多重線性回歸與相關(guān)spss

1、多重線性回歸與相關(guān)上海交通大學(xué)醫(yī)學(xué)院公共衛(wèi)生學(xué)院QIU YulanShanghai Jiao Tong University School of MedicineRegression 菜單SPSS 的 Regression 菜單中的內(nèi)容極為豐富，大致分為四大部分：QIU YulanShanghai Jiao Tong University School of Medicine²²Linear：線性回歸，簡(jiǎn)單線性回歸和多元線性回歸。Curve Estimation 過(guò)程和 Nonlinear Regression 過(guò)非線性回歸：程。²：它們以 Logistic 模型

2、為代表，包應(yīng)變量為分類資料的回歸括二分類（Binary Logistic）、無(wú)序多分類（Multinomial Logistic）和有序多分類（Ordinal Logistic）的 Logistic 過(guò)程以及 Probit（概率回歸分析用于分析劑量-反應(yīng)）過(guò)程。²其它回歸過(guò)程線性回歸假設(shè)被的各種情況而推出的一些“補(bǔ)Weight Estimation 過(guò)程、Two-Stage Least-Squares充”，過(guò)程和Optimal Scaling 過(guò)程，這些有其特定用途，不能隨意使用。QIU YulanShanghai Jiao Tong University School of Med

3、icineLinear 過(guò)程主要用于擬合多元線性回歸模型。引例：某地一年級(jí) 12名女大學(xué)生體重與肺活量數(shù)據(jù)如下，見數(shù)據(jù)文件corr.sav，請(qǐng)據(jù)此計(jì)算肺活量對(duì)體重的直線回歸方程。424246464650505052525858體重肺活量 2.552.202.75 2.40 2.80 2.81 3.41 3.10 3.462.853.503.00QIU YulanShanghai Jiao Tong University School of Medicine操作步驟如下：AnalyzeRegressionLinearDependent 框：lungIndependent 框：weightF 應(yīng)變

4、量為 lungF 自變量為 weight界面說(shuō)明：【主框】1、Dependent 框：用于選入回歸分析的應(yīng)變量，只能選入一個(gè)。2、Block：由 Previous和 Next按兩個(gè)按成，用于將下面Independent 框中選入的自變量分組。由于多元回歸分析中自變量的入選方式有前進(jìn)、后退、逐步等，如果對(duì)不同的自變量選入的不同，則用該按將自變量分組選入即可。3、Independent 框：用于選入回歸分析的自變量，它們進(jìn)入模型的使用 Block 按鈕進(jìn)行不同的定義。可QIU YulanShanghai Jiao Tong University School of MedicineOK4、Meth

5、od下拉列表：用于選擇對(duì)自變量的選入，該選項(xiàng)對(duì)當(dāng)前Independent 框中的所有變量均有效。Enter：強(qiáng)行進(jìn)入法，候選自變量全部納入模型，不做任何篩選，默認(rèn)選項(xiàng)。²QIU YulanShanghai Jiao Tong University School of Medicine²Stepwise：逐步法，根據(jù)在 Options 框中設(shè)定的納入和排除標(biāo)準(zhǔn)進(jìn)行變量篩選。Remove：強(qiáng)制剔除法，只出不進(jìn)。²²²Backward：法，只出不進(jìn)。Forward：向前法，只進(jìn)不出。5、Selection Variable 框：進(jìn)入一個(gè)篩選變量，并利

6、用右側(cè)的 Rules立一個(gè)選擇條件，這樣只有滿足該條件的義僅在當(dāng)前回歸過(guò)程有效。才會(huì)進(jìn)入回歸分析，該定6、Case Labels 框：選擇一個(gè)變量，它的取值將作為每條的。典ID 號(hào)的變量。最小二乘法的回歸分析。型的情況是使用7、WLS Weight：進(jìn)行QIU YulanShanghai Jiao Tong University School of Medicine【子框】用于選擇所需要的描述統(tǒng)計(jì)量。1、Regression Coefficients 復(fù)選框組：定義回歸系數(shù)的輸出情況。Estimates回歸系數(shù) B 及其標(biāo)準(zhǔn)誤，t 值和 p 值，標(biāo)準(zhǔn)化回歸系數(shù) Beta；Confidence

7、Intervals回歸系數(shù)的 95%區(qū)間。QIU YulanShanghai Jiao Tong University School of MedicineStatistics2、Residuals 復(fù)選框組：用于選擇輸出殘差信息。3、Mfit：模型擬合過(guò)程中進(jìn)入、的變量列表，一些擬合優(yōu)度的檢數(shù) R，決定系數(shù) R2 和調(diào)整的 R2，標(biāo)準(zhǔn)誤及方差分析表。驗(yàn)，復(fù)相4、R squared change：顯示模型擬合過(guò)程中 R2、F 值和 P 值的改變情況5、Descriptives：提供一些變量描述，給出一個(gè)自變量間的相關(guān)矩陣。6、Part and partial Correlations：顯示自變

8、量間的相關(guān)、部分相關(guān)和偏相數(shù)。效例數(shù)、均數(shù)、標(biāo)準(zhǔn)差等，還7、Collinearity diagnostics：給出一些用于共線性的統(tǒng)計(jì)量。QIU YulanShanghai Jiao Tong University School of Medicine【子框】1、Stepping Method Criteria 單選或 F 值來(lái)設(shè)置。：設(shè)置納入和排除標(biāo)準(zhǔn)，可按 P 值2、Include const3、Missing Values 單選quation：用于決定是否在模型中常數(shù)項(xiàng)。：用于選擇對(duì)值的處理方式。QIU YulanShanghai Jiao Tong University School

9、of MedicineOptions結(jié)果解釋：擬合過(guò)程中變量進(jìn)入/模型的情況：QIU YulanShanghai Jiao Tong University School of MedicineVariables Entered/Remov ebdMVariables EnteredVariables RemovedMethod1weighta.Entera. All requested variables entered.b. Dependent Variable: lung擬合模型的擬合優(yōu)度情況簡(jiǎn)報(bào)：QIU YulanShanghai Jiao Tong University School

10、of MedicineMSummaryMRR SquareAdjusted R SquareStd. Error of the Estimate1.741a.550.504.29385a. Predictors: (Constant), weight模型假設(shè)檢驗(yàn)結(jié)果：QIU YulanShanghai Jiao Tong University School of MedicineANOVAbMSum of SquaresdfMean SquareFSig.1RegressionResidual Total1.053.8631.917110111.053.08612.199.006aa. Pre

11、dictors: (Constant), weightb. Dependent Variable: lung回歸系數(shù)的檢驗(yàn)結(jié)果：QIU YulanShanghai Jiao Tong University School of MedicineCoefficientsaUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BBStd. ErrorBetaLower BoundUpper BoundM1(Constant)weight.003.059.832.017.741.0033

12、.493.997.006-1.851.0211.857.096a. Dependent Variable: lung例：QIU YulanShanghai Jiao Tong University School of MedicineQIU YulanShanghai Jiao Tong University School of Medicine結(jié)果：QIU YulanShanghai Jiao Tong University School of MedicineVariables Entered/Remov eadMVariables EnteredVariables RemovedMeth

13、od12體重指數(shù)瘦素.Stepwise (Criteri a: Probabili ty-of-F-to-ente r <= .050,Probabili ty-of-F-to-remo ve >= .100).Stepwise (Criteri a: Probabili ty-of-F-to-ente r <= .050,Probabili ty-of-F-to-remo ve >= .100).a. Dependent Variable: 脂聯(lián)素QIU YulanShanghai Jiao Tong University School of MedicineMSum

14、maryMRR SquareAdjusted R SquareStd. Error of the Estimate12.776a.841b.602.707.588.6855.872925.13104a. Predictors: (Constant), 體重指數(shù)b. Predictors: (Constant), 體重指數(shù), 瘦素QIU YulanShanghai Jiao Tong University School of MedicineANOVAcSum of SquaresdfMean SquareFSig.M1RegressionResidual Total1459.549965.75

15、22425.301128291459.54934.49142.317.000a2RegressionResidual Total1714.458710.8442425.30122729857.22926.32832.560.000ba. Predictors: (Constant), 體重指數(shù)b. Predictors: (Constant), 體重指數(shù), 瘦素c. Dependent Variable: 脂聯(lián)素QIU YulanShanghai Jiao Tong University School of Medicinea. Dependent Variable: 脂聯(lián)素Coefficie

16、ntsaMUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BCorrelationsBStd. ErrorBetaLower BoundUpper BoundZero-orderPartialPart1(Constant)體重指數(shù)76.802-2.3288.976.358-.7768.556-6.505.000.00058.415-3.06195.189-1.595-.776-.776-.7762(Constant) 體重指數(shù)瘦素53.481-1.087-.75310.848.507.242-.362-.5254.930-2.145-3.112.000.041.00431.223-2.127-1.24975.739-.047-.256-.776-.811-.382-.514-.223-.324c.Dependent Variable: 脂聯(lián)素QIU YulanShanghai Jiao Tong University School of MedicineExcluded VariablecsPartialCollinearity St