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： _ 叶勇_ 专业班级： _ 统计三班_ 学生姓名： _ 黄坤龙_ 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：方差膨胀因子

2、是用来诊断一个序列是否存在多重共线性。自变量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0<VIF<10时，不存在多重共线性；当10VIF<100,存在较强的多重共线性；当VIF100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

3、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-Watson1.994a.988.981.246341.681a. 预测变量: (常量), x8, x7, x3, x6, x1, x2, x4。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0.988，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

4、.000a残差.72812.061总计60.33619a. 预测变量: (常量), x8, x7, x3, x6, x1, x2, x4。b. 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140.325，概率P值为0.000<0.05，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b模型Beta IntSig.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-5a. 模型中的预测变量: (常量), x8, x7, x3, x6, x1, x2, x4。b

5、. 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)3.964.24116.477.000x1.000.001-.956-.817.430.0011361.278x2-.001.001-2.180-2.195.049.001980.463x3.001.002.749.627.542.0011418.704x4.000.000-2.480-2.067.061.0011431.296x6.001.0005.1556.301.000.002665.3

6、97x73.285E-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,常数项的P值为0.000<0.05，即是通过了显著性检验；x1的P值为0.43>0.05，没有通过显著性检验；x2的P照顾为0.049<0.05，通过了显著性检验；x3的P值为0.542>0.05,即是没有通过显著性检验；x4的P值为0.061>0.05，没有通过显著性检验；x6的P值为0.000<0.05，通过了显著性检验；x7的P值

7、为0.052>0.05,没有通过显著性检验；x8的P值为0.009<0.05，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a模型维数特征值条件索引方差比例(常量)x1x2x3x4x6x7x8117.4441.000.00.00.00.00.00.00.00.002.4843.923.09.00.00.00.00.00.00.003.04512.870.00.00.00.00.00.00.45.004.02318.096.21.00.00.00.00.00.01.085.00348.783.30.0

8、1.01.02.02.06.37.196.00199.386.00.14.00.07.17.17.10.037.000144.498.09.04.95.02.00.29.05.128.000239.240.31.80.04.89.81.48.02.58a. 因变量: y残差统计量a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-1.4381.840.0001.00020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

9、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）：Include "d:Ridge regression.sps".岭回归命令格式：ridgereg enter=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 ridgereg enter=x1 x2 x3 x4 x6 x7 x8 /dep = y /inc=0.01.

10、点运行按钮 run 。得到结果为：R-SQUARE AND BETA COEFFICIENTS FOR ESTIMATED VALUES OF K K RSQ x1 x2 x3 x4 x6 x7 x8_ _ _ _ _ _ _ _ _.00000 .98793 -.955631 -2.18005 .748792 -2.47981 5.154638 .349141 .329859.01000 .94831 .378142 .176599 -.612495 -.498101 1.173739 .185817 .140657.02000 .93217 .308957 .200793 -.400480

11、 -.301644 .779982 .112638 .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 .40305

12、9 .066384 .277872.07000 .90614 .209373 .178488 -.109634 -.050802 .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 .25464

13、3.11000 .89847 .186626 .167394 -.040419 .004278 .292467 .071127 .249094.12000 .89710 .182904 .165354 -.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 .1741

14、90 .160313 -.002974 .033125 .253263 .077291 .230079.16000 .89283 .171875 .158908 .003862 .038311 .246253 .078698 .226069.17000 .89197 .169776 .157611 .009996 .042943 .239989 .080036 .222318.18000 .89118 .167863 .156407 .015531 .047103 .234353 .081304 .218805.19000 .89045 .166108 .155285 .020549 .050

15、859 .229252 .082503 .215509.20000 .88976 .164491 .154236 .025117 .054264 .224610 .083636 .212414.21000 .88911 .162995 .153252 .029293 .057364 .220365 .084705 .209501.22000 .88850 .161603 .152325 .033124 .060197 .216467 .085713 .206756.23000 .88792 .160304 .151449 .036648 .062795 .212871 .086664 .204

16、165.24000 .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 .88588 .155853 .148370 .048304 .071311 .200883 .089958 .195104.28000 .88543 .154890

17、 .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 .187689.32000 .88376 .151483 .145222 .058942 .078966

18、 .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 .180094

19、.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 .1

20、40778 .071574 .087844 .175591 .097048 .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 .1

21、70884 .098257 .169584.46000 .87910 .143023 .138746 .076373 .091123 .169813 .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 .165820.50

22、000 .87794 .141193 .137276 .079458 .093188 .165878 .099441 .164946.51000 .87765 .140763 .136926 .080144 .093642 .164972 .099641 .164096.52000 .87737 .140342 .136583 .080799 .094073 .164094 .099830 .163269.53000 .87709 .139931 .136247 .081426 .094484 .163241 .100009 .162464.54000 .87681 .139528 .1359

23、16 .082026 .094874 .162414 .100178 .161679.55000 .87653 .139133 .135591 .082599 .095245 .161610 .100337 .160915.56000 .87626 .138747 .135271 .083148 .095598 .160828 .100488 .160169.57000 .87598 .138368 .134956 .083674 .095935 .160067 .100630 .159442.58000 .87571 .137996 .134646 .084178 .096255 .1593

24、27 .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 .097126 .157217 .101118 .156699.62000 .87462 .136575 .133453 .085993 .097390 .156548 .101222 .156051.63000

25、 .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 .087530 .098322 .154024 .101574 .153594.67000 .87328 .134926 .132050

26、.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 .130989 .089129 .099254 .151165

27、.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 .8

28、7085 .132243 .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 .09

29、1307 .100426 .146670 .102179 .146335.81000 .86949 .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 .10

30、2216 .144556.85000 .86840 .129839 .127606 .092213 .100860 .144459 .102218 .144128.86000 .86812 .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 .8672

31、9 .128841 .126715 .092814 .101118 .142810 .102199 .142476.90000 .86701 .128598 .126497 .092949 .101172 .142412 .102188 .142077.91000 .86673 .128357 .126280 .093078 .101221 .142021 .102174 .141683.92000 .86645 .128118 .126065 .093202 .101267 .141634 .102159 .141295.93000 .86617 .127881 .125852 .09332

32、0 .101309 .141253 .102141 .140912.94000 .86589 .127646 .125640 .093433 .101347 .140877 .102121 .140533.95000 .86561 .127413 .125430 .093541 .101382 .140506 .102099 .140160.96000 .86532 .127182 .125221 .093645 .101414 .140139 .102075 .139791.97000 .86504 .126953 .125013 .093743 .101442 .139778 .10205

33、0 .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 .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 ridgereg enter=x1 x

34、2 x3 x4 x6 x7 x8 /dep = y /k=0.04.点运行按钮 run 。得到结果为：* Ridge Regression with k = 0.04 *Mult R .9575649365RSquare .9169306076Adj RSqu .8684734620SE .6462778971ANOVA table df SS MSRegress 7.000 55.324 7.903Residual 12.000 5.012 .418F value Sig F18.92250558 .00001362-Variables in the Equation- B SE(B) Be

35、ta B/SE(B)x1 .00011390 .00003901 .24695791 2.91987225x2 .00010380 .00003940 .19203674 2.63494995x3 -.00044223 .00024457 -.22138060 -1.80816742x4 -.00002525 .00001708 -.14393913 -1.47795434x6 .00013360 .00002858 .51087579 4.67394070x7 .00000007 .00000016 .07333497 .41832885x8 .00029688 .00018805 .282

36、12907 1.57870586Constant 5.62392041 .27034346 .00000000 20.80287204估计结果如下y=5.623920+0.00011x1+0.000103x2-0.000442x3-0.000025x4+0.000133x6+0.00000007x7+0.000296x8t 20.8028 2.9198 2.6349 -1.8081 -1.4779 4.6739 .4183 1.5787R2=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加0.00011；北京人均住房面积

37、与自变量人均可支配收入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加0.000103；北京人均住房面积与自变量城镇储蓄存款余额x3呈负相关，即是x3每增加一个单位时，人均住房面积就会减少0.000442；北京人均住房面积与自变量人均储蓄存款余额x4呈负相关，即是x4每增加一个单位时，人均住房面积就会减少0.000025；北京人均住房面积与自变量人均生产总值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0.000133；北京人均住房面积与自变量基本投资额额x7呈正相关，即是x7每增加一个单位时，人均住房面积就会增加0.00000007；北京人均住房面积与自变量人均基本

38、投资额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。(1).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。(2).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x4200321.198093.672555.72100.6108.5200422.769

39、220.963034.58103.7114.7200522.1710243.993467.72100.8107200624.5211569.743907.23102.4103.2200729.2813715.254676.13104.7108200829.6815708.745793.66105.6107.2200931.4217191.16530.0198.4101.3201031.6919099.737925.58103.2110.8201131.7721954.9710011.37105.3104.1201232.1722968.1411409.6102.699.2(3).利用SPSS进

40、行多元线性回归分析，得到结果：模型汇总b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。Anovab模型平方和df均方FSig.1回归174.813443.70340.674.001a残差5.37251.074总计180.1869a. 预测变量: (常量), x4, x3, x2,

41、x1。b. 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40.674，概率P值为0.001<0.05，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)6.98815.963.438.680x1.002.0002.7056.061.002.03033.400x2-.003.001-1.775-3.988.010.03033.212x3-.020.188-.010-.107.919.6461.548x4.037.110.038.341.747.4712.125a

42、. 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0.680>0.05，即是没有通过了显著性检验；x1的P值为0.02<0.05，通过显著性检验；x2的P值为0.01<0.05，通过了显著性检验；x3的P值为0.919>0.05,即是没有通过显著性检验；x4的P值为0.747>0.05，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

43、型汇总b模型RR 方调整 R 方标准 估计的误差Durbin-Watson1.985a.970.955.947342.254a. 预测变量: (常量), x4, x1, x2。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0.955.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。Anovab模型平方和df均方FSig.1回归174.801358.26764.925.000a残差5.3856.897总计180.1869a. 预测变量: (常量), x4, x1, x2。b. 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0.000<0.05，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