實驗11-多元及嶺回歸分析

1、重慶工商大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院統(tǒng)計專業(yè)實驗課程實驗報告實驗課程： 統(tǒng)計專業(yè)實驗 _ 指導(dǎo)教師： _ 葉勇_ 專業(yè)班級： _ 統(tǒng)計三班_ 學(xué)生姓名： _ 黃坤龍_ 學(xué)生學(xué)號： 2012101328_1 / 27實 驗 報 告實驗項目實驗11 多元及嶺回歸分析實驗日期2015-6-10實驗地點81010實驗?zāi)康恼莆斩嘣貧w模型的變量選擇，嶺回歸分析的思想和操作方法。實驗內(nèi)容1.根據(jù)數(shù)據(jù)文件估計北京市人均住房面積的影響模型。并進行相應(yīng)分析。2.建立重慶市人均住房面積的影響模型，根據(jù)統(tǒng)計年鑒收集整理指標數(shù)據(jù)，并進行模型估計和分析。實驗思考題解答：1方差膨脹因子VIF的用途和計算公式是什么，其判斷標準？答：

2、方差膨脹因子是用來診斷一個序列是否存在多重共線性。自變量xj的方差膨脹因子記為VIF，它的計算方法為：VIF=1/1-Rj2。Rj2為以xj為因變量時對其他自變量回歸的復(fù)測定系數(shù)。 VIF越大，表明多重共線性越嚴重。當0VIF10時，不存在多重共線性；當10VIF100,存在較強的多重共線性；當VIF100時，存在嚴重的多重共線性。實驗運行程序、基本步驟及運行結(jié)果：1.根據(jù)數(shù)據(jù)文件估計北京市人均住房面積的影響模型，并進行相應(yīng)分析。 (1).首先，要確定因變量和自變量，根據(jù)題目，因變量為：人均住房面積y自變量為：人均全年收入x1人均可支配收入x2城鎮(zhèn)儲蓄存款余額x3人均儲蓄余額x4國內(nèi)生產(chǎn)總值x

3、5人均生產(chǎn)總值x6基本投資額x7人均基本投資額x8 (2).然后利用SPSS進行多元線性回歸分析,得到結(jié)果為：模型匯總b模型RR 方調(diào)整 R 方標準 估計的誤差Durbin-Watson1.994a.988.981.246341.681a. 預(yù)測變量: (常量), x8, x7, x3, x6, x1, x2, x4。b. 因變量: y分析：根據(jù)擬合出來的模型可以知道，可決系數(shù)為0.988，調(diào)整后的可決系數(shù)為0.981.說明解釋變量解釋了被解釋變量變異程度的98.1%，進而可以說明模型的擬合效果好。Anovab模型平方和df均方FSig.1回歸59.60878.515140.325.000a殘

4、差.72812.061總計60.33619a. 預(yù)測變量: (常量), x8, x7, x3, x6, x1, x2, x4。b. 因變量: y分析：這是對于模型的整體顯著性檢驗(F檢驗)，根據(jù)結(jié)果可以看出F檢驗統(tǒng)計量為140.325，概率P值為0.0000.05，說明模型通過了顯著性檢驗，模型的擬合是有效的。已排除的變量b模型Beta IntSig.偏相關(guān)共線性統(tǒng)計量容差VIF最小容差1x510.462a1.469.170.4051.809E-555278.7791.780E-5a. 模型中的預(yù)測變量: (常量), x8, x7, x3, x6, x1, x2, x4。b. 因變量: y分析

5、：根據(jù)多元線性回歸模型的建立，將變量x5排除，它與模型中的其他解釋變量存在很嚴重的多重共線性。系數(shù)a模型非標準化系數(shù)標準系數(shù)tSig.共線性統(tǒng)計量B標準 誤差試用版容差VIF1(常量)3.964.24116.477.000x1.000.001-.956-.817.430.0011361.278x2-.001.001-2.180-2.195.049.001980.463x3.001.002.749.627.542.0011418.704x4.000.000-2.480-2.067.061.0011431.296x6.001.0005.1556.301.000.002665.397x73.285E

6、-7.000.3492.505.028.05219.316x8.000.000.330.972.350.009114.391a. 因變量: y分析：這是對于模型的系數(shù)顯著性檢驗(t檢驗)，根據(jù)結(jié)果可以看出,常數(shù)項的P值為0.0000.05，沒有通過顯著性檢驗；x2的P照顧為0.0490.05,即是沒有通過顯著性檢驗；x4的P值為0.0610.05，沒有通過顯著性檢驗；x6的P值為0.0000.05,沒有通過顯著性檢驗；x8的P值為0.0090.05，通過了顯著性檢驗。再根據(jù)方差擴大因子可以看出x1,x2,x3,x4,x6,x8存在多重共線性，只有x7不存在多重共線性。共線性診斷a模型維數(shù)特征值

7、條件索引方差比例共線性診斷a模型維數(shù)特征值條件索引方差比例(常量)x1x2x3x4x6x7x8117.4441.000.00.00.00.00.00.00.00.002.4843.923.09.00.00.00.00.00.00.003.04512.870.00.00.00.00.00.00.45.004.02318.096.21.00.00.00.00.00.01.085.00348.783.30.01.01.02.02.06.37.196.00199.386.00.14.00.07.17.17.10.037.000144.498.09.04.95.02.00.29.05.128.00023

8、9.240.31.80.04.89.81.48.02.58(常量)x1x2x3x4x6x7x8117.4441.000.00.00.00.00.00.00.00.002.4843.923.09.00.00.00.00.00.00.003.04512.870.00.00.00.00.00.00.45.004.02318.096.21.00.00.00.00.00.01.085.00348.783.30.01.01.02.02.06.37.196.00199.386.00.14.00.07.17.17.10.037.000144.498.09.04.95.02.00.29.05.128.00023

9、9.240.31.80.04.89.81.48.02.58a. 因變量: y殘差統(tǒng)計量a極小值極大值均值標準 偏差N預(yù)測值5.314111.12147.86201.7712320殘差-.41181.38168.00000.1957720標準 預(yù)測值-1.4381.840.0001.00020標準 殘差-1.6721.549.000.79520a. 因變量: y(3).利用嶺回歸法對模型進行修正 嶺回歸法就是用過增加一個偏倚量c，使得模型估計更加穩(wěn)定和顯著。在SPSS中嶺回歸的實現(xiàn)：新建一個syntax窗口，調(diào)入嶺回歸語句（引號內(nèi)為該文件實際所在路徑）：Include d:Ridge regre

10、ssion.sps.嶺回歸命令格式：ridgereg enter=自變量列表 /dep = 因變量 /start=c初始值，默認為0 /stop=c終止值，默認為1 /inc=漸進步長，默認0.05) /k=c 指定偏倚系數(shù)，輸出詳細回歸結(jié)果 .最后一定要有一個點.輸入 ridgereg enter=x1 x2 x3 x4 x6 x7 x8 /dep = y /inc=0.01.點運行按鈕 run 。得到結(jié)果為：R-SQUARE AND BETA COEFFICIENTS FOR ESTIMATED VALUES OF K K RSQ x1 x2 x3 x4 x6 x7 x8_ _ _ _ _

11、 _ _ _ _.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 -.301644 .779982 .112638 .242594.03000 .92303 .270773 .197581 -.290430 -.203683 .608333 .085146 .273692.0400

12、0 .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 -.050802 .369855 .066208 .272429.08000 .90378 .202011

13、 .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 -.029124

14、 .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 .078

15、698 .226069.17000 .89197 .169776 .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

16、 .162995 .153252 .029293 .057364 .220365 .084705 .209501.22000 .88850 .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

17、 .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 .147687 .050725 .073064 .198362 .090669 .193116.29000 .88499 .153975 .147033 .052985 .074695 .195994 .091340

18、 .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 .189671 .093141 .186039.33000 .88338 .150724 .144662 .060690 .080210 .187786 .093676 .184458.34000 .88301 .1

19、49997 .144122 .062336 .081378 .185997 .094183 .182944.35000 .88264 .149298 .143599 .063888 .082475 .184296 .094662 .181490.36000 .88229 .148626 .143093 .065353 .083507 .182675 .095116 .180094.37000 .88194 .147979 .142603 .066736 .084478 .181130 .095546 .178751.38000 .88160 .147355 .142127 .068045 .0

20、85394 .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 .097048 .173851.42000 .88031 .145057 .140351 .072633 .088573 .174345 .097375 .1

21、72731.43000 .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 .098520 .168600.47000 .87880 .1425

22、48 .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 .0936

23、42 .164972 .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 .1609

24、15.56000 .87626 .138747 .135271 .083148 .095598 .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

25、.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 .87435 .136234 .133165 .086402 .097640 .155895 .101319 .155417.64000 .87408 .135900 .132881 .086793 .097879

26、.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 .087876 .098527 .153428 .101647 .153011.68000 .87301 .134611 .131780 .088209 .098723 .152844 .101715 .152439.

27、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 .101889 .150788.72000 .87193 .133396 .130731 .089412 .099413 .150627 .101938 .150258.73000 .87166 .133102 .13

28、0476 .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 .132243 .129727 .090436 .099974 .148577 .102089 .148230.77000 .87058 .131964 .129482 .090667 .100097 .14

29、8088 .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 .130878 .128527 .091503 .100523 .146214 .102193 .145880.820

30、00 .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 .86812 .129586 .12738

31、0 .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 .14241

32、2 .102188 .142077.91000 .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

33、.86561 .127413 .125430 .093541 .101382 .140506 .102099 .140160.96000 .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 .

34、093927 .101488 .139068 .101993 .1387111.0000 .86418 .126277 .124400 .094012 .101507 .138720 .101962 .138360可以看出，當偏倚系數(shù)C=0.04時，參數(shù)估計量趨于穩(wěn)定，方差膨脹因子VIF小于10，共線性現(xiàn)象得到消除，進行詳細嶺回歸估計：輸入 ridgereg enter=x1 x2 x3 x4 x6 x7 x8 /dep = y /k=0.04.點運行按鈕 run 。得到結(jié)果為：* Ridge Regression with k = 0.04 *Mult R .9575649365RSquar

35、e .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) Beta B/SE(B)x1 .00011390 .00003901 .24695791 2.91987225x2 .00010380 .00003940 .19203674 2.63494995x3 -.00044223

36、 .00024457 -.22138060 -1.80816742x4 -.00002525 .00001708 -.14393913 -1.47795434x6 .00013360 .00002858 .51087579 4.67394070x7 .00000007 .00000016 .07333497 .41832885x8 .00029688 .00018805 .28212907 1.57870586Constant 5.62392041 .27034346 .00000000 20.80287204估計結(jié)果如下y=5.623920+0.00011x1+0.000103x2-0.00

37、0442x3-0.000025x4+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積與自變量人均全年收入x1呈正相關(guān)，即是當x1每增加一個單位時，人均住房面積就會增加0.00011；北京人均住房面積與自變量人均可支配收入x2呈正相關(guān)，即是x2每增加一個單位時，人均住房面積就會增加0.000103；北京人均住房面積與自變量城鎮(zhèn)儲蓄存款余額x3呈負相關(guān)，即是x3每增加一個單位時，人均住房面積就會減少0.000442；

38、北京人均住房面積與自變量人均儲蓄存款余額x4呈負相關(guān)，即是x4每增加一個單位時，人均住房面積就會減少0.000025；北京人均住房面積與自變量人均生產(chǎn)總值x6呈正相關(guān)，即是x6每增加一個單位時，人均住房面積就會增加0.000133；北京人均住房面積與自變量基本投資額額x7呈正相關(guān)，即是x7每增加一個單位時，人均住房面積就會增加0.00000007；北京人均住房面積與自變量人均基本投資額x8呈負相關(guān)，即是x8每增加一個單位時，人均住房面積就會增加0.000296。2.建立重慶市人均住房面積的影響模型，根據(jù)統(tǒng)計年鑒收集整理指標數(shù)據(jù)，并進行模型估計和分析。(1).選取2003-2012年這10年的數(shù)

39、據(jù)進行分析，因變量為重慶人均住房面積y，選取了4項指標來建立模型，這4個指標分別為：人均可支配收入x1、國民生產(chǎn)總值x2、城鎮(zhèn)居民價格消費指數(shù)x3、住房銷售價格指數(shù)x4。(2).取得數(shù)據(jù)得到數(shù)據(jù)如下：年份人均住房面積y人均可支配收入x1國民生產(chǎn)總值x2城鎮(zhèn)居民價格消費指數(shù)x3住房銷售價格指數(shù)x4200321.198093.672555.72100.6108.5200422.769220.963034.58103.7114.7200522.1710243.993467.72100.8107200624.5211569.743907.23102.4103.2200729.2813715.25467

40、6.13104.7108200829.6815708.745793.66105.6107.2200931.4217191.16530.0198.4101.3201031.6919099.737925.58103.2110.8201131.7721954.9710011.37105.3104.1201232.1722968.1411409.6102.699.2(3).利用SPSS進行多元線性回歸分析，得到結(jié)果：模型匯總b模型RR 方調(diào)整 R 方標準 估計的誤差Durbin-Watson1.985a.970.9461.036572.213a. 預(yù)測變量: (常量), x4, x3, x2, x1。b. 因變量: y分析：根據(jù)擬合出來的模型可以知道，可決系數(shù)為0.970，調(diào)整后的可決系數(shù)為0.946.說明解釋變量解釋了被解釋變量變異程度的94.6%，進而可以說明模型的擬合效果較好。Anovab模型平方和df均方FSig.1回歸174.813443.70340