31個省、市、自治區(qū)人均GDP的研究與分析

LinearregressionstatisticsforFinalPaper31個省、帀、自治區(qū)人均GDP的研究與分析姓名：白家源學(xué)號：0933012年級：09級院系：理學(xué)院專業(yè)：統(tǒng)計(jì)學(xué)2012年6月16日09統(tǒng)計(jì)期末論文09統(tǒng)計(jì)期末論文#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有圖4.1可以看出最優(yōu)子集為x,x），因此由向后回歸法得到的回歸方程為：有圖4.1可以看出最優(yōu)子集為34y二1.322x一1.136x34五、逐步回歸法建立回歸方程（一）、方法原理簡介逐步回歸的基本思想是有進(jìn)有出。具體做法是將變量一個一個引入，當(dāng)每引入一個自變量后，對已選入的變量要進(jìn)行逐個檢驗(yàn)，當(dāng)原引入的變量由于后面變量的引入而變得不再顯著時，要將其剔除。引入一個變量或從回歸方程中剔除一個變量，為逐步回歸的一步，每一步要進(jìn)行F檢驗(yàn)，以確保每次引入新的變量之前回歸方程中只包含顯著的變量。依次下去，直到既無顯著的自變量選入回歸方程，也無不顯著自變量從回歸方程中剔除為止。（二）、實(shí)證分析過程基于上述原理，通過SAS運(yùn)行得到結(jié)果如圖5.1所示：圖5.1：逐步回歸法運(yùn)行結(jié)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由圖四的結(jié)果可以知道：最優(yōu)子集為（x,x），則有逐步回歸法得到的方程為34y二1.322x一1.136x34六、四種回歸方法的評價（一）理論評價（1）Cp統(tǒng)計(jì)量的評價Cp統(tǒng)計(jì)量是從預(yù)測的角度提出的一個可以用于選擇最優(yōu)自變量子集的方法，但單純考慮預(yù)測還是有一些片面的。（2）向前回歸法的評價前進(jìn)法德明顯不足：不能反映引進(jìn)新的自變量后的變化情況。因?yàn)槟硞€自變量開始時是顯著的，但當(dāng)引入其他自變量后而變的不顯著，從而將新引入的自變量剔除，這種引入是“終身制”的，這種只考慮引入，而沒有考慮剔除的做法顯然是不全面的。（3）向后回歸法的評價向后回歸法的明顯不足：一開始把全部的自變量引入回歸方程，這樣計(jì)算量很大，如果有些自變量不太重要，一開始就不引入，就可減少一些計(jì)算量，與此同時，一旦某個自變量被剔除，就再也沒有機(jī)會重新進(jìn)入回歸方程。（4）逐步回歸法的評價逐步回歸法融合了向前回歸和向后回歸的思想，似的每個自變量基于回歸方程有進(jìn)有出，這種有進(jìn)有出可以說明自變量之間具有的相關(guān)性，如果自變量之間是完全不相關(guān)的，則新被引入的自變量就不會被剔除，而被剔除的自變量也不會再引入，全面考慮了自變量之間的關(guān)系。（二）實(shí)證分析評價c由分析過程中的到的結(jié)果可以看到，P統(tǒng)計(jì)量方法，向后回歸向前回歸及逐步回歸得到的方程是一致的，向前回歸中有X］這個變量，下面考慮變量之間的相關(guān)矩陣：

圖6.1相關(guān)矩陣圖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).由圖6.1的結(jié)果可以知道：x,x的相關(guān)系數(shù)為0.811,x,x之間的相關(guān)系數(shù)為0.798,1334x,x之間的相關(guān)系數(shù)為0.43814因此可以知道，最優(yōu)的方程為：y=1.322x-1.136x34七、結(jié)論通過四種方法對該問題建立線性回歸模型，可以得到線性回歸方程為y二1.322x-1.136x，即人均GDP與社會消費(fèi)品零售總額與年末人口之間有線性關(guān)系。34八、參考文獻(xiàn)1】線性統(tǒng)計(jì)模型王松桂陳敏陳立萍編高等教育出版社2】統(tǒng)計(jì)學(xué)案例與分析賈俊平郝靜等編著中國人民大學(xué)出版社3】應(yīng)用回歸分析何曉群劉文卿編著中國人民大學(xué)出版社[4】/view/97.htm[5】/question/250482365.html

九、附錄一）原始數(shù)據(jù)集地區(qū)gdp總值人均GDP進(jìn)出口總額固定資產(chǎn)投資社會消費(fèi)品零售總額年末人口數(shù)政府購買（元）（萬美兀）（億元）（億元）（萬人）（億元）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內(nèi)蒙古9740.2540214.56859463717336.82855.32422638.8637遼寧15212.4935222.2505698473212292.55812.64319837.5412吉林7278.7526569.144611883096411.62957.32740500.9333黑龍江8587.0022443.805513360875028.83401.83826608.4898上海15046.4578326.1322273329025043.85173.21921723.1081江蘇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山東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廣東39482.5640965.51156319885212933.114891.896381869.8007廣西7759.1615978.500813559905237.22790.74856646.559海南1654.2119144.398848318988.3537.5864164.4745重慶6530.0122840.18897717095214.32479.02859422.3409四川14151.2817289.2853215157011371.95758.781851034.4003貴州3912.6810301.94842727162412.01247.33798539.2601云南6169.7513497.59357457434526.42051.14571684.5816西藏441.3615217.736128875378.3156.6290184.682陜西8169.8021659.06688673006246.92699.73772669.4632甘肅3387.5612853.77134484602363.01183.02635415.6014青海1081.2719401.937971710798.2300.5557143.6008寧夏1353.3121646.03331961331075.9339.3625135.1241新疆4277.0519813.724416125352725.51177.52159525.6889二）分析數(shù)據(jù)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內(nèi)家古0.699389-0.455770.057045-0.39811-0.67142-0.17725遼寧0.399575-0.010061.0735420.4282870.0264440.325948吉林-0.12009-0.43791-0.13273-0.36961-0.55462-0.5266黑龍江-0.36784-0.427-0.41636-0.24539-0.15493-0.25418上海2.9881811.491869-0.41330.249611-0.855760.036116江蘇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山東0.4338260.6813662.4564452.258751.9215571.