《SPSS線性回歸分析》ppt課件

1、SPSS線性回歸 回歸回歸Regression，或，或Linear Regression和相關(guān)都用來分析兩個(gè)定距變和相關(guān)都用來分析兩個(gè)定距變量間的關(guān)系，但回歸有明確的因果關(guān)系假設(shè)。量間的關(guān)系，但回歸有明確的因果關(guān)系假設(shè)。即要假設(shè)一個(gè)變量為自變量，一個(gè)為因變量，即要假設(shè)一個(gè)變量為自變量，一個(gè)為因變量，自變量對(duì)因變量的影響就用回歸表示。如年齡自變量對(duì)因變量的影響就用回歸表示。如年齡對(duì)收入的影響。由于回歸構(gòu)建了變量間因果關(guān)對(duì)收入的影響。由于回歸構(gòu)建了變量間因果關(guān)系的數(shù)學(xué)表達(dá)，它具有統(tǒng)計(jì)預(yù)測(cè)功能。系的數(shù)學(xué)表達(dá)，它具有統(tǒng)計(jì)預(yù)測(cè)功能。一、回歸的原理一、回歸的原理 線性回歸的統(tǒng)計(jì)原理：線性回歸的統(tǒng)計(jì)原理：兩

2、個(gè)定距變量的回歸是用函數(shù)兩個(gè)定距變量的回歸是用函數(shù)y= fx來分析的。我們最常用的是一元回歸方程來分析的。我們最常用的是一元回歸方程bxay其中其中x為自變量；為自變量；y為因變量；為因變量；a為截距，即常量；為截距，即常量；b為回歸系數(shù)，闡明自變量對(duì)因變量的影響程度。為回歸系數(shù)，闡明自變量對(duì)因變量的影響程度。360370380390400410420430440012345工齡工資在統(tǒng)計(jì)學(xué)中，這一方程中的系數(shù)是靠在統(tǒng)計(jì)學(xué)中，這一方程中的系數(shù)是靠x與與y變量的大變量的大量數(shù)據(jù)擬合出來的。量數(shù)據(jù)擬合出來的。XYY=a+bxx，y由圖中可以看出，回歸直線應(yīng)該是到一切數(shù)據(jù)點(diǎn)最由圖中可以看出，回歸直線

3、應(yīng)該是到一切數(shù)據(jù)點(diǎn)最短間隔的直線。該直線的求得即使用短間隔的直線。該直線的求得即使用“最小二乘方法最小二乘方法，使，使:02iiyy在擬合的回歸直線方程中，回歸系數(shù)：在擬合的回歸直線方程中，回歸系數(shù)：2)()(xxyyxxiiib表示表示x每變化一個(gè)單位時(shí)，每變化一個(gè)單位時(shí)，x與與y共同變化的程度。共同變化的程度。xbya常數(shù)常數(shù):比如經(jīng)過上學(xué)年數(shù)和工資的關(guān)系計(jì)算得出以下比如經(jīng)過上學(xué)年數(shù)和工資的關(guān)系計(jì)算得出以下的回歸公式：的回歸公式：y=472+14.8x可知上學(xué)年數(shù)每增長(zhǎng)可知上學(xué)年數(shù)每增長(zhǎng)1年，工資會(huì)添加年，工資會(huì)添加14.8元；元；也可推測(cè)，上學(xué)年數(shù)為也可推測(cè)，上學(xué)年數(shù)為15年的人，工資收

4、入應(yīng)年的人，工資收入應(yīng)為為472 + 14.8 *15=694元。元。二、線性回歸的適用條件二、線性回歸的適用條件n線性趨勢(shì)：即自變量與因變量的關(guān)系是線線性趨勢(shì)：即自變量與因變量的關(guān)系是線性的。性的。n獨(dú)立性：因變量獨(dú)立性：因變量Y的取值相互獨(dú)立。反映在的取值相互獨(dú)立。反映在方程中即殘差獨(dú)立。方程中即殘差獨(dú)立。n正態(tài)性：即自變量的任何一個(gè)線性組合，正態(tài)性：即自變量的任何一個(gè)線性組合，Y應(yīng)該服從正態(tài)分布。反映在方程中即殘差應(yīng)該服從正態(tài)分布。反映在方程中即殘差Ei服從正態(tài)分布。服從正態(tài)分布。n方差齊性方差齊性:自變量的任何一個(gè)線性組合，自變量的任何一個(gè)線性組合，Y的方差一樣。的方差一樣。三、線性回

5、歸菜單簡(jiǎn)介三、線性回歸菜單簡(jiǎn)介L(zhǎng)inear Regression對(duì)話框?qū)υ捒騨Enter：進(jìn)入法。默許選項(xiàng)。一切所選自變量：進(jìn)入法。默許選項(xiàng)。一切所選自變量都進(jìn)入回歸模型，不作任何挑選。都進(jìn)入回歸模型，不作任何挑選。nStepwise：逐漸法。根據(jù)在：逐漸法。根據(jù)在Option框中設(shè)頂框中設(shè)頂?shù)募{入和排除規(guī)范進(jìn)展變量挑選。詳細(xì)做法是的納入和排除規(guī)范進(jìn)展變量挑選。詳細(xì)做法是首先分別計(jì)算各自變量首先分別計(jì)算各自變量X對(duì)對(duì)Y的奉獻(xiàn)大小，按的奉獻(xiàn)大小，按由大到小的順序挑選奉獻(xiàn)最大的一個(gè)先進(jìn)入方由大到小的順序挑選奉獻(xiàn)最大的一個(gè)先進(jìn)入方程；隨后重新計(jì)算各自變量程；隨后重新計(jì)算各自變量X對(duì)對(duì)Y的奉獻(xiàn)，引的奉

6、獻(xiàn)，引入方程，同時(shí)調(diào)查已在方程中的變量能否由于入方程，同時(shí)調(diào)查已在方程中的變量能否由于新變量的引入而不再有統(tǒng)計(jì)意義。假設(shè)是，那新變量的引入而不再有統(tǒng)計(jì)意義。假設(shè)是，那么將它剔除。如此反復(fù)，直到方程內(nèi)沒有變量么將它剔除。如此反復(fù)，直到方程內(nèi)沒有變量可剔除，方程外沒有變量可引入為止?？商蕹?，方程外沒有變量可引入為止。nRemoveRemove：剔除法移去法。只出不進(jìn)。：剔除法移去法。只出不進(jìn)。留意其挑選以留意其挑選以BlockBlock為單位。為單位。nBackwardBackward：向后法。步驟類逐漸法，但只：向后法。步驟類逐漸法，但只出不進(jìn)。即對(duì)已納入方程的變量按對(duì)出不進(jìn)。即對(duì)已納入方程的變

7、量按對(duì)Y Y奉獻(xiàn)奉獻(xiàn)的由小到大依次剔除，每剔除一個(gè)變量，的由小到大依次剔除，每剔除一個(gè)變量，重新計(jì)算對(duì)重新計(jì)算對(duì)Y Y奉獻(xiàn)的大小。直到方程中一切奉獻(xiàn)的大小。直到方程中一切變量都符合選入的規(guī)范為止。變量都符合選入的規(guī)范為止。nForwardForward：向前法。與逐漸法類似，但只進(jìn)：向前法。與逐漸法類似，但只進(jìn)不出。即對(duì)納入方程的變量不再調(diào)查它的不出。即對(duì)納入方程的變量不再調(diào)查它的顯著性。直到方程外變量均達(dá)不到進(jìn)入規(guī)顯著性。直到方程外變量均達(dá)不到進(jìn)入規(guī)范，沒有自變量引入方程為止。范，沒有自變量引入方程為止。變量挑選方法的選擇應(yīng)留意變量挑選方法的選擇應(yīng)留意n1.變量選擇不僅僅是數(shù)學(xué)問題，不能脫離

8、研變量選擇不僅僅是數(shù)學(xué)問題，不能脫離研討的目的進(jìn)展。討的目的進(jìn)展。n2.最好多做嘗試，對(duì)不同方法之間所結(jié)果的最好多做嘗試，對(duì)不同方法之間所結(jié)果的差別仔細(xì)思索。差別仔細(xì)思索。Statistics 對(duì)話框?qū)υ捒騊lots Plots 對(duì)話框?qū)υ捒騒軸或軸或Y軸中有軸中有一個(gè)是因變量一個(gè)是因變量規(guī)范化的預(yù)測(cè)規(guī)范化的預(yù)測(cè)值值規(guī)范化的殘差規(guī)范化的殘差刪除的殘差刪除的殘差修正后的預(yù)測(cè)修正后的預(yù)測(cè)值。值。用戶的殘差用戶的殘差用戶的刪除的用戶的刪除的殘差殘差輸出帶有正態(tài)曲線的規(guī)范化殘差的直方圖。輸出帶有正態(tài)曲線的規(guī)范化殘差的直方圖。輸出規(guī)范化殘差的正態(tài)概率圖。輸出規(guī)范化殘差的正態(tài)概率圖。對(duì)每一個(gè)自變量，會(huì)產(chǎn)生

9、一個(gè)自變量與因變對(duì)每一個(gè)自變量，會(huì)產(chǎn)生一個(gè)自變量與因變量殘差的散點(diǎn)圖，主要用于回歸診斷。量殘差的散點(diǎn)圖，主要用于回歸診斷。Options 對(duì)話框?qū)υ捒蛉缫粋€(gè)變量的如一個(gè)變量的F統(tǒng)計(jì)量統(tǒng)計(jì)量的的p值是小于值是小于Entry值的，值的，這個(gè)變量就進(jìn)入模型。這個(gè)變量就進(jìn)入模型。如一個(gè)變量的如一個(gè)變量的F統(tǒng)計(jì)量統(tǒng)計(jì)量的的p值是大于值是大于Removal值值的，這個(gè)變量就從模型的，這個(gè)變量就從模型中刪除。中刪除。 Entry值必需值必需小于小于Removal值且都為值且都為正。如想模型中有更多正。如想模型中有更多的變量就提高的變量就提高Entry值；值；如想模型中減少變量就如想模型中減少變量就減少減少R

10、emoval值。值。用用F統(tǒng)計(jì)量的值，同上統(tǒng)計(jì)量的值，同上選擇此項(xiàng)不顯示回選擇此項(xiàng)不顯示回歸方程中常數(shù)項(xiàng)。歸方程中常數(shù)項(xiàng)。Save Save 對(duì)話框?qū)υ捒蛩摹⒒貧w分析的步驟四、回歸分析的步驟1.1.做出散點(diǎn)圖做出散點(diǎn)圖, ,察看變量間的趨勢(shì)；察看變量間的趨勢(shì)；2.2.調(diào)查數(shù)據(jù)的分布調(diào)查數(shù)據(jù)的分布, ,進(jìn)展必要的預(yù)處置；進(jìn)展必要的預(yù)處置；3.3.進(jìn)展直線回歸分析；進(jìn)展直線回歸分析；4.4.殘差分析；殘差分析；5.5.強(qiáng)影響點(diǎn)的診斷及多重共線性問題的判別。強(qiáng)影響點(diǎn)的診斷及多重共線性問題的判別。n例例1:1:以以SPSSSPSS自帶的數(shù)據(jù)文件自帶的數(shù)據(jù)文件“1991 1991 U.S. Genera

11、l Social Survey.savU.S. General Social Survey.sav為例分析影響職業(yè)聲望的要素。為例分析影響職業(yè)聲望的要素。Highest Year of School Completed3020100-10Rs Occupational Prestige Score (1980)908070605040302010Age of Respondent100806040200Rs Occupational Prestige Score (1980)908070605040302010Highest Year School Completed, Mother30201

12、00-10Rs Occupational Prestige Score (1980)908070605040302010Highest Year School Completed, Father3020100-10Rs Occupational Prestige Score (1980)908070605040302010Highest Year School Completed, Spouse3020100-10Rs Occupational Prestige Score (1980)908070605040302010Descriptive Statistics44.7113.066332

13、44.0214.02833213.752.67133210.603.94633210.853.11333213.402.8843321.41.511332Rs OccupationalPrestige Score (1980)Age of RespondentHighest Year of SchoolCompletedHighest Year SchoolCompleted, FatherHighest Year SchoolCompleted, MotherHighest Year SchoolCompleted, SpouseRs Federal Income TaxMeanStd. D

14、eviationNCorrelations1.000-.002.559.227.175.339.006-.0021.000-.171-.316-.380-.115.052.559-.1711.000.347.367.552.027.227-.316.3471.000.657.356.084.175-.380.367.6571.000.400.066.339-.115.552.356.4001.000-.088.006.052.027.084.066-.0881.000.487.000.000.001.000.458.487.001.000.000.018.174.000.001.000.000

15、.000.315.000.000.000.000.000.063.001.000.000.000.000.114.000.018.000.000.000.054.458.174.315.063.114.054.332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332332Rs OccupationalPrestige Score (1980)Age of Respo

16、ndentHighest Year of SchoolCompletedHighest Year SchoolCompleted, FatherHighest Year SchoolCompleted, MotherHighest Year SchoolCompleted, SpouseRs Federal Income TaxRs OccupationalPrestige Score (1980)Age of RespondentHighest Year of SchoolCompletedHighest Year SchoolCompleted, FatherHighest Year Sc

17、hoolCompleted, MotherHighest Year SchoolCompleted, SpouseRs Federal Income TaxRs OccupationalPrestige Score (1980)Age of RespondentHighest Year of SchoolCompletedHighest Year SchoolCompleted, FatherHighest Year SchoolCompleted, MotherHighest Year SchoolCompleted, SpouseRs Federal Income TaxPearson C

18、orrelationSig. (1-tailed)NRsOccupationalPrestigeScore (1980)Age ofRespondentHighest Yearof SchoolCompletedHighest YearSchoolCompleted,FatherHighest YearSchoolCompleted,MotherHighest YearSchoolCompleted,SpouseRs FederalIncome TaxVariables Entered/RemovedaHighestYear ofSchoolCompleted.Stepwise(Criteri

19、a:Probability-of-F-to-enter =.100).Age ofRespondent.Stepwise(Criteria:Probability-of-F-to-enter =.100).Model12VariablesEnteredVariablesRemovedMethodDependent Variable: Rs OccupationalPrestige Score (1980)a. Model Summaryc.559a.312.31010.855.312149.6501330.000.567b.321.31710.799.0094.4031329.0371.955

20、Model12RR SquareAdjustedR SquareStd. Error ofthe EstimateR SquareChangeF Changedf1df2Sig. F ChangeChange StatisticsDurbin-WatsonPredictors: (Constant), Highest Year of School Completeda. Predictors: (Constant), Highest Year of School Completed, Age of Respondentb. Dependent Variable: Rs Occupational

21、 Prestige Score (1980)c. ANOVAc17631.872117631.872149.650.000a38880.788330117.82156512.66033118145.33229072.66677.798.000b38367.328329116.61856512.660331RegressionResidualTotalRegressionResidualTotalModel12Sum ofSquaresdfMean SquareFSig.Predictors: (Constant), Highest Year of School Completeda. Pred

22、ictors: (Constant), Highest Year of School Completed, Age of Respondentb. Dependent Variable: Rs Occupational Prestige Score (1980)c. Coefficientsa7.1423.1282.283.0232.732.223.55912.233.0002.0613.943.523.6022.813.226.57512.474.000.090.043.0972.098.037(Constant)Highest Year ofSchool Completed(Constan

23、t)Highest Year ofSchool CompletedAge of RespondentModel12BStd. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientstSig.Dependent Variable: Rs Occupational Prestige Score (1980)a. Excluded Variablesc.097a2.098.037.115.971.038a.773.440.043.880-.035a-.711.477-.039.866.045a.818.414.045.696-.009a

24、-.199.843-.011.999.071b1.418.157.078.812.001b.011.991.001.762.048b.875.382.048.695-.015b-.320.749-.018.996Age of RespondentHighest Year SchoolCompleted, FatherHighest Year SchoolCompleted, MotherHighest Year SchoolCompleted, SpouseRs Federal Income TaxHighest Year SchoolCompleted, FatherHighest Year

25、 SchoolCompleted, MotherHighest Year SchoolCompleted, SpouseRs Federal Income TaxModel12Beta IntSig.PartialCorrelationToleranceCollinearityStatisticsPredictors in the Model: (Constant), Highest Year of School Completeda. Predictors in the Model: (Constant), Highest Year of School Completed, Age of R

26、espondentb. Dependent Variable: Rs Occupational Prestige Score (1980)c. Casewise Diagnosticsa-3.697223.209733.23468Case Number6348601201Std. ResidualRsOccupationalPrestigeScore (1980)Dependent Variable: Rs OccupationalPrestige Score (1980)a. Residuals Statisticsa7.7465.2642.818.0671413-39.9334.92.12

27、11.0621413-4.9932.776-.2571.0891413-3.6973.234.0111.0241413Predicted ValueResidualStd. Predicted ValueStd. ResidualMinimumMaximum Mean Std. DeviationNDependent Variable: Rs Occupational Prestige Score (1980)a. Regression Standardized Residual3.252.752.251.751.25.75.25-.25-.75-1.25-1.75-2.25-2.75-3.2

28、5-3.75HistogramDependent Variable: Rs Occupational Prestige Score (1980)Frequency160140120100806040200Std. Dev = 1.02 Mean = .01N = 1413.00ScatterplotDependent Variable: Rs Occupational Prestige Score (1980)Rs Occupational Prestige Score (1980)908070605040302010Regression Standardized Residual43210-

29、1-2-3-4例例2：n請(qǐng)分析請(qǐng)分析SPSS自帶數(shù)據(jù)文件自帶數(shù)據(jù)文件plastic.sav中變中變量擠壓量擠壓extrusn、附加、附加(addition)、光、光澤澤(gloss)、不透明度、不透明度(opacity)對(duì)變量拉扯對(duì)變量拉扯強(qiáng)度強(qiáng)度(tear_res)的大小有無影響？知擠壓對(duì)的大小有無影響？知擠壓對(duì)拉扯強(qiáng)度的大小有影響。拉扯強(qiáng)度的大小有影響。知壓對(duì)拉扯強(qiáng)度有影響，故不需挑選，可用進(jìn)入法。知壓對(duì)拉扯強(qiáng)度有影響，故不需挑選，可用進(jìn)入法。其他變量不知道有無影響，需求用逐漸法進(jìn)展挑選。其他變量不知道有無影響，需求用逐漸法進(jìn)展挑選。Variables Entered/Removedb擠

30、壓a.Enter附 加.Stepwise(Criteria:Probability-of-F-to-enter =.100).Model12VariablesEnteredVariablesRemovedMethodAll requested variables entered.a. Dependent Variable: 抗 扯 強(qiáng) 度b. Model Summary.639a.408.375.37450.766b.586.538.32220Model12RR SquareAdjustedR SquareStd. Error ofthe EstimatePredictors: (Consta

31、nt), 擠壓a. Predictors: (Constant), 擠壓, 附加b. ANOVAc1.74011.74012.408.002a2.52518.1404.266192.50121.25012.048.001b1.76517.1044.26619RegressionResidualTotalRegressionResidualTotalModel12Sum ofSquaresdfMean SquareFSig.Predictors: (Constant), 擠壓a. Predictors: (Constant), 擠壓, 附加b. Dependent Variable: 抗扯強(qiáng)度c. Coefficientsa5.900.26522.278.000.590.167.6393.522.0025.315.31416.926.000.590.144.6394.095.0