198234.0416.05196835.0317.36198316.0317.38198421.7916.79第一步：描述统计量YX

Mean

22.35857

14.55500

Median

17.36500

16.85500

Maximum

53.72000

34.86000

Minimum

0.060000

0.920000

Std.Dev.

14.95748

8.646472

Skewness

0.324925

0.293930

Kurtosis

2.144772

2.808145

Jarque-Bera

1.346006

0.446120

Probability

0.510174

0.800067

Sum

626.0400

407.5400

SumSq.Dev.

6040.606

2018.560

Observations

28

28由表可知：y和x的最值，平均值，中位数，方差等数据。由经济理论知，农产品收购量受销售量影响，当销售量增加时，农产品收购量也会增加，它们之间有同步变动趋势，农产品收购量除受销售量的影响之外，还受到其他一些变量及随机因素的影响，将这些变量均归并到随机变量u中，根据X与Y的样本数据作散点图散点图由图可知，它们的变化趋势是线性的，由此建立农产品收购量与销售量之间的一元线性回归模型，通过Eviews一元线性回归模型参数DependentVariable:YMethod:LeastSquaresDate:06/10/12Time:16:31Sample:19551982Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.

C4.8570824.1098471.1818160.2480X1.2024380.2439014.9300350.0000R-squared0.483155

Meandependentvar22.35857AdjustedR-squared0.463277

S.D.dependentvar14.95748S.E.ofregression10.95806

Akaikeinfocriterion7.694777Sumsquaredresid3122.055

Schwarzcriterion7.789934Loglikelihood-105.7269

Hannan-Quinncriter.7.723867F-statistic24.30524

Durbin-Watsonstat0.964078Prob(F-statistic)0.000040一、即样本回归方程为在显著水平为0.05的条件下，查自由度为28-2=26的t分布，得临界值2.06，两参数的t值分别为1.181816,4.930035，故回归系数均显著不为零，回归模型中应包含常数项，X对Y有显著影响。二、通过 White检验该模型中随机误差项是否存在异方差HeteroskedasticityTest:WhiteF-statistic4.502771

Prob.F(2,25)0.0214Obs*R-squared7.415120

Prob.Chi-Square(2)0.0245ScaledexplainedSS10.42735

Prob.Chi-Square(2)0.0054TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/10/12Time:16:39Sample:19551982Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.

C8.50754993.962200.0905420.9286X-0.06378212.23389-0.0052140.9959X^20.3660030.3650621.0025780.3257R-squared0.264826

Meandependentvar111.5020AdjustedR-squared0.206012

S.D.dependentvar205.0724S.E.ofregression182.7318

Akaikeinfocriterion13.35487Sumsquaredresid834773.1

Schwarzcriterion13.49761Loglikelihood-183.9682

Hannan-Quinncriter.13.39851F-statistic4.502771

Durbin-Watsonstat1.736188Prob(F-statistic)0.021374由检验结果可知，Obs*R-squared值为,7.415120明显大于在显著水平0.05，自由度为2的5.991，故该模型存在异方差。用加权最小二乘法剔除异方差，权重为w=(8.507549-0063782*x+0.366003*x^2)^(-0.5)所得结果为DependentVariable:YMethod:LeastSquaresDate:06/10/12Time:16:47Sample:19551982Includedobservations:28Weightingseries:WVariableCoefficientStd.Errort-StatisticProb.

C-0.1478591.484471-0.0996040.9214X1.5922710.1690469.4191350.0000WeightedStatisticsR-squared0.773361

Meandependentvar15.62696AdjustedR-squared0.764645

S.D.dependentvar7.817281S.E.ofregression6.546334

Akaikeinfocriterion6.664437Sumsquaredresid1114.217

Schwarzcriterion6.759594Loglikelihood-91.30211

Hannan-Quinncriter.6.693527F-statistic88.72011

Durbin-Watsonstat0.888837Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.430297

Meandependentvar22.35857AdjustedR-squared0.408386

S.D.dependentvar14.95748S.E.ofregression11.50476

Sumsquaredresid3441.349Durbin-Watsonstat1.148584修正后再次进行怀特检验HeteroskedasticityTest:WhiteF-statistic0.653557

Prob.F(2,25)0.5289Obs*R-squared1.391228

Prob.Chi-Square(2)0.4988ScaledexplainedSS1.066437

Prob.Chi-Square(2)0.5867TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:06/10/12Time:16:50Sample:19551982Includedobservations:28CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.

C2461.9892805.3630.8776010.3885WGT^2-412.8241474.0004-0.8709360.3921X^2*WGT^2-17.6234720.46509-0.8611480.3973R-squared0.049687

Meandependentvar39.79345AdjustedR-squared-0.026338

S.D.dependentvar54.03521S.E.ofregression54.74218

Akaikeinfocriterion10.94410Sumsquaredresid74917.66

Schwarzcriterion11.08684Loglikelihood-150.2174

Hannan-Quinncriter.10.98774F-statistic0.653557

Durbin-Watsonstat1.624385Prob(F-statistic)0.528853结果中Obs*R-squared比原来小,故在一定程度上剔除了异方差，那么一元线性回归方程为三、检验误差项是否存在自相关，由DW 值为0.964078，小于显著水平为0.05,样本容量为28下的值1.33，所以存在自相关。检验是否存在高阶自相关，最后结果如下：用广义差分法消除自相关：Breusch-GodfreySerialCorrelationLMTest:F-statistic9.222670Obs*R-squared7.545722

Prob.F(1,25)0.0055

Prob.Chi-Square(1)0.0060TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/10/12Time:17:09Sample:19551982Includedobservations:28Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.

C2.0850973.647450X-0.1302000.216870RESID(-1)0.5383710.1772770.5716590.5727-0.6003590.55373.0368850.0055R-squared0.269490AdjustedR-squared0.211049S.E.ofregression9.551319

Meandependentvar1.46E-15Sumsquaredresid2280.692

S.D.dependentvar10.75322Loglikelihood-101.3307

Akaikeinfocriterion7.452193F-statistic4.611335

Schwarzcriterion7.594929Prob(F-statistic)0.019739

Hannan-Quinncriter.7.495829

Durbin-Watsonstat1.757452DependentVariable:YYMethod:LeastSquaresDate:06/10/12Time:17:22Sample(adjusted):19561982Includedobservations:27afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

C0.5118980.3673101.3936420.1757XX0.0496680.0214442.3162190.0290R-squared0.176680

Meandependentvar1.251790AdjustedR-squared0.143747

S.D