回归分析的一般步骤

1、回归分析的一般步骤案例1为了研究货运量与工业总产值、农业总产值、居民非商品支出的关系。收集了这三者的数据。试完成下列问题（显著性水平:二0.05）（1）构造多元线性计量经济模型，并进行参数估计；（2）对模型参数以及变量之间线性关系进行显著性检验；（3）是否需要对模型进行调整，给出调整后的模型，并重新估计模型参数。解：（1）根据经济理论可以认为，货运量与工业总产值、农业总产值、居民非商品支出具有较强的关系，分别以r, X 1, X 2, X 3表示，建立如下的线性模型：Y = p +p X +p X +p X + ui 01 1i 2 2i3 3ii利用Eviews软件得到的结果如表1所示。表1

2、Dependent Variable: YMethod: Least SquaresDate: 11/22/08 Time: 16:41Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb.C-340.4483157.9296-2.1556960.0745X14.0204401.6985522.3669810.0558X26.4167412.7597412.3251250.0059X311.435377.2222231.5833590.1644R-squared0.831115Mean

3、 dependent var231.5000Adjusted R-squared0.746673S.D.dependent var43.40059S.E. of regression21.84423Akaike info criterion9.294925Sum squared resid2863.022Schwarz criterion9.415959Log likelihood-42.47463F-statistic9.842380Durbin-Watson stat2.228638Prob(F-statistic)0.009845根据多元线性回归关于Eviews输出结果可以得到参数的估计

4、值为：p 0 =340.448, p 1 = 4.020, p 2 = 6.416, p 3 = 11.435从而初步得到的回归方程为Y = 340.448 + 4.020X + 6.416X +11.435Xi1i2i3i（2）从Eviews输出的结果可以看出：调整的样本可决系数为0.746673，说 明回归方程拟合优度比较好。回归方程显著性检验的F值为9.842380，其对应的 检验概率为0.009845，小于显著性水平:=0.05，说明变量之间线性关系显著。解 释变量的检验概率都大于0.05,说明这两个变量X 1, X3没有通过t检验，而X2通 过了t检验，所以需要对这个模型做出调整。（

5、3）根据（2）的分析，需要删除不显著的解释变量，鉴于X3最不显著，所以首先剔除X，重新拟合得到的回归结果如表2。3表2Dependent Variable: YMethod: Least SquaresDate: 11/22/08 Time: 16:53Sample: 1 10Included observations: 10VariableCoefficientStd. Error t-StatisticProb.C-459.6237153.0576-3.0029460.0199X14.6756301.8160712.5745860.0368X28.9709612.4684613.63423

6、20.0084R-squared0.760549Mean dependent var231.5000Adjusted R-squared0.692134S.D. dependent var43.40059S.E. of regression24.08112Akaike info criterion9.444058Sum squared resid4059.301Schwarz criterion9.534834Log likelihood-44.22029F-statistic11.11674Durbin-Watson stat1.894940Prob(F-statistic)0.006718

7、显然此时的估计结果都比较满意，无论是回归方程检验，还是参数显著性检 验的检验概率，都显著小于0.05。D-W值为1.894940，显著性水平:=0.05下查Durbin-Watson表，其中n=10，解释变量的个数为1,得到下限临界值* = 1.077， 上限临界值du = 1.361，因为统计量du = 1.361D-W=1.8949404-匕=1.361，这 时表明随机误差项不存在自相关。可以认为此时得到的模型是适合的，因此最终 的模型为Y =459.624 + 4.676X + 8.971Xi1i2i两个回归系数的经济意义为：当农业总产值不变时，工业总产值每增加1 亿元，货运量就增加约4

8、.676万吨，当工业总产值不变时，农业总产值每增加1 亿元，货运量就增加约8.971万吨。案例2利用表中的数据，对随机误差项具有异方差的回归模型给出一般解 决方法和步骤。解：第一步，用OLS估计参数。根据经济理论可以设模型为丫 =0 +P X + u i 01 i i利用Eviews软件得到的结果如表1所示。表1Dependent Variable: YMethod: Least SquaresDate: 11/22/08 Time: 17:28Sample: 1 38Included observations: 38VariableCoefficientStd. Error t-Statis

9、ticProb.C3.77260633.532080.1125070.9110X0.0636940.0124425.1193660.0000R-squared0.421295Mean dependent var100.9732Adjusted R-squared0.405220S.D. dependent var220.9185S.E. of regression170.3767Akaike info criterion13.16510Sum squared resid1045016.Schwarz criterion13.25129Log likelihood-248.1368F-stati

10、stic26.20790Durbin-Watson stat2.024988Prob(F-statistic)0.000010根据表整理可以得到如下结果Y = 3.773 + 0.064X。ii从回归结果看，在显著性水平:二0.05下，X的系数是显著的，且F值很大，但是决定系数为0.421295较小，且截距项并不显著，所以此模型并不理想。第二步，异方差检验（White检验）表2White Heteroskedasticity Test:F-statistic2.163749Probability0.0130019Obs*R-squared4.181423Probability0.0123599

11、Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 11/22/08 Time: 17:38Sample: 1 38Included observations: 38VariableCoefficientStd. Errort-StatisticProb.C-19186.2332216.87-0.5955340.5553X60.6915829.609192.0497550.0479R-squared0.110037Mean dependent var27500.42Adjusted R-squared0.059

12、182S.D. dependent var143442.9S.E. of regression139133.5Akaike info criterion26.59991Sum squared resid6.78E+11Schwarz criterion26.72920Log likelihood-502.3983F-statistic2.163749Durbin-Watson stat2.020277Prob(F-statistic)0.130019由表2中得到White检验的检验概率为0.0123599,小于=0.05, 拒绝原假设，故随机误差项存在异方差。第三步，异方差处理表3Depend

13、ent Variable: LY Method: Least SquaresDate: 11/22/08 Time: 17:50Sample: 1 38Included observations: 37VariableCoefficientStd. Error t-StatisticProb.C-4.2489130.591023-7.1890770.0000LX1.1239740.09145012.290540.0000R-squared0.811886Mean dependent var2.687126Adjusted R-squared0.806511S.D. dependent var2

14、.428033S.E. of regression1.068028Akaike info criterion3.022043Sum squared resid39.92392Schwarz criterion3.109120Log likelihood-53.90780F-statistic151.0573Durbin-Watson stat1.952035Prob(F-statistic)0.000000表4White Heteroskedasticity Test:F-statistic4.055962Probability0.045662Obs*R-squared7.121401Prob

15、ability0.041105XA2-0.0063240.003506-1.8034920.0799Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 11/22/08 Time: 17:51Sample: 1 38Included observations: 37VariableCoefficientStd. Error t-StatisticProb.C0.5487182.4810490.2211640.0263LX0.0893040.8965550.0996080.0212LXA2-0.0004980.082257-0.0060510.0952R-squared0.953281Mean dependent var1.079025Adjusted R-squared0.911349S.D.dependent var2.858163S.E. of regression2.936197Akaike info criterion5.069712Sum squared resid293.1226Schw