影響財(cái)政收入因素的回歸分析

1、2011-2012學(xué)年第二學(xué)期數(shù)據(jù)分析期末論文題目影響財(cái)政收入因素的回歸分析姓名李天龍學(xué)號(hào)20091021255系（院）數(shù)學(xué)系專業(yè)數(shù)學(xué)與應(yīng)用數(shù)學(xué)2012年6月20日 TOC o 1-5 h z HYPERLINK l bookmark7 o Current Document 摘 要2 HYPERLINK l bookmark10 o Current Document 1問(wèn)題的提出32對(duì)國(guó)家財(cái)政收入及各項(xiàng)指標(biāo)做多元線性回歸分析和逐步回歸分析32.1指標(biāo)的選取32.2利用Eviews軟件，對(duì)數(shù)據(jù)建立回歸方程42.3利用Eviews軟件，對(duì)數(shù)據(jù)預(yù)處理53自變量的選擇9 HYPERLINK l boo

2、kmark17 o Current Document 3.1 t檢驗(yàn)法9 HYPERLINK l bookmark20 o Current Document 3.2冗余變量檢驗(yàn)法11 HYPERLINK l bookmark23 o Current Document 3.3前進(jìn)逐步回歸.13 HYPERLINK l bookmark26 o Current Document 3.4后退逐步回歸.14 HYPERLINK l bookmark29 o Current Document 3.5.最大R平方增量逐次交換回歸15 HYPERLINK l bookmark32 o Current Doc

3、ument 3.6最小R平方增量逐次交換回歸16 HYPERLINK l bookmark35 o Current Document 3.7組合逐步回歸17 HYPERLINK l bookmark38 o Current Document 4單向逐步前進(jìn)回歸靜態(tài)預(yù)測(cè)18 HYPERLINK l bookmark41 o Current Document 5結(jié)果分析與對(duì)策19 HYPERLINK l bookmark44 o Current Document 6結(jié)語(yǔ)19影響財(cái)政收入因素的回歸分析摘 要我們主要是要來(lái)研究影響財(cái)政收入的主要因素有哪些，之所以研究這一問(wèn)題，是因?yàn)椋?財(cái)政收入對(duì)于國(guó)民

4、經(jīng)濟(jì)的運(yùn)行及社會(huì)發(fā)展具有重要影響。我們通過(guò)對(duì)1980到2003年影響財(cái)政收入的6種行業(yè)的收入以及財(cái)政收入的數(shù)據(jù)做多元線 性回歸分析，建立回歸模型，并通過(guò)對(duì)回歸系數(shù)做顯著性檢驗(yàn)與逐步回歸來(lái)分析數(shù)據(jù)，從國(guó) 民經(jīng)濟(jì)部門結(jié)構(gòu)看，財(cái)政收入又表現(xiàn)為來(lái)自各經(jīng)濟(jì)部門的收入。財(cái)政收入的部門構(gòu)成就是在 財(cái)政收入中，由來(lái)自國(guó)民經(jīng)濟(jì)各部門的收入所占的不同比例來(lái)表現(xiàn)財(cái)政收入來(lái)源的結(jié)構(gòu)，它 體現(xiàn)國(guó)民經(jīng)濟(jì)各部門與財(cái)政收入的關(guān)系。我國(guó)財(cái)政收入主要來(lái)自于工業(yè)、農(nóng)業(yè)、商業(yè)、交通 運(yùn)輸和服務(wù)業(yè)等部門。其中工業(yè)和農(nóng)業(yè)對(duì)財(cái)政收入的影響最大。關(guān)鍵詞多元線性回歸分析；顯著性檢驗(yàn)；前進(jìn)逐步回歸；預(yù)測(cè)；冗余變量；后退逐步回歸；最 大及最小R平

5、方逐次交換回歸。1問(wèn)題的提出首先，財(cái)政收入是一個(gè)國(guó)家各項(xiàng)收入得以實(shí)現(xiàn)的物質(zhì)保證。一個(gè)國(guó)家財(cái)政收入規(guī)模大小 往往是衡量其經(jīng)濟(jì)實(shí)力的重要標(biāo)志。其次，財(cái)政收入是國(guó)家對(duì)經(jīng)濟(jì)實(shí)行宏觀調(diào)控的重要經(jīng)濟(jì) 杠桿。宏觀調(diào)控的首要問(wèn)題是社會(huì)總需求與總供給的平衡問(wèn)題，實(shí)現(xiàn)社會(huì)總需求與總供給的 平衡，包括總量上的平衡和結(jié)構(gòu)上的平衡兩個(gè)層次的內(nèi)容。財(cái)政收入的杠桿既可通過(guò)增收和 減收來(lái)發(fā)揮總量調(diào)控作用，也可通過(guò)對(duì)不同財(cái)政資金繳納者的財(cái)政負(fù)擔(dān)大小的調(diào)整，來(lái)發(fā)揮 結(jié)構(gòu)調(diào)整的作用。此外，財(cái)政收入分配也是調(diào)整國(guó)民收入初次分配格局，實(shí)現(xiàn)社會(huì)財(cái)富公平 合理分配的主要工具。在我國(guó)，財(cái)政收入的主體是稅收收入。因此，在稅收體制及政策不變的情

6、況下，財(cái)政收入會(huì) 隨著經(jīng)濟(jì)繁榮而增加，隨著經(jīng)濟(jì)衰退而下降。本文根據(jù)1980到2003年中國(guó)財(cái)政收入的統(tǒng)計(jì)年鑒相關(guān)數(shù)據(jù)，利用多元線性回歸分析，確定影 響我國(guó)財(cái)政收入主要因素，探討財(cái)政收入對(duì)于國(guó)民經(jīng)濟(jì)的運(yùn)行及社會(huì)發(fā)展具有重要影響。2對(duì)國(guó)家財(cái)政收入及各項(xiàng)指標(biāo)做多元線性回歸分析和逐步回歸分析2.1指標(biāo)的選取x 1財(cái)政收入（億元）X 2工業(yè)總產(chǎn)值（億元）X 3農(nóng)業(yè)總產(chǎn)值（億元）x 4 建筑業(yè)總產(chǎn)值（億元）X 5受災(zāi)面積（十萬(wàn)公頃）X6人口數(shù)目（百萬(wàn)人）社會(huì)消費(fèi)品零售總額（億元）相關(guān)數(shù)據(jù)如下表：年份財(cái)政收入工業(yè)總產(chǎn)值農(nóng)業(yè)總產(chǎn)值建筑業(yè)總產(chǎn)社會(huì)消費(fèi)品零售總額（億元）受災(zāi)面積人口數(shù)目（億元）（億元）（億元）值（

7、億元）（十萬(wàn)公頃）（百萬(wàn)人）obsyX1X2X3X4X5X619801159.9351541922.6286.931794445.26987.0519811175.7954002180.6282.32002.5397.91000.7219821212.3358112483.3345.332181.5331.31015.919831366.9564602750419.512426.1347.11030.0819841642.8676173214.1517.152899.2318.91043.5719852004.8297163619.5675.13801.4443.651058.51198621

8、22.01111944013808.074374471.41075.0719872199.35138134675.7954.655115420.9109319882357.24182255865.31131.656534.6508.71110.2619892664.9220176534.71282.987074.2469.911127.0419902937.1239247662.11345.017250.3384.741143.3319913149.482662581571564.338245.7554.721158.2319923483.37345999084.72174.449704.85

9、13.331171.7119934348.954840210995.53253.512462.1488.291185.171994521854653.3216264.7550.431198.519956242.29189420340.95793.7520620546.881267.4319967407.999959522353.78282.2524774.1458.211211.2119978651.1411373323788.49126.4827298.9469.891223.8919989875.9511904824541.910061.9929152.5521.

10、551276.27199911444.0812611124519.111152.8631134.7534.291236.26200013395.2385673.6624915.812497.634152.6471.191284.53200116386.0495448.9826179.615361.5637595.2501.451247.61200218903.64110776.527390.818527.1842027.1499.811257.86200321715.25142271.229691.823083.8745842545.061292.27表3.122利用Eviews軟件，對(duì)數(shù)據(jù)建

11、立回歸方程建立回歸方程的實(shí)現(xiàn)方式有菜單方式、命令方式、對(duì)象方式。用菜單方式建立回歸模型，在主窗口菜單單擊Quick/Estimate Equation在 Specification窗口填寫方程y= c(1) +c(2)*x1 +c(3)*x2 +c(4)*x3+c(5)* x4 +c(6)*x5 +c(7)*x6點(diǎn)擊確定可得到如下結(jié)果Dependent Variable: YMethod: Least SquaresDate: 06/13/12 Time: 11:15Sample: 1 24Included observations: 24VariableCoefficientStd. Err

12、ort-StatisticProb.C-3870.7391967.075-1.9677630.0656X1-0.0151530.008981-1.6872490.1098X2-0.3200190.111507-2.8699460.0106X30.5317070.1090494.8758600.0001X40.4094760.0975584.1972660.0006X50.6165651.2790890.4820350.6359X64.6270162.1750782.1272880.0483R-squared0.998534Mean dependent var6294.363Adjusted R

13、-squared0.998016S.D. dependent var6024.478S.E. of regression Sum squared resid Log likelihood F-statisticProb(F-statistic)268.34771224179.-164.13121929.2220.000000Akaike info criterionSchwarz criterionHannan-Quinn criter.Durbin-Watson stat14.2609414.6045414.352092.329706因而y對(duì)六個(gè)自變量的線性回歸方程為：y = 3870.73

14、9 - 0.015x - 0.032x + 0.532x + 0.409x + 0.617x + 4.627x123456輸出結(jié)果中，Prob即為F統(tǒng)計(jì)量的收尾概率，由Prob值=0.000 (近似值)可知其回歸方程高度顯著。即可以以99.9%以上的概率斷言自變量x ,x ,x，,x全體對(duì)因變量y產(chǎn)生顯著 1236性影響由F檢驗(yàn)知回歸方程的整體是顯著的，然而這種顯著是6個(gè)自變量作為一個(gè)整體對(duì)因變量y 有十分顯著的影響。那么，每一個(gè)自變量x.(j = 1,2,.,6)是否對(duì)y有顯著影響呢？2.3利用Eviews軟件，對(duì)數(shù)據(jù)預(yù)處理2.3.1繪制統(tǒng)計(jì)圖繪制統(tǒng)計(jì)圖基本操作方式有三個(gè)：菜單式操作、命令式

15、操作和對(duì)象操作。利用菜單式操 作在主窗口中單擊Quick/Graph彈出Series List對(duì)話框，在對(duì)話框中輸入y，x1,x2,x3,x4,x5,x6 點(diǎn)擊 ok，在 Graph Options 窗 口選擇 Lin Symbol 把 Axis 設(shè)置為 Boxplot 把 Multiple 設(shè)置 為Multiple graphs，各變量的動(dòng)態(tài)曲線圖如下30,00025,00020,00015,00010,00020,00016,00020,00015,00024,00012,000120,00040,00030,00020,0002.3.2簡(jiǎn)單相關(guān)分析繪制散點(diǎn)圖菜單法：主窗口 Quick/G

16、raph,Type選項(xiàng)設(shè)為scatter, Axis設(shè)為Boxplot, Multiple graphs設(shè)為Multiple graphsfirest vs all;也可用命令法或創(chuàng)建圖形對(duì)象操作來(lái)繪制 散點(diǎn)圖這不做介紹。散點(diǎn)圖如下從三點(diǎn)圖中可看出X和X對(duì)一得影響不是很大但是尤，X ,尤，X對(duì)y的影響比較 152346的明顯。2.3.3計(jì)算簡(jiǎn)單相關(guān)系數(shù)計(jì)算簡(jiǎn)單相關(guān)系數(shù)的方法有三種：菜單法、命令法、對(duì)群對(duì)象進(jìn)行操作。菜單路徑為:主窗口 Quick/Group Statistic/Correlation;結(jié)果如下從樣本的相關(guān)系數(shù)結(jié)果可看出某些自變量之間的相關(guān)性很高如X1和x2等。2.3.4異方差性

17、診斷懷特檢驗(yàn)：打開方程對(duì)象窗口，選View/Residual Tests/White Heteroskedasticity在彈出 的對(duì)話框中選擇White檢驗(yàn)法，然后確認(rèn)。Heteroskedasticity Test: WhiteF-statistic5.716534Prob. F(21,2)0.1593Obs*R-squared23.60671Prob. Chi-Square(21)0.3125Scaled explained SS16.51853Prob. Chi-Square(21)0.7398Test Equation:Dependent Variable: RESIDA2Metho

18、d: Least SquaresDate: 06/14/12 Time: 18:46Sample: 1 24Included observations: 24VariableCoefficientStd. Errort-StatisticProb.C2326501.4208125.0.5528590.6359X1A2-0.0043560.009205-0.4732100.6827X1*X20.0485470.0787090.6167950.6002X1*X30.0427400.0551390.7751360.5194X1*X4-0.0205580.039474-0.5208050.6544X1

19、*X5-0.6277700.755060-0.8314180.4932X1*X60.1403010.2624880.5345060.6465X2A2-0.0658960.191736-0.3436800.7639X2*X3-0.1245160.702968-0.1771290.8757X2*X4-0.0600920.523470-0.1147950.9191X2*X50.7783365.3556350.1453300.8978X2*X60.2139290.9098040.2351370.8360X3A20.1431000.8798330.1626440.8857X3*X4-0.2568811.

20、200632-0.2139550.8504X3*X59.72966015.538970.6261460.5952X3*X6-2.6756033.627377-0.7376140.5376X4A20.1335170.4248620.3142610.7831X4*X5-1.1271346.540784-0.1723240.8790X4*X60.1108821.8209270.0608930.9570X5A29.49290310.132640.9368640.4477X5*X6-6.2467578.201490-0.7616610.5258X6A2-1.5841055.741493-0.275905

21、0.8085R-squared0.983613Mean dependent var62625.41Adjusted R-squared0.811548S.D. dependent var100905.3S.E. of regression43804.02Akaike info criterion23.56127Sum squared resid3.84E+09Schwarz criterion24.64115Log likelihood-260.7352Hannan-Quinn criter.23.84776F-statistic5.716534Durbin-Watson stat3.0244

22、44Prob(F-statistic)0.159274由于收尾概率大于顯著性水平0.1，0.5 或 0.01，接受原假設(shè)，殘差不存在異方差通過(guò)上面的分析說(shuō)明盡管回歸方程通過(guò)了顯著性檢驗(yàn)，但也出現(xiàn)某些單個(gè)變量X.對(duì)y 并不顯著的情況。3自變量的選擇3.1 t檢驗(yàn)法通過(guò)回歸系數(shù)的顯著性檢驗(yàn)來(lái)決定自變量的取舍。X5的收尾概率為0.6359，應(yīng)從模型 中刪除，再對(duì)剩余變量做回歸得到Dependent Variable: YMethod: Least SquaresDate: 06/13/12 Time: 20:08Sample: 1 24Included observations: 24Variabl

23、e Coefficient Std. Error t-Statistic Prob.X1-0.0154420.009147-1.6882490.1077X2-0.2921930.112887-2.5883580.0180X30.4744060.1146664.1372670.0006X40.4401330.1035744.2494350.0004X61.0751490.1279978.3998230.0000R-squared0.998062Mean dependent var6294.363Adjusted R-squared0.997654S.D. dependent var6024.47

24、8S.E. of regression291.7900Akaike info criterion14.37300Sum squared resid1617686.Schwarz criterion14.61843Log likelihood-167.4760Hannan-Quinn criter.14.43811Durbin-Watson stat1.800817x1的收尾概率為0.1077，應(yīng)從模型中刪除，再對(duì)剩余變量做回歸得到Dependent Variable: YMethod: Least SquaresDate: 06/13/12 Time: 20:11Sample: 1 24Inc

25、luded observations: 24VariableCoefficientStd. Errort-StatisticProb.X2-0.4546510.061691-7.3698730.0000X30.3580140.0957703.7382480.0013X40.5541570.0820766.7517440.0000X61.1653730.1215669.5863140.0000R-squared0.997771Mean dependent var6294.363Adjusted R-squared0.997437S.D. dependent var6024.478S.E. of

26、regression304.9881Akaike info criterion14.42943Sum squared resid1860355.Schwarz criterion14.62578Log likelihood-169.1532Hannan-Quinn criter.14.48152Durbin-Watson stat1.532904在上述模型中自變量的收尾概率都小于給定的顯著性水平，剔除七,氣最優(yōu)回歸子集模型的 回歸方程為A. 一_一_ 一. - ._一 ._y = -4478.309 - 0.483七 + 0.424% + 0.517 x4 + 5.554x6決定系數(shù)為R2 =

27、 0.997771，修正的決定系數(shù)為R2 = 0.997437，而全模型的決定系數(shù)為R2 = 0.998534，修正的決定系數(shù)為R2 = 0.998016。3.2冗余變量檢驗(yàn)法創(chuàng)建一個(gè)方程，其中包含X ,尤，X , X , X , X六個(gè)自變量，然后檢驗(yàn)一些變量是否為冗余變 123456量，在方程對(duì)象窗口中選擇View/Coefficient Tests/Redundant Variables-Likelihood Ratio 在彈出的對(duì)話框中填寫待檢驗(yàn)序列的名稱x1。Redundant Variables: X1F-statistic3.894073Prob. F(1,18)0.0640Lo

28、g likelihood ratio4.700261Prob. Chi-Square(1)0.0302Test Equation:Dependent Variable: YMethod: Least SquaresDate: 06/13/12 Time: 20:55Sample: 1 24Included observations: 24VariableCoefficientStd. Errort-StatisticProb.X2-0.4551620.062749-7.2536430.0000X30.3610690.0975483.7014600.0015X40.5529210.0835046

29、.6214940.0000X50.7644731.3217400.5783840.5698X60.8642590.5350941.6151540.1228R-squared0.997810Mean dependent var6294.363Adjusted R-squared0.997349S.D. dependent var6024.478S.E. of regression310.1924Akaike info criterion14.49531Sum squared resid1828167.Schwarz criterion14.74074Log likelihood-168.9438

30、Hannan-Quinn criter.14.56043Durbin-Watson stat1.566028從上面的結(jié)果可以看出F-statistic的值為3.894073,其收尾概率為0.0640，顯然大于給定的顯著性水平，因此不能拒絕原假設(shè)，即X1是冗余變量，應(yīng)該刪除。Redundant Variables: X2F-statistic5.041881Prob. F(1,18)0.0375Log likelihood ratio5.926601Prob. Chi-Square(1)0.0149Test Equation:Dependent Variable: YMethod: Least

31、SquaresDate: 06/14/12 Time: 18:00Sample: 1 24Included observations: 24VariableCoefficientStd. Errort-StatisticProb.X1-0.0370340.005288-7.0034200.0000X30.7333740.06255911.722850.0000X40.1924980.0401464.7949890.0001X52.2200141.3746961.6149130.1228X60.0774280.5624000.1376740.8919R-squared0.997695Mean d

32、ependent var6294.363Adjusted R-squared0.997210S.D. dependent var6024.478S.E. of regression318.2195Akaike info criterion14.54641Sum squared resid1924010.Schwarz criterion14.79184Log likelihood-169.5569Hannan-Quinn criter.14.61152Durbin-Watson stat1.988014從上面的結(jié)果可以看出Log likelihood ratio的值為5.926601，其收尾概

33、率為0.0149, 顯然小于給定的顯著性水平，因此可以拒絕原假設(shè)，即* 2不是冗余變量，應(yīng)該保留。根據(jù)上面的方法，同理依次檢驗(yàn)* ,* ,* ,*是否為冗余變量，通過(guò)多次的檢驗(yàn)我們 3456發(fā)現(xiàn)除了 * 1和*5是冗余變量外，其他的都不是冗余變量。對(duì)剩余變量做回歸有Dependent Variable: YMethod: Least SquaresDate: 06/14/12 Time: 18:20Sample: 1 24Included observations: 24VariableCoefficientStd. Errort-StatisticProb.X2-0.4546510.0616

34、91-7.3698730.0000X30.3580140.0957703.7382480.0013X40.5541570.0820766.7517440.0000X61.1653730.1215669.5863140.0000R-squared0.997771Mean dependent var6294.363Adjusted R-squared0.997437S.D. dependent var6024.478S.E. of regression304.9881Akaike info criterion14.42943Sum squared resid1860355.Schwarz crit

35、erion14.62578Log likelihood-169.1532 Hannan-Quinn criter. 14.48152Durbin-Watson stat 1.532904剔除七,氣最優(yōu)回歸子集模型的回歸方程為A. 一 一一一一 一一一. 一y = -4478.309 - 0.483% + 0.424氣 + 0.517 七 + 5.554七輸出結(jié)果中，Prob即為F統(tǒng)計(jì)量的收尾概率，由Prob值=0.000 （近似值）可知其回歸方 程高度顯著。即可以以99.9%以上的概率斷言自變量七，氣，七全體對(duì)因變量y產(chǎn)生 顯著性影響決定系數(shù)為R2 = 0.997771，修正的決定系數(shù)為R2

36、= 0.997437，而全模型的決定系數(shù)為R2 = 0.998534，修正的決定系數(shù)為R2 = 0.998016。3.3前進(jìn)逐步回歸在工具欄中選擇Quick/Estimate Equation建立一個(gè)Equation對(duì)象，在窗口所示的Method中 選擇STEP LS-Stepwise Least Squares在得到的對(duì)話框中輸入因變量與自變量，選擇Options標(biāo) 簽，再在得到的圖中選擇Stepwise最后選擇Forwards選項(xiàng)，設(shè)置點(diǎn)確a進(jìn)=0.15，a出=0.10， 回歸量最大數(shù)目為6,得出結(jié)果Dependent Variable: YMethod: Stepwise Regress

37、ionDate: 06/14/12 Time: 19:38Sample: 1 24Included observations: 24Number of always included regressors: 1Number of search regressors: 6Selection method: Stepwise forwardsStopping criterion: p-value forwards/backwards = 0.15/0.1Stopping criterion: Number of search regressors = 6VariableCoefficientStd

38、. Errort-StatisticProb.*C-4478.3091872.379-2.3917740.0273X30.4239820.0904504.6874630.0002X65.5537771.8380453.0215670.0070X40.5173670.0754106.8607140.0000X2-0.4828450.056727-8.5117450.0000R-squared0.998287Mean dependent var6294.363Adjusted R-squared0.997927S.D. dependent var6024.478S.E. of regression

39、274.3270Akaike info criterion14.24957Sum squared resid1429851.Schwarz criterion14.49500Log likelihood-165.9948Hannan-Quinn criter.14.31468F-statistic2768.375 Durbin-Watson stat 1.945101Prob(F-statistic)0.000000Selection Summary從上面的結(jié)果可以看出，最后的出的結(jié)果與t檢驗(yàn)和冗余變量法得到的結(jié)果是一樣的。 最終也是得到方程A. _ . _.一y = -4478.309 -

40、0.483七 + 0.424氣 + 0.517 七 + 5.554七3.4后退逐步回歸在工具欄中選擇Quick/Estimate Equation建立一個(gè)Equation對(duì)象，在窗口所示的Method中 選擇STEP LS-Stepwise Least Squares在得到的對(duì)話框中輸入因變量與自變量，選擇Options標(biāo) 簽，再在得到的圖中選擇Stepwise最后選擇Backwards選項(xiàng)，設(shè)置a進(jìn)=0.05，a出=0.。1， 回歸量最小數(shù)目為1，點(diǎn)確定，得出結(jié)果Dependent Variable: YMethod: Stepwise RegressionDate: 06/14/12 Ti

41、me: 20:01Sample: 1 24Included observations: 24Number of always included regressors: 1Number of search regressors: 6Selection method: Stepwise backwardsStopping criterion: p-value forwards/backwards = 0.05/0.1Stopping criterion: Number of search regressors = 1VariableCoefficientStd. Errort-StatisticP

42、rob.*C-4207.0231799.564-2.3378010.0311X30.5231170.1052644.9695740.0001X1-0.0136830.008265-1.6554950.1152X40.4185640.0936564.4691840.0003X2-0.3371880.103387-3.2614070.0043X65.2079931.7715822.9397410.0088R-squared0.998513Mean dependent var6294.363Adjusted R-squared0.998101S.D. dependent var6024.478S.E

43、. of regression262.5633Akaike info criterion14.19118Sum squared resid1240911.Schwarz criterion14.48569Log likelihood-164.2942Hannan-Quinn criter.14.26931F-statistic2418.146Durbin-Watson stat2.348711Prob(F-statistic)0.000000Selection SummaryRemoved X5*Note: p-values and subsequent tests do not accoun

44、t for stepwise selection.在上述的結(jié)果中遴選出了X , x , X , X , X這與前面的幾種檢驗(yàn)不相符合，這31426可能是氣與X2有很強(qiáng)的相關(guān)性可以把氣或X2隨便剔除一個(gè)，比較得到的模型那個(gè)更好。前進(jìn)法和后退法顯然都有明顯不足。前進(jìn)法可能存在這樣的問(wèn)題，即不能反應(yīng)引進(jìn)新 的變量后的變化情況。因?yàn)槟硞€(gè)變量開始可能是顯著的，但當(dāng)引入某個(gè)自變量后它變得并不 顯著了，但是也沒有機(jī)會(huì)將其剔除，即一旦引入，就是“終身制”的；這種只考慮引入，而 沒有考慮剔除的做法顯然是不全面的。而且，我們?cè)谠S多例子中會(huì)發(fā)現(xiàn)可能最先引入的某個(gè) 變量，當(dāng)其他自變量相繼引入后，它會(huì)變得對(duì)因變量y很不

45、顯著。后退法的明顯不足是，一開始把全部自變量引入方程，這樣計(jì)算量很大。如果有些自變量不 太重要，一開始就不引入，就可以減少一些計(jì)算量；再就是一旦某個(gè)自變量被剔除了，它就 再也沒有機(jī)會(huì)重新進(jìn)入回歸方程。35.最大R平方增量逐次交換回歸在工具欄中選擇Q uick/Estimate Equation建立一個(gè)Equation對(duì)象，在窗口所示的Method 中選擇STEP LS-Stepwise Least Squares在得到的對(duì)話框中輸入因變量與自變量，選擇Options 標(biāo)簽，再在得到的圖中選擇Swapwise，在得到的對(duì)話框中選擇Max Rsquared increment點(diǎn) 擊確定得到如下結(jié)果

46、Dependent Variable: YMethod: Stepwise RegressionDate: 06/15/12 Time: 20:52Sample: 1 24Included observations: 24Number of always included regressors: 1Number of search regressors: 6Selection method: Swapwise - Max R-squaredNumber of search regressors: 6VariableCoefficientStd. Errort-StatisticProb.*C-

47、4207.0231799.564-2.3378010.0311X30.5231170.1052644.9695740.0001X2-0.3371880.103387-3.2614070.0043X40.4185640.0936564.4691840.0003X65.2079931.7715822.9397410.0088X1-0.0136830.008265-1.6554950.1152R-squared0.998513Mean dependent var6294.363Adjusted R-squared0.998101S.D. dependent var6024.478S.E. of re

48、gression262.5633Akaike info criterion14.19118Sum squared resid1240911.Schwarz criterion14.48569Log likelihood-164.2942Hannan-Quinn criter.14.26931F-statistic2418.146Durbin-Watsonstat2.348711Prob(F-statistic)0.000000Selection SummaryAdded X3Added X1Added X4Removed X1Added X2Added X6Added X1*Note: p-v

49、alues and subsequent tests do not account for stepwise selection.最終也是得到方程A. 一 _ 一一一. - ._ 一y = -4478.309 - 0.483七 + 0.424% + 0.517 七 + 5.554七3.6最小R平方增量逐次交換回歸在工具欄中選擇Q uick/Estimate Equation建立一個(gè)Equation對(duì)象，在窗口所示的Method 中選擇STEP LS-Stepwise Least Squares在得到的對(duì)話框中輸入因變量與自變量，選擇Options 標(biāo)簽，再在得到的圖中選擇Swapwise，在得

50、到的對(duì)話框中選擇Min Rsquared increment點(diǎn) 確定得到如下結(jié)果Dependent Variable: YMethod: Stepwise Regression Date: 06/15/12 Time: 20:56Sample: 1 24Included observations: 24Number of always included regressors: 1Number of search regressors: 6Selection method: Swapwise - Min R-squaredNumber of search regressors: 6Variabl

51、eCoefficientStd. Errort-StatisticProb.*C-4207.0231799.564-2.3378010.0311X30.5231170.1052644.9695740.0001X2-0.3371880.103387-3.2614070.0043X40.4185640.0936564.4691840.0003X65.2079931.7715822.9397410.0088X1-0.0136830.008265-1.6554950.1152R-squared0.998513Mean dependent var6294.363Adjusted R-squared0.9

52、98101S.D. dependent var6024.478S.E. of regression262.5633Akaike info criterion14.19118Sum squared resid1240911.Schwarz criterion14.48569Log likelihood-164.2942Hannan-Quinn criter.14.26931F-statistic2418.146Durbin-Watson stat2.348711Prob(F-statistic)0.000000Selection SummaryAdded X3Added X1Added X4Re

53、moved X1Added X2Added X6Added X1*Note: p-values and subsequent tests do not account for stepwiseselection.從上面的結(jié)果可以看出，最后的出的結(jié)果與前面幾種方法得到的結(jié)果是一樣的。最終也 是得到方程A. 一 _ 一一一. -._ 一y = -4478.309 - 0.483% + 0.424% + 0.517 七 + 5.554七3.7組合逐步回歸在工具欄中選擇Q uick/Estimate Equation建立一個(gè)Equation對(duì)象，在窗口所示的Method 中選擇STEP LS-Step

54、wise Least Squares在得到的對(duì)話框中輸入因變量與自變量，選擇Options 標(biāo)簽，再在得到的圖中選擇Swapwise，在得到的對(duì)話框中選擇Combinatorial點(diǎn)擊確定得到如 下結(jié)果Dependent Variable: YMethod: Stepwise RegressionDate: 06/15/12 Time: 21:05Sample: 1 24Included observations: 24Number of always included regressors: 1Number of search regressors: 6Selection method: C

55、ombinatorialNumber of search regressors: 4VariableCoefficientStd. Errort-StatisticProb.*C-4478.3091872.379-2.3917740.0273X30.4239820.0904504.6874630.0002X40.5173670.0754106.8607140.0000X2X6-0.4828455.5537770.056727 -8.5117451.8380453.0215670.00000.0070R-squared0.998287Mean dependent var6294.363Adjusted R-squared0.997927S.D.dependent var6024.478S.E. of regression274.3270Akaike info criterion14.24957Sum squared resid1429851.S