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教材P115(1)：影响中国电信业务总量Y变换的主要因素：邮政业务总量（X1，百亿元），中国人口数X2（亿人），市镇人口比重X3（%），人均GDPX4（千元），人均消费水平X5(千元)的历年数据资料年份YX1X2X3X4X519911.51630.527511.58230.26371.8790.89619922.26570.636711.71710.27632.2871.07019933.82450.802611.85170.28142.9391.33119945.92300.958911.98500.28623.9231.74619958.75511.133412.11210.29044.8542.236199612.08751.332912.23890.29375.5762.641199712.68951.443412.36260.29926.0532.834199822.64941.662812.48100.30406.3072.972199931.32381.984412.59090.30896.5343.143要求：利用eviews软件，（1）建立关于中国电信业务总量的多元线性回归模型，并进行检验（R2，t检验和F检验）；（2）采用相关系数法、辅助回归判定系数法和方差膨胀因子法检验模型是否存在多重共线性；（3）若存在多重共线性，对模型进行修正，给出一个比较合理的模型。（1）Y=781.5127+85.43091X1-74.95793X2+190.0814X3+1.105414X4-10.25376X51.2812272.834714-1.2026760.4730050.133324-0.643591R2检验:R-squared0.992785由可决系数可知，模型对观测数据的拟合度良好。T检验：自由度为n-k-1,9-5-1=3,显著性水平为5%的情况下的临界值为3.182，我们可以看到参数都是不显著的。F检验：F-statistic55.04055通过查表可得：临界值为9.01，由此可知，模型在总体上是显著的。（2）相关系数法检验：YX1X2X3X4X5Y10.958036229670.9374632689630.8971049058990.9092721687180.916461592287X10.9580362296710.9968424596020.9700228717170.9883125918740.989432148651X20.9374632689630.99684245960210.9839266333170.9914441435140.989685126413X30.8971049058990.9700228717170.98392663331710.9647023284620.957769394639X40.9092721687180.9883125918740.9914441435140.96470232846210.998809926768X50.9164615922870.9894321486510.9896851264130.9577693946390.9988099267681由表我们可以看出解释变量之间两两高度相关。辅助回归判定系数法：X1=-14.23331+1.270257X2其可决系数为0.993695同理可得其它相关关系，可以判断出两两之间存在显著的线性关系。方差膨胀因子法：1/（1-R2）大于100，因此，模型存在严重的多重共线性。（3）1Y=-9.110972+16.77988X1-3.9450448.186720R-squared0.917833Durbin-Watsonstat1.543622AdjustedR-squared0.904139F-statistic67.022392Y=-243.2283+20.92310X2-6.3669096.596986R-squared0.878837AdjustedR-squared0.858644Durbin-Watsonstat1.590634F-statistic43.520225Y=-130.5249+485.3849X3-4.6582094.973657R-squared0.804797AdjustedR-squared0.772263Durbin-Watsonstat1.416653F-statistic24.737274Y=-6.935319+3.701980X4-2.2151745.351374R-squared0.826776AdjustedR-squared0.797905Durbin-Watsonstat1.453186F-statistic28.637213Y=-6.764767+7.874166X5-2.2846735.610438R-squared0.839902AdjustedR-squared0.813219Durbin-Watsonstat1.490024F-statistic31.47701判断标准：t=2.365F=5.59可知，x1与y线性关系强，拟合度较好。逐步回归：将其余变量逐一代入式Y=-9.110972+16.77988X1得如下几个模型：Y=687.2329+65.37207X1-62.11620X22.6713343.630019-2.706802R-squared0.966672AdjustedR-squared0.953340Durbin-Watsonstat1.610925F-statistic72.51090Y=531.6960+531.6960X1-48.39733X2-9.860049X53.5985017.300064-3.675631-3.552079R-squared0.991977AdjustedR-squared0.985960Durbin-Watsonstat2.823010F-statistic164.8635Y=534.7930+74.70843X1-48.67406X2+0.100719X4+-10.05465X5R-squared0.991978AdjustedR-squared0.981282Durbin-Watsonstat2.827862F-statistic92.74236Y=781.5127+85.43091X1-74.95793X2+190.0814X3+1.105414XX4-10.25376X51.2812272.834714-1.2026760.4730050.133324-0.643591R-squared0.992785AdjustedR-squared0.974748Durbin-Watsonstat2.792228F-statistic55.04055由此可见，模型为Y=531.6960+531.6960X1-48.39733X2-9.860049X5