31个省、市、自治区人均GDP的研究与分析

LinearregressionstatisticsforFinalPaper31个省、帀、自治区人均GDP的研究与分析姓名：白家源学号：0933012年级：09级院系：理学院专业：统计学2012年6月16日09统计期末论文09统计期末论文#VariableLabelParameDFEstimateInterceptInterceptVariableLabelParameDFEstimateInterceptIntercept1-6.9903E-1611.322861-1.13579StandardErrortValuePr>|t|StandardizedEstimate0.11136-0.001.000000.187947.04<.00011.322860.18794-6.04<.0001-1.13579StepVariableRemovedLabelNumberVarsInPartialR-SquareModelR-SquareC(p)FValuePr>F1XIXI40.00360.67484.27800.280.60262X5X530.01410.66073.37041.120.29893X2X220.01950.64122.88611.550.2236有图4.1可以看出最优子集为x,x），因此由向后回归法得到的回归方程为：有图4.1可以看出最优子集为34y二1.322x一1.136x34五、逐步回归法建立回归方程（一）、方法原理简介逐步回归的基本思想是有进有出。具体做法是将变量一个一个引入，当每引入一个自变量后，对已选入的变量要进行逐个检验，当原引入的变量由于后面变量的引入而变得不再显著时，要将其剔除。引入一个变量或从回归方程中剔除一个变量，为逐步回归的一步，每一步要进行F检验，以确保每次引入新的变量之前回归方程中只包含显著的变量。依次下去，直到既无显著的自变量选入回归方程，也无不显著自变量从回归方程中剔除为止。（二）、实证分析过程基于上述原理，通过SAS运行得到结果如图5.1所示：图5.1：逐步回归法运行结果TheREGProcedureModel:M0DEL1DependentVariable：YYStepwiseSelection：Step1VariableXIEntered：R-Square=0.2942andC（p）=27.8552AnalysisofVarianceSumofMeanSourceDFSquaresSquareFValuePr>FModel18.826528.8265212.090.0016Error2921.173480.73012CorrectedTotal3030.00000ParameterStandardVariableEstimateErrorTypeIISSFValuePr>FIntercept-3.1558E-160.153473.08738E-300.001.0000XI0.542420.156008.8265212.080.0016Boundsonconditionnumber：1,1

ModeI:MODEL1DependentVariable：YYBackwardElimination：Step1Boundsonconditionnumber：18.002,180.08

StepwiseSelection：Step2VariableX4Entered：R-Square=0.4188andC(p)=20.1665AnalysisofVarianceSourceDFSumofSquaresMeanSquareFValuePr>FModel212.566236.2831210.090.0005Error2817.488770.62263CorrectedTotal3030.00000ParameterStandardVariab1eEmtimateErrorTypeIISSFValuePr>FIntercept-2.9597E-160.141722.71559E-300.001.0000XI0.714460.1602612.3752319.880.0001X4-0.392750.160263.739726.010.0208Boundsonconditionnumber：1.2374,4.9497StepwiseSelection：Step3TheREGProcedureModel：MODEL1

DependentVariable：¥YStepwiseSelection：Step3VariableX3Entered：R-Square=0.6462andC(p)=4.5019AnalysisofVarianceSourceDFSumofSquaresMeanSquareFValuePr>FModel319.384596.4615316.43<.0001Error2710.615410.39316CorrectedTotal3030.00000ParameterStandardVariab1eEstimateErrorTypeIISSFValuePr>FIntcreept-7.8013E-160.112621.79118E-290.001.0000XI-0.149500.243430.148290.300.5443X31.513030.363326.0183517.340.0003X4-1.222100.2363910.5085526.73<.0001Boundsonconditionnumber：10.073,56.574Boundsonconditionnumber：18.002,180.08

StepwiseSelection：Step4VariableXIRemoved：R-Square二0.6412andC(p)二2.88611234143LabelNumberVarsInPartialR-SquareModelR-SquareC(p)FYalue1234143LabelNumberVarsInPartialR-SquareModelR-SquareC(p)FYaluePr>FXI10.29420.294227.355212.090.0016X420.12470.418920.16656.010.0208X330.22730.64624.501917.340.0003XI20.00490.64122.88810.380.5443VariableVariableSt已pEnteredRemovedSummaryofStepwiseSelectionVariableLabelInterceptIriterceptX3X3X4X4ParameterEstimatestValuePr>ItlStandardizedEstimatEParameE吐imeitEStandardError-6.9983E-1E0.11136-0.001.000001.322860.187947.04<.00011.32286-1.135790.18794-6.04<.0001-1.13579DF111AnalysisofVarianceSourceDFSumofSquaresMeanSquareFValuePr>FModel219.236299.6181525.02<.0001Error2810.763710.38442CorrectedTotal3030.00000VariableParameterEstimateStandardErrorTypeIISSFValuePr>FIritercept-6.9983E-160.111361.51826E-290.001.0000X31.322860.1879419.0452949.54<.0001X4-1.135790.1879414.0395136.52<.0001Boundsonccinditi口仃number：2.7565,11.026由图四的结果可以知道：最优子集为（x,x），则有逐步回归法得到的方程为34y二1.322x一1.136x34六、四种回归方法的评价（一）理论评价（1）Cp统计量的评价Cp统计量是从预测的角度提出的一个可以用于选择最优自变量子集的方法，但单纯考虑预测还是有一些片面的。（2）向前回归法的评价前进法德明显不足：不能反映引进新的自变量后的变化情况。因为某个自变量开始时是显著的，但当引入其他自变量后而变的不显著，从而将新引入的自变量剔除，这种引入是“终身制”的，这种只考虑引入，而没有考虑剔除的做法显然是不全面的。（3）向后回归法的评价向后回归法的明显不足：一开始把全部的自变量引入回归方程，这样计算量很大，如果有些自变量不太重要，一开始就不引入，就可减少一些计算量，与此同时，一旦某个自变量被剔除，就再也没有机会重新进入回归方程。（4）逐步回归法的评价逐步回归法融合了向前回归和向后回归的思想，似的每个自变量基于回归方程有进有出，这种有进有出可以说明自变量之间具有的相关性，如果自变量之间是完全不相关的，则新被引入的自变量就不会被剔除，而被剔除的自变量也不会再引入，全面考虑了自变量之间的关系。（二）实证分析评价c由分析过程中的到的结果可以看到，P统计量方法，向后回归向前回归及逐步回归得到的方程是一致的，向前回归中有X］这个变量，下面考虑变量之间的相关矩阵：

图6.1相关矩阵图CorrelationsX1X2X3X4X5X1PearsonCorrelationSig.(2-tailed)N131.521**.00331.811**.00031.438*.01431.755**.00031X2PearsonCorrelationSig.(2-tailed)N.521**.00331131.878**.00031.867**.00031.879**.00031X3PearsonCorrelationSig.(2-tailed)N.811**.00031.878**.00031131.798**.00031.952**.00031X4PearsonCorrelationSig.(2-tailed)N.438*.01431.867**.00031.798**.00031131.876**.00031X5PearsonCorrelationSig.(2-tailed)N.755**.00031.879**.00031.952**.00031.876**.00031131**.Correlationissignificantatthe0.01level(2-tailed).*.Correlationissignificantatthe0.05level(2-tailed).由图6.1的结果可以知道：x,x的相关系数为0.811,x,x之间的相关系数为0.798,1334x,x之间的相关系数为0.43814因此可以知道，最优的方程为：y=1.322x-1.136x34七、结论通过四种方法对该问题建立线性回归模型，可以得到线性回归方程为y二1.322x-1.136x，即人均GDP与社会消费品零售总额与年末人口之间有线性关系。34八、参考文献1】线性统计模型王松桂陈敏陈立萍编高等教育出版社2】统计学案例与分析贾俊平郝静等编著中国人民大学出版社3】应用回归分析何晓群刘文卿编著中国人民大学出版社[4】/view/97.htm[5】/question/250482365.html

九、附录一）原始数据集地区gdp总值人均GDP进出口总额固定资产投资社会消费品零售总额年末人口数政府购买（元）（万美兀）（亿元）（亿元）（万人）（亿元）北京12153.0369248.034287087054616.95309.91755744.5414天津7521.8561244.870472034884738.22430.81228358.7004河北17235.4824501.7059402672812269.85764.97034941.529山西7358.3121469.32339322624943.22809.03427627.1456内蒙古9740.2540214.56859463717336.82855.32422638.8637辽宁15212.4935222.2505698473212292.55812.64319837.5412吉林7278.7526569.144611883096411.62957.32740500.9333黑龙江8587.0022443.805513360875028.83401.83826608.4898上海15046.4578326.1322273329025043.85173.21921723.1081江苏34457.3044604.91913659319418949.911484.177251545.0502浙江22990.3544382.91512107117310742.38622.351801139.485安徽10062.8216413.015815655218990.73527.86131699.5846福建12236.5333737.331181239526231.24481.03627584.1033江西7655.1817271.901913830946643.12484.44432534.8133山东33896.6535792.58311635221619034.512363.094701309.4222河南19480.4620533.8463150682413704.56746.494871154.8495湖北12961.1022659.265717672947866.95928.45720764.9666湖南13059.6920386.653111607397703.44913.76406825.5987广东39482.5640965.51156319885212933.114891.896381869.8007广西7759.1615978.500813559905237.22790.74856646.559海南1654.2119144.398848318988.3537.5864164.4745重庆6530.0122840.18897717095214.32479.02859422.3409四川14151.2817289.2853215157011371.95758.781851034.4003贵州3912.6810301.94842727162412.01247.33798539.2601云南6169.7513497.59357457434526.42051.14571684.5816西藏441.3615217.736128875378.3156.6290184.682陕西8169.8021659.06688673006246.92699.73772669.4632甘肃3387.5612853.77134484602363.01183.02635415.6014青海1081.2719401.937971710798.2300.5557143.6008宁夏1353.3121646.03331961331075.9339.3625135.1241新疆4277.0519813.724416125352725.51177.52159525.6889二）分析数据集REGIONYX1X2X3X4X5BJ北京2.4429950.117185-0.500850.287811-0.916830.090402天津1.9623650.006083-0.47597-0.51673-1.11065-0.88684河北-0.24425-0.22841.0688870.4149571.0254130.589325山西-0.42636-0.45681-0.43393-0.41105-0.30158-0.20693内家古0.699389-0.455770.057045-0.39811-0.67142-0.17725辽宁0.399575-0.010061.0735420.4282870.0264440.325948吉林-0.12009-0.43791-0.13273-0.36961-0.55462-0.5266黑龙江-0.36784-0.427-0.41636-0.24539-0.15493-0.25418上海2.9881811.491869-0.41330.249611-0.855760.036116江苏0.9630512.1753872.4390822.0131471.2794782.117901浙江0.9497191.029680.7555761.2134380.3431981.0907安徽-0.73001-0.410070.396295-0.210180.693061-0.02346福建0.3103980.074024-0.169730.056181-0.22814-0.31595江西-0.67843-0.42353-0.08523-0.501760.068074-0.44079山东0.4338260.6813662.4564452.258751.9215571.