1、第五章异方差性作业 为了研究中国出口商品总额EXPORT对国内生产总值GDP的影响,搜集了19902015年相关的指标数据,如表所示。表3 中国出口商品总额与国内生产总值 (单位:亿元)时间出口商品总额 EXPORT 国内生产总值GDP 时间出口商品总额 EXPORT国内生产总值GDP1991200419922005199320061994200719952008199620091997201019982011199920122000201320012014200220152003资料来源:国家统计局网站 (1) 根据以上数据,建立适当线性回归模型。(2) 试分别用White检验法与ARCH检
2、验法检验模型是否存在异方差(3) 如果存在异方差,用适当方法加以修正。解:(1)Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 15:38Sample: 1991 2015Included observations: 25VariableCoefficientStd. Errort-StatisticProb.CXR-squaredMean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squ
3、ared resid+10Schwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)模型回归的结果:(2)white: 该模型存在异方差Heteroskedasticity Test: WhiteF-statisticProb. F(2,22)Obs*R-squaredProb. Chi-Square(2)Scaled explained SSProb. Chi-Square(2)Test Equation:Dependent Variable: RESID2
4、Method: Least SquaresDate: 04/18/20 Time: 17:45Sample: 1991 2015Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C+09+09X2XR-squaredMean dependent var+09Adjusted R-squared. dependent var+09. of regression+09Akaike info criterionSum squared resid+20Schwarz criterionLog likelihood
5、Hannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)ARCH检验:该模型存在异方差Heteroskedasticity Test: ARCHF-statisticProb. F(1,22)Obs*R-squaredProb. Chi-Square(1)Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 04/18/20 Time: 19:55Sample (adjusted): 1992 2015Included observatio
6、ns: 24 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C+08+08RESID2(-1)R-squaredMean dependent var+09Adjusted R-squared. dependent var+09. of regression+09Akaike info criterionSum squared resid+20Schwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-st
7、atistic)(3)修正:加权最小二乘法修正Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 20:46Sample: 1991 2015Included observations: 25Weighting series: W2Weight type: Inverse variance (average scaling)VariableCoefficientStd. Errort-StatisticProb.CXWeighted StatisticsR-squaredMean dependent varAdjuste
8、d R-squared. dependent var. of regressionAkaike info criterionSum squared resid+09Schwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Weighted mean dep.Unweighted StatisticsR-squaredMean dependent varAdjusted R-squared. dependent var. of regressionSum squ
9、ared resid+10修正后进行white检验:Heteroskedasticity Test: WhiteF-statisticProb. F(2,22)Obs*R-squaredProb. Chi-Square(2)Scaled explained SSProb. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 04/18/20 Time: 20:41Sample: 1991 2015Included observations: 25Collinear test re
10、gressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.CX*WGT2WGT2R-squaredMean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared resid+16Schwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statis
11、tic)修正后的模型为 表的数据是2011年各地区建筑业总产值(X)和建筑业企业利润总额(Y)。 表 各地区建筑业总产值(X)和建筑业企业利润总额(Y) (单位:亿元)地 区建筑业总产值X建筑业企业利润总额Y地 区建筑业总产值X建筑业企业利润总额Y 北 京 湖 北 天 津 湖 南 河 北 广 东 山 西 广 西 内蒙古 海 南 辽 宁 重 庆 吉 林 四 川 黑龙江 贵 州 上 海 云 南 江 苏 西 藏 浙 江 陕 西 安 徽 甘 肃 福 建 青 海 江 西 宁 夏 山 东 新 疆 河 南 数据来源:国家统计局网站根据样本资料建立回归模型,分析建筑业企业利润总额与建筑业总产值的关系,并判断模
12、型是否存在异方差,如果有异方差,选用最简单的方法加以修正。解:散点图:建立线性回归模型:Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 21:16Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.CXR-squaredMean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squa
13、red residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)white检验:Heteroskedasticity Test: WhiteF-statisticProb. F(2,28)Obs*R-squaredProb. Chi-Square(2)Scaled explained SSProb. Chi-Square(2)Test Equation:Dependent Variable: RESID2Method: Least SquaresD
14、ate: 04/18/20 Time: 21:19Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.CX2XR-squaredMean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson
15、statProb(F-statistic)模型存在异方差模型修正:加权最小二乘法Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 21:24Sample: 1 31Included observations: 31Weighting series: W2Weight type: Inverse variance (average scaling)VariableCoefficientStd. Errort-StatisticProb.CXWeighted StatisticsR-squaredMean dependen
16、t varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Weighted mean dep.Unweighted StatisticsR-squaredMean dependent varAdjusted R-squared. dependent var. of regressi
17、onSum squared residDurbin-Watson stat加权后进行white检验:Heteroskedasticity Test: WhiteF-statisticProb. F(2,28)Obs*R-squaredProb. Chi-Square(2)Scaled explained SSProb. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 04/18/20 Time: 21:25Sample: 1 31Included observations:
18、31Collinear test regressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.CX*WGT2WGT2R-squaredMean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson s
19、tatProb(F-statistic)修正成功,修正后的模型为: 表是2015年中国各地区人均可支配收入(X)与居民每百户汽车拥有量(Y)的数据。 表 中国各地区人均可支配收入X与居民每百户汽车拥有量时间人均可支配收入(元)X居民每百户汽车拥有量(辆)Y时间人均可支配收入(元)X居民每百户汽车拥有量(辆)Y 北 京湖 北天 津湖 南河 北广 东山 西广 西内蒙古海 南辽 宁重 庆吉 林四 川黑龙江贵 州上 海云 南江 苏西 藏浙 江陕 西安 徽甘 肃福 建青 海江 西宁 夏山 东新 疆河 南 (1)试根据上述数据建立各地区人均可支配收入与各地区居民每百户汽车拥有量的线性回归模型。(2)选用适
20、当方法检验模型是否存在异方差,并说明存在异方差的理由。(3)如果存在异方差,用适当方法修正。 解:(1)散点图:建立线性回归模型Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 21:32Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.CXR-squaredMean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum
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