计量经济学·多元线性回归模型2006年 217656.6 77597.2 63376.86 2007年 268019.4 93563.6 73300.1 2008年 316751.7 100394.94 79526.53 2009年 345629.2 82029.69 68618.37 2010年 408903 107022.84 94699.3 2011年 484123.5 123240.56 113161.392012年 534123 129359.3 114801 2013年 588018.8 137131.4 121037.5 2014年636138.7143911.66120422.84数据来源：国家统计局三、模型的检验及结果的解释、评价 (一）OLS 法的检验 相关系数：Y X1 X2 Y 10.97999191759670260.983524229450628 X1 0.9799919175967026 1 0.9975652794446187X20.9835242294506280.99756527944461871线性图：100,000200,000300,000400,000500,000600,000700,000YX1X2估计参数：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sample: 1985 2014Included observations: 30Variable Coefficient Std. Error t-Statistic Prob.C 3775.3193593260248769.92804671830.43048464471025450.6702600664360232X1 -0.91272630855511891.938518631883585-0.47083700591944140.6415389475333828X2 5.522785592511612.2548570541426052.4492841275083020.021087030146243R-squared 0.9675860494429319 Mean dependent var173871.8233333334Adjusted R-squared 0.9651850160683343 S.D. dependent var187698.4414104575S.E. of regression 35022.22758863741 Akaike info criterion23.8599929764685Sum squared resid 33117023482.29852 Schwarz criterion24.00011271463471Log likelihood -354.8998946470274 Hannan-Quinn criter.23.90481848460881F-statistic 402.9873385683694 Durbin-Watson stat0.5432849836158895Prob(F-statistic) 7.850214650 723685e-21统计检验：（1）拟合优度：从上表可以得到R2=0.9675860494429319，修正后的可决系数R2=0.9651850160683343，这说明模型对样本的拟合很好。

（2）F检验：针对H0：（二）多重共线性的检验及修正相关系数矩阵：X1 X2X1 1 0.9975652794446187X2 0.9975652794446187 1辅助回归的R2值Dependent Variable: X1Method: Least SquaresDate: 12/14/15 Time: 15:13Sample: 1985 2014Included observations: 30Variable Coefficient Std. Error t-Statistic Prob.C -236.1503079858336853.796869002943-0.27658839773166180.7841276813528842X2 1.1603536176166710.015330102952961675.691182321284056.205455045312624e-34R-squared 0.9951364867534203 Mean dependent var43924.96633333334Adjusted R-squared 0.9949627898517566 S.D. dependent var48106.05415975261S.E. of regression 3414.245696799649 Akaike info criterion19.17364126464171Sum squared resid 326398062.9872178 Schwarz criterion19.26705442341918Log likelihood -285.6046189696256 Hannan-Quinn criter.19.20352493673524F-statistic 5729.155081193856 Durbin-Watson stat0.730903182658975Prob(F-statistic) 6.205455045 312711e-34因为方差扩大因子VIF大于等于10 为204.081，所以存在严重的多重共线性。

对多重共线性的处理：Dependent Variable: LOG(Y)Method: Least SquaresDate: 12/14/15 Time: 15:35Sample: 1985 2014Included observations: 30Variable Coefficient Std. Error t-Statistic Prob.C 3.2221181949992160.233348310985516513.808191631604349.378486825750091e-14LOG(X1) 0.29961479256469490.23109796252290661.2964839209043080.2057807637271318LOG(X2) 0.53925469393756130.24855479727493982.169560595288220.03901090355174436R-squared 0.9877359836279073 Mean dependent var11.38310574067848Adjusted R-squared 0.9868275379707153 S.D. dependent var1.306196606830758S.E. of regression 0.1499139436548128 Akaike info criterion-0.8628711662239941Sum squared resid 0.6068031435577368 Schwarz criterion-0.7227514280577785Log likelihood 15.94306749335991 Hannan-Quinn criter.-0.8180456580836856F-statistic 1087.28130935309 Durbin-Watson stat0.4125950217515378Prob(F-statistic) 1.572322907 613123e-26检验模型的异方差：（一）图形法.00.01.02.03.04.05.06.07.08X1E 2.00.01.02.03.04.05.06.07.08X2E 2（goldfeld-Quandt 检验） Dependent Variable: Y Method: Least Squares Date: 12/14/15 Time: 16:04 Sample: 1 11Included observations: 11VariableCoefficientStd. Error t-StatisticProb.C5479.8790801364.28929584.01665475000.00385909682394 68848 41509 8436432651X1 1.4331353437969051.7592030257396050.81465034042582160.4388484070935154X2 3.2482294959499731.9835618267750021.6375741114312250.1401455299675676R-squared 0.9848299439189845 Mean dependent var25135.82727272728Adjusted R-squared 0.9810374298987306 S.D. dependent var16782.16114325512S.E. of regression 2310.981594158292 Akaike info criterion18.55573317233263Sum squared resid 42725087.42830722 Schwarz criterion18.664250064914Log likelihood -99.05653244782944 Hannan-Quinn criter.18.48732847210918F-statistic 259.6773376866937 Durbin-Watson stat2.590461609402877Prob(F-statistic) 5.296009374 728331e-08Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:05Sample: 20 30Included observations: 11Variable Coefficient Std. Error t-Statistic Prob.C -131209.061546085344951.25277685769-2.9189189052732220.01932324601265213X1 0.90801015214794812.5137156596208070.36122230001340770.7272868120760894X2 4.8280901698092332.8182139453930281.713173755917920.1250330211123522R-squared 0.9492597452885157 Mean dependent var376906.7363636364Adjusted R-squared 0.9365746816106446 S.D. dependent var165542.7249904584S.E. of regression 41690.91509980208 Akaike info criterion24.34095492221962Sum squared resid 1390505921 Schwarz criterion 24.44947184.87124 14801Log likelihood -130.8752520722079 Hannan-Quinn criter.24.27255022199618F-statistic 74.8328719030782 Durbin-Watson stat2.016741299693539Prob(F-statistic) 6.628428440 105899e-06（三）WHITE检验Heteroskedasticity Test: WhiteF-statistic 8.065639360788028 Prob. F(5,24)0.0001401031747031907Obs*R-squared 18.80739651082681 Prob. Chi-Square(5)0.002087524503307292Scaled explained SS 24.48540340808745 Prob. Chi-Square(5)0.0001751046944911128Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/14/15 Time: 16:18Sample: 1 30Included observations: 30Variable Coefficient Std. Error t-Statistic Prob.C -172076058.1206036441097474.8325652-0.39010891682370530.6998968080763495X1 -434816.1859048981264665.0535233542-1.6428923279307430.1134443283056973X1^2 -14.0260807141404617.43640515048546-0.80441355847652770.4290549805564741X1*X2 41.0314734815675239.804889285300281.0308149128986580.3129044598250328X2 532589.0240447041306551.76908160161.7373542669164410.09514332316116304X2^2 -28.6178784222710922.88697651710863-1.2504001304356840.2232078922692591R-squared0.6269132170275604 Mean dependent var 1103900782.743284 Adjusted R-squared 0.5491868039083021 S.D. dependent var 2013044843.410424 S.E. of regression 1351611130.658886 Akaike info criterion 45.06385981098074 Sum squared resid 4.384446356450382e+19 Schwarz criterion 45.34409928731318 Log likelihood -669.9578971647112 Hannan-Quinn criter. 45.15351082726136 F-statistic 8.065639360788028 Durbin-Watson stat 1.62042765626833Prob(F-statistic) 0.0001401031747031907所以存在异方差 异方差修正： 自相关的检验与修正： 一 图示检验法-80,000-40,000040,00080,000120,0000200,000400,000600,000800,000Residual ActualFittedDW 检验DW 0.54328498 对样本容量为30、两个解释变量的模型，5%的显著水平，查DW 统计表可知，d=1.567 l d=1.284 模型中DW<l d,显然模型u中有自相关。