實(shí)驗(yàn)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(jì)學(xué)院統(tǒng)計(jì)專業(yè)實(shí)驗(yàn)課程實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)課程： 統(tǒng)計(jì)專業(yè)實(shí)驗(yàn) _ 指導(dǎo)教師： _ 葉勇_ 專業(yè)班級(jí)： _ 統(tǒng)計(jì)三班_ 學(xué)生姓名： _ 黃坤龍_ 學(xué)生學(xué)號(hào)： 2012101328_1 / 27實(shí) 驗(yàn) 報(bào) 告實(shí)驗(yàn)項(xiàng)目實(shí)驗(yàn)11 多元及嶺回歸分析實(shí)驗(yàn)日期2015-6-10實(shí)驗(yàn)地點(diǎn)81010實(shí)驗(yàn)?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(shí)驗(yàn)內(nèi)容1.根據(jù)數(shù)據(jù)文件估計(jì)北京市人均住房面積的影響模型。并進(jìn)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(jì)年鑒收集整理指標(biāo)數(shù)據(jù)，并進(jìn)行模型估計(jì)和分析。實(shí)驗(yàn)思考題解答：1方差膨脹因子VIF的用途和計(jì)算公式是什么，其判斷標(biāo)準(zhǔn)？答：

2、方差膨脹因子是用來(lái)診斷一個(gè)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(jì)算方法為：VIF=1/1-Rj2。Rj2為以xj為因變量時(shí)對(duì)其他自變量回歸的復(fù)測(cè)定系數(shù)。 VIF越大，表明多重共線性越嚴(yán)重。當(dāng)0VIF10時(shí)，不存在多重共線性；當(dāng)10VIF100,存在較強(qiáng)的多重共線性；當(dāng)VIF100時(shí)，存在嚴(yán)重的多重共線性。實(shí)驗(yàn)運(yùn)行程序、基本步驟及運(yùn)行結(jié)果：1.根據(jù)數(shù)據(jù)文件估計(jì)北京市人均住房面積的影響模型，并進(jìn)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(chǔ)蓄存款余額x3人均儲(chǔ)蓄余額x4國(guó)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(jìn)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(biāo)準(zhǔn) 估計(jì)的誤差Durbin-Watson1.994a.988.981.246341.681a. 預(yù)測(cè)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(lái)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(shuō)明解釋變量解釋了被解釋變量變異程度的98.1%，進(jìn)而可以說(shuō)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(jì)60.33619a. 預(yù)測(cè)變量: (常量), x8, x7, x3, x6, x1, x2, x4。b. 因變量: y分析：這是對(duì)于模型的整體顯著性檢驗(yàn)(F檢驗(yàn))，根據(jù)結(jié)果可以看出F檢驗(yàn)統(tǒng)計(jì)量為140.325，概率P值為0.0000.05，說(shuō)明模型通過(guò)了顯著性檢驗(yàn)，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(jì)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(cè)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(yán)重的多重共線性。系數(shù)a模型非標(biāo)準(zhǔn)化系數(shù)標(biāo)準(zhǔn)系數(shù)tSig.共線性統(tǒng)計(jì)量B標(biāo)準(zhǔn) 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(duì)于模型的系數(shù)顯著性檢驗(yàn)(t檢驗(yàn))，根據(jù)結(jié)果可以看出,常數(shù)項(xiàng)的P值為0.0000.05，沒有通過(guò)顯著性檢驗(yàn)；x2的P照顧為0.0490.05,即是沒有通過(guò)顯著性檢驗(yàn)；x4的P值為0.0610.05，沒有通過(guò)顯著性檢驗(yàn)；x6的P值為0.0000.05,沒有通過(guò)顯著性檢驗(yàn)；x8的P值為0.0090.05，通過(guò)了顯著性檢驗(yàn)。再根據(jù)方差擴(kuò)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(jì)量a極小值極大值均值標(biāo)準(zhǔn) 偏差N預(yù)測(cè)值5.314111.12147.86201.7712320殘差-.41181.38168.00000.1957720標(biāo)準(zhǔn) 預(yù)測(cè)值-1.4381.840.0001.00020標(biāo)準(zhǔn) 殘差-1.6721.549.000.79520a. 因變量: y(3).利用嶺回歸法對(duì)模型進(jìn)行修正 嶺回歸法就是用過(guò)增加一個(gè)偏倚量c，使得模型估計(jì)更加穩(wěn)定和顯著。在SPSS中嶺回歸的實(shí)現(xiàn)：新建一個(gè)syntax窗口，調(diào)入嶺回歸語(yǔ)句（引號(hào)內(nèi)為該文件實(shí)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(rèn)為0 /stop=c終止值，默認(rèn)為1 /inc=漸進(jìn)步長(zhǎng)，默認(rèn)0.05) /k=c 指定偏倚系數(shù)，輸出詳細(xì)回歸結(jié)果 .最后一定要有一個(gè)點(diǎn).輸入 ridgereg enter=x1 x2 x3 x4 x6 x7 x8 /dep = y /inc=0.01.點(diǎn)運(yùn)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(dāng)偏倚系數(shù)C=0.04時(shí)，參數(shù)估計(jì)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(jìn)行詳細(xì)嶺回歸估計(jì)：輸入 ridgereg enter=x1 x2 x3 x4 x6 x7 x8 /dep = y /k=0.04.點(diǎn)運(yùn)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(jì)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(dāng)x1每增加一個(gè)單位時(shí)，人均住房面積就會(huì)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(gè)單位時(shí)，人均住房面積就會(huì)增加0.000103；北京人均住房面積與自變量城鎮(zhèn)儲(chǔ)蓄存款余額x3呈負(fù)相關(guān)，即是x3每增加一個(gè)單位時(shí)，人均住房面積就會(huì)減少0.000442；

38、北京人均住房面積與自變量人均儲(chǔ)蓄存款余額x4呈負(fù)相關(guān)，即是x4每增加一個(gè)單位時(shí)，人均住房面積就會(huì)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(gè)單位時(shí)，人均住房面積就會(huì)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(gè)單位時(shí)，人均住房面積就會(huì)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(fù)相關(guān)，即是x8每增加一個(gè)單位時(shí)，人均住房面積就會(huì)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(jì)年鑒收集整理指標(biāo)數(shù)據(jù)，并進(jìn)行模型估計(jì)和分析。(1).選取2003-2012年這10年的數(shù)

39、據(jù)進(jìn)行分析，因變量為重慶人均住房面積y，選取了4項(xiàng)指標(biāo)來(lái)建立模型，這4個(gè)指標(biāo)分別為：人均可支配收入x1、國(guó)民生產(chǎn)總值x2、城鎮(zhèn)居民價(jià)格消費(fèi)指數(shù)x3、住房銷售價(jià)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(guó)民生產(chǎn)總值x2城鎮(zhèn)居民價(jià)格消費(fèi)指數(shù)x3住房銷售價(jià)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(jìn)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(biāo)準(zhǔn) 估計(jì)的誤差Durbin-Watson1.985a.970.9461.036572.213a. 預(yù)測(cè)變量: (常量), x4, x3, x2, x1。b. 因變量: y分析：根據(jù)擬合出來(lái)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(shuō)明解釋變量解釋了被解釋變量變異程度的94.6%，進(jìn)而可以說(shuō)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