实验11多元及岭回归分析

1、重庆工商大学数学与统计学院统计专业实验课程实验报告实验课程：统计专业实验.指导教师：也i专业班级：统计三班学生姓名：_黄坤龙一学生学号：2012101328实验报告实验项目实验11多元及岭回归分析实验日期2015-6-10实验地点81010实验目的掌握多元回归模型的变量选择，岭回归分析的思想和操作方法。实验内容1. 根据数据文件估计北京市人均住房面积的影响模型。并进行相应分析。2. 建立重庆市人均住房面积的影响模型，根据统计年鉴收集整理指标数据，并进行模型估计和分析。实验思考题解答：1.方差膨胀因子VIF的用途和计算公式是什么，其判断标准？答：膨胀因子是用来诊断一个序列是否存在多重共线性。自变

2、量xj的方差膨胀因子记为VIF，它的计算方法为：VIF=1/1-Rj2。Rj2为以xj为因变量时对其他自变量回归的复测定系数。VIF越大，表明多重共线性越严重。当0VIF10时，不存在多重共线性；当10VIF100时，存在严重的多重共线性。实验运行程序、基本步骤及运行结果：1. 根据数据文件估计北京市人均住房面积的影响模型，并进行相应分析。(1) .首先，要确定因变量和自变量，根据题目，因变量为：人均住房面积y自变量为：人均全年收入x1人均可支配收入x2城镇储蓄存款余额x3人均储蓄余额x4国内生产总值x5人均生产总值x6基本投资额x7人均基本投资额x8(2) .然后利用SPSS进行多元线性回归

3、分析，得到结果为：模型汇总模型RR方调整R方标准估计的误差Durbin-Watson1.994a.988.981.246341.681预测变量：(常量),x8,x7,x3,x6,x1,x2,x4因变量：y分析：根据拟合出来的模型可以知道，可决系数为0.988，调整后的可决系数为0.981.说明解释变量解释了被解释变量变异程度的98.1%,进而可以说明模型的拟合效果好。Anovab模型平方和df均方FSig.1回归59.60878.515140.325,000a残差.72812.061总计60.33619预测变量：（常量）,x8,x7,x3,x6,x1,x2,x4因变量：y分析：这是对于模型的整

4、体显著性检验（F检验），根据结果可以看出F检验统计量为140.325，概率P值为0.0000.05,说明模型通过了显著性检验，模型的拟合是有效的。已排除的变量模型BetaIntSig.偏相关共线性统计量容差VIF最小容差1x510.462a1.469.170.4051.809E-555278.7791.780E-5b. 模型中的预测变量：（常量）,x8,x7,x3,x6,x1,x2,x4因变量：y分析：根据多元线性回归模型的建立，将变量x5排除，它与模型中的其他解释变量存在很严重的多重共线性。系数模型非标准化系数标准系数tSig.共线性统计量B标准误差试用版容差VIF1（常量）3.964.24

5、116.477.000x1.000.001-.956-.817.430.0011361.278x2-.001.001-2.180-2.195.049.001980.463x3.001.002.749.627.542.0011418.704x4.000.000-2.480-2.067.061.0011431.296x6.001.0005.1556.301.000.002665.397x73.285E-7.000.3492.505.028.05219.316x8.000.000.330.972.350.009114.391a.因变量：y分析：这是对于模型的系数显著性检验（t检验），根据结果可以看出

6、，常数项的P值为0.0000.05，没有通过显著性检验；x2的P照顾为0.0490.05,即是没有通过显著性检验；x4的P值为0.0610.05,没有通过显著性检验；x6的P值为0.0000.05,没有通过显著性检验；x8的P值为0.0090.05，通过了显著性检验。再根据方差扩大因子可以看出x1,x2,x3,x4,x6,x8存在多重共线性，只有x7不存在多重共线性。共线性诊断模型维数特征值条件索引方差比例（常量）x1x2x3x4x6x7x8117.4441.000.00.00.00.00.00.00.00.002.4843.923.09.00.00.00.00.00.00.003.04512

7、.870.00.00.00.00.00.00.45.004.02318.096.21.00.00.00.00.00.01.085.00348.783.30.01.01.02.02.06.37.196.00199.386.00.14.00.07.17.17.10.037.000144.498.09.04.95.02.00.29.05.128.000239.240.31.80.04.89.81.48.02.58a.因变量：y残差统计量极小值极大值均值标准偏差N预测值5.314111.12147.86201.7712320残差-.41181.38168.00000.1957720标准预测值-1.43

8、81.840.0001.00020标准残差-1.6721.549.000.79520a.因变量：y（3）.利用岭回归法对模型进行修正岭回归法就是用过增加一个偏倚量c,使得模型估计更加稳定和显著。在SPSS中岭回归的实现:新建一个syntax窗口，调入岭回归语句（引号内为该文件实际所在路径）：Included:Ridgeregression.sps.岭回归命令格式：ridgeregenter=自变量歹U表/dep=因变量/start=c初始值，默认为0/stop=c终止值，默认为1/inc=渐进步长，默认0.05）/k=c指定偏倚系数，输出详细回归结果.最后一定要有一个点.输入ridgerege

9、nter=x1x2x3x4x6x7x8/dep=y/inc=0.01.点运行按钮run。得到结果为：R-SQUAREANDBETACOEFFICIENTSFORESTIMATEDVALUESOFKKRSQx1x2x3x4x6x7x8.00000.98793-.955631-2.18005.748792-2.479815.154638.349141.329859.01000.94831.378142.176599-.612495-.4981011.173739.185817.140657.02000.93217.308957.200793-.400480-.301644.779982.11263

10、8.242594.03000.92303.270773.197581-.290430-.203683.608333.085146.273692.04000.91693.246958.192037-.221381-.143939.510876.073335.282129.05000.91246.230606.186853-.173260-.103246.447625.068238.281821.06000.90897.218606.182354-.137464-.073540.403059.066384.277872.07000.90614.209373.178488-.109634-.0508

11、02.369855.066208.272429.08000.90378.202011.175147-.087294-.032788.344093.066928.266472.09000.90176.195980.172235-.068922-.018140.323481.068126.260469.10000.90001.190929.169671-.053524-.005982.306587.069571.254643.11000.89847.186626.167394-.040419.004278.292467.071127.249094.12000.89710.182904.165354

12、-.029124.013054.280476.072714.243863.13000.89588.179646.163513-.019285.020647.270154.074287.238957.14000.89477.176764.161841-.010636.027280.261166.075818.234368.15000.89376.174190.160313-.002974.033125.253263.077291.230079.16000.89283.171875.158908.003862.038311.246253.078698.226069.17000.89197.1697

13、76.157611.009996.042943.239989.080036.222318.18000.89118.167863.156407.015531.047103.234353.081304.218805.19000.89045.166108.155285.020549.050859.229252.082503.215509.20000.88976.164491.154236.025117.054264.224610.083636.212414.21000.88911.162995.153252.029293.057364.220365.084705.209501.22000.88850

14、.161603.152325.033124.060197.216467.085713.206756.23000.88792.160304.151449.036648.062795.212871.086664.204165.24000.88738.159088.150620.039902.065183.209544.087561.201715.25000.88686.157946.149833.042913.067386.206453.088407.199395.26000.88636.156870.149084.045706.069423.203573.089205.197194.27000.

15、88588.155853.148370.048304.071311.200883.089958.195104.28000.88543.154890.147687.050725.073064.198362.090669.193116.29000.88499.153975.147033.052985.074695.195994.091340.191221.30000.88457.153105.146406.055100.076216.193764.091975.189415.31000.88416.152276.145802.057082.077637.191660.092574.187689.3

16、2000.88376.151483.145222.058942.078966.189671.093141.186039.33000.88338.150724.144662.060690.080210.187786.093676.184458.34000.88301.149997.144122.062336.081378.185997.094183.182944.35000.88264.149298.143599.063888.082475.184296.094662.181490.36000.88229.148626.143093.065353.083507.182675.095116.180

17、094.37000.88194.147979.142603.066736.084478.181130.095546.178751.38000.88160.147355.142127.068045.085394.179654.095952.177458.39000.88127.146752.141665.069285.086258.178241.096338.176212.40000.88095.146169.141215.070460.087073.176889.096702.175011.41000.88063.145604.140778.071574.087844.175591.09704

18、8.173851.42000.88031.145057.140351.072633.088573.174345.097375.172731.43000.88000.144526.139936.073639.089263.173148.097685.171648.44000.87970.144011.139530.074595.089916.171995.097979.170599.45000.87939.143510.139133.075506.090535.170884.098257.169584.46000.87910.143023.138746.076373.091123.169813.

19、098520.168600.47000.87880.142548.138367.077200.091680.168779.098770.167646.48000.87851.142085.137996.077988.092209.167780.099006.166720.49000.87822.141634.137632.078740.092711.166813.099229.165820.50000.87794.141193.137276.079458.093188.165878.099441.164946.51000.87765.140763.136926.080144.093642.16

20、4972.099641.164096.52000.87737.140342.136583.080799.094073.164094.099830.163269.53000.87709.139931.136247.081426.094484.163241.100009.162464.54000.87681.139528.135916.082026.094874.162414.100178.161679.55000.87653.139133.135591.082599.095245.161610.100337.160915.56000.87626.138747.135271.083148.0955

21、98.160828.100488.160169.57000.87598.138368.134956.083674.095935.160067.100630.159442.58000.87571.137996.134646.084178.096255.159327.100763.158732.59000.87544.137631.134341.084661.096560.158606.100889.158039.60000.87517.137273.134041.085124.096850.157903.101007.157361.61000.87489.136921.133745.085568

22、.097126.157217.101118.156699.62000.87462.136575.133453.085993.097390.156548.101222.156051.63000.87435.136234.133165.086402.097640.155895.101319.155417.64000.87408.135900.132881.086793.097879.155257.101410.154796.65000.87381.135570.132600.087169.098106.154634.101495.154189.66000.87355.135246.132324.0

23、87530.098322.154024.101574.153594.67000.87328.134926.132050.087876.098527.153428.101647.153011.68000.87301.134611.131780.088209.098723.152844.101715.152439.69000.87274.134301.131513.088528.098909.152273.101778.151878.70000.87247.133995.131250.088835.099086.151713.101836.151328.71000.87220.133694.130

24、989.089129.099254.151165.101889.150788.72000.87193.133396.130731.089412.099413.150627.101938.150258.73000.87166.133102.130476.089684.099565.150100.101982.149738.74000.87139.132812.130224.089945.099709.149583.102021.149227.75000.87112.132526.129974.090195.099845.149075.102057.148724.76000.87085.13224

25、3.129727.090436.099974.148577.102089.148230.77000.87058.131964.129482.090667.100097.148088.102116.147745.78000.87031.131688.129240.090889.100213.147607.102141.147267.79000.87004.131415.129000.091102.100322.147135.102161.146798.80000.86976.131145.128762.091307.100426.146670.102179.146335.81000.86949.

26、130878.128527.091503.100523.146214.102193.145880.82000.86922.130614.128294.091692.100615.145764.102203.145432.83000.86894.130353.128062.091873.100702.145322.102211.144991.84000.86867.130095.127833.092047.100783.144887.102216.144556.85000.86840.129839.127606.092213.100860.144459.102218.144128.86000.8

27、6812.129586.127380.092373.100931.144038.102217.143706.87000.86784.129335.127157.092526.100998.143622.102213.143290.88000.86757.129087.126935.092673.101060.143213.102207.142880.89000.86729.128841.126715.092814.101118.142810.102199.142476.90000.86701.128598.126497.092949.101172.142412.102188.142077.91

28、000.86673.128357.126280.093078.101221.142021.102174.141683.92000.86645.128118.126065.093202.101267.141634.102159.141295.93000.86617.127881.125852.093320.101309.141253.102141.140912.94000.86589.127646.125640.093433.101347.140877.102121.140533.95000.86561.127413.125430.093541.101382.140506.102099.1401

29、60.96000.86532.127182.125221.093645.101414.140139.102075.139791.97000.86504.126953.125013.093743.101442.139778.102050.139427.98000.86475.126726.124808.093837.101466.139421.102022.139067.99000.86447.126501.124603.093927.101488.139068.101993.1387111.0000.86418.126277.124400.094012.101507.138720.101962

30、.138360可以看出，当偏倚系数C=0.04时，参数估计量趋于稳定，方差膨胀因子VIF小于10,共线性现象得到消除，进行详细岭回归估计：输入ridgeregenter=x1x2x3x4x6x7x8/dep=y/k=0.04.点运行按钮run。得到结果为：*RidgeRegressionwithk=0.04*MultR.9575649365RSquare.9169306076AdjRSqu.8684734620SE.6462778971ANOVAtabledfSSMSRegress7.00055.3247.903Residual12.0005.012.418FvalueSigF18.92250

31、558.00001362VariablesintheEquationBSE(B)BetaB/SE(B)x1.00011390.00003901.246957912.91987225x2.00010380.00003940.192036742.63494995x3-.00044223.00024457-.22138060-1.80816742x4-.00002525.00001708-.14393913-1.47795434x6.00013360.00002858.510875794.67394070x7.00000007.00000016.07333497.41832885x8.0002968

32、8.00018805.282129071.57870586Constant5.62392041.27034346.0000000020.80287204估计结果如下y=5.623920+0.00011x1+0.000103x2-0.000442x3-0.000025x4+0.000133x6+0.00000007x7+0.000296x8t20.80282.91982.6349-1.8081-1.47794.6739.41831.5787R2=0.9169由此可以看出北京人均住房面积与自变量人均全年收入加0.00011;北京人均住房面积与自变量人均可支配收入加0.000103;北京人均住房面积

33、与自变量城镇储蓄存款余额减少0.000442;北京人均住房面积与自变量人均储蓄存款余额减少0.000025;北京人均住房面积与自变量人均生产总值0.000133;北京人均住房面积与自变量基本投资额额0.00000007;北京人均住房面积与自变量人均基本投资额x1呈正相关，即是当x1每增加一个单位时，人均住房面积就会增x2呈正相关，即是x2每增加一个单位时，人均住房面积就会增x3呈负相关，即是x3每增加一个单位时，人均住房面积就会x4呈负相关，即是x4每增加一个单位时，人均住房面积就会x6呈正相关，即是x6每增加一个单位时，人均住房面积就会增加x7呈正相关，即是x7每增加一个单位时，人均住房面积

34、就会增加x8呈负相关，即是x8每增加一个单位时，人均住房面积就会增加0.000296。2. 建立重庆市人均住房面积的影响模型，根据统计年鉴收集整理指标数据，并进行模型估计和分析。.选取2003-2012年这10年的数据进行分析，因变量为重庆人均住房面积y,选取了4项指标来建立模型，这4个指标分别为：人均可支配收入x1、国民生产总值x2、城镇居民价格消费指数x3、住房销售价格指数x4。.取得数据得到数据如下:年份人均住房面积y人均可支配收入x1国民生产总值x2城镇居民价格消费指数x3住房销售价格指数x4200321.198093.672555.72100.6108.5200422.769220.

35、963034.58103.7114.7200522.1710243.993467.72100.8107200624.5211569.743907.23102.4103.2200729.2813715.254676.13104.7108200829.6815708.745793.66105.6107.2200931.4217191.16530.0198.4101.3201031.6919099.737925.58103.2110.8201131.7721954.9710011.37105.3104.1201232.1722968.1411409.6102.699.2(3).利用SPSSS行多元线

36、性回归分析，得到结果:模型汇总模型RR方调整R方标准估计的误差Durbin-Watson1.985a.970.9461.036572.213a. 预测变量：（常量）,x4,x3,x2,x1。b. 因变量：y分析：根据拟合出来的模型可以知道，可决系数为0.970,调整后的可决系数为0.946.说明解释变量解释了被解释变量变异程度的94.6%,进而可以说明模型的拟合效果较好。bAnova模型平方和df均方FSig.1回归174.813443.70340.674.001a残差5.37251.074总计180.1869预测变量：（常量）,x4,x3,x2,x1因变量：y分析：这是对于模型的整体显著性检

37、验（F检验），根据结果可以看出F检验统计量为40.674，概率P值为0.0010.05,即是没有通过了显著性检验；x1的P值为0.020.05,通过显著性检验；x2的P值为0.010.05,即是没有通过显著性检验；x4的P值为0.7470.05,没有通过显著性检验。再根据方差扩大因子可以看出x1,x2存在多重共线性，x3,x4不存在多重共线性。（4）.模型优化变量x3、x4没有通过显著性检验，所以可以进行以下3种检验： 剔除变量x3,对变量x1、x2、x4进行分析，得到结果为：模型汇总模型RR方调整R方标准估计的误差Durbin-Watson1.985a.970.955.947342.254a

38、. 预测变量：（常量）,x4,x1,x2o因变量：y分析：根据拟合出来的模型可以知道，可决系数为0.970,调整后的可决系数为0.955.说明解释变量解释了被解释变量变异程度的95.5%，进而可以说明模型的拟合效果较好，比原来的模型拟合有所提高。模型平方和df均方FSig.1回归174.801358.26764.925.000a残差5.3856.897总计180.1869bAnova预测变量：（常量）,x4,x1,x2因变量：y分析：这是对于模型的整体显著性检验（F检验），根据结果可以看出F检验统计量为64.925，概率P值为0.0000.05,即是没有通过了显著性检验；x1的P值为0.010

39、.05,即是没有通过显著性检验。再根据方差扩大因子可以看出x1,x2存在多重共线性,x4不存在多重共线性。综合应该剔除变量x4。 剔除变量x4,对变量x1、x2、x3进行分析，得到结果为:模型汇总模型RR方调整R方标准估计的误差Durbin-Watson1.985a.969.954.957222.334预测变量：（常量）,x3,x2,x1因变量：y分析：根据拟合出来的模型可以知道，可决系数为0.969,调整后的可决系数为0.954.说明解释变量解释了被解释变量变异程度的95.4%，进而可以说明模型的拟合效果较好，比原来的模型拟合有所提高。Anovab模型平方和df均方FSig.1回归174.6

40、88358.22963.551.000a残差5.4986.916总计180.1869a. 预测变量：（常量）,x3,x2,x1因变量：y分析：这是对于模型的整体显著性检验（F检验），根据结果可以看出F检验统计量为63.551，概率P值为（t检验），根据结果可以看出，常数项的P值为0.5210.05,即是没,没有通过了显著性x1,x2存在多重共线0.0000.05,说明模型通过了显著性检验，模型的拟合是有效的。系数a模型非标准化系数标准系数tSig.共线性统计量B标准误差试用版容差VIF1（常量）7.62414.641.521.621x1.002.0002.6936.554.001.03033.

41、208x2-.003.001-1.790-4.376.005.03032.892x3.015.145.008.104.920.9261.079a.因变量：y 分析：这是对于模型的系数显著性检验有通过了显著性检验；x1的P值为0.010.05,即是没有通过显著性检验。再根据方差扩大因子可以看出x3。性,x3不存在多重共线性。综合应该剔除变量剔除变量x3、x4,对变量x1、x2进行分析，得到结果为:模型汇总b模型RR方调整R方标准估计的误差Durbin-Watson1.985a.969.961.887022.321a. 预测变量：（常量）,x2,x1因变量：y分析：根据拟合出来的模型可以知道，可决

42、系数为0.969，调整后的可决系数为0.961.说明解释变量解释了被解释变量变异程度的96.1%，进而可以说明模型的拟合效果较好，比原来的模型拟合有所提高。Anovab模型平方和df均方FSig.1回归174.678287.339111.006.000a残差5.5087.787a. |总计|180.1869预测变量：（常量）,x2,x1o因变量：y分析：这是对于模型的整体显著性检验（F检验），根据结果可以看出F检验统计量111.006,F检验统计量较大，概率P值为0.0000.05,说明模型通过了显著性检验，模型的拟合是有效的。系数模型非标准化系数标准系数tSig.共线性统计量B标准误差试用版

43、容差VIF1（常量）9.1401.6635.498.001x1.002.0002.6997.145.000.03132.671x2-.003.001-1.793-4.748.002.03132.671a.因变量：y分析：这是对于模型的系数显著性检验（t检验），根据结果可以看出，常数项的P值为0.0010.05,即是通过了显著性检验；x1的P值为0.000.05，通过显著性检验；x2的P值为0.020.05,通过了显著性检验。说明模型拟合较好。（4）.最后，选择剔除变量x3、x4变量，得到模型形式为：Y=9.14+0.002x1-0.003x2t5.4987.145-4.748R2=0.969F

44、=111.006（5）.由于变量x1,x2存在多重共线性，运用岭回归方法对其进行优化。在SPSS岭回归的实现：新建一个syntax窗口，调入岭回归语句（引号内为该文件实际所在路径）：Included:Ridgeregression.sps.岭回归命令格式：ridgeregenter=自变量列表/dep=因变量/start=c初始值，默认为0/stop=c终止值，默认为1/inc=渐进步长，默认0.05）/k=c指定偏倚系数，输出详细回归结果.最后一定要有一个点.输入ridgeregenter=x1x2/dep=y/inc=0.01.点运行按钮run。得到结果为：R-SQUAREANDBETAC

45、OEFFICIENTSFORESTIMATEDVALUESOFKKRSQx1x2.00000.969432.698825-1.79320.01000.945341.813100-.912017.02000.919751.426199-.529612.03000.901381.208686-.316549.04000.888061.068883-.181153.05000.87805.971167-.087800.06000.87026.898805-.019758.07000.86400.842900.031868.08000.85884.798285.072246.09000.85450.761752.104583.10000.85076.731207.130