多重线性回归与相关spss

1、多重线性回归与相关上海交通大学医学院公共卫生学院QIU YulanShanghai Jiao Tong University School of MedicineRegression 菜单SPSS 的 Regression 菜单中的内容极为丰富，大致分为四大部分：QIU YulanShanghai Jiao Tong University School of Medicine²²Linear：线性回归，简单线性回归和多元线性回归。Curve Estimation 过程和 Nonlinear Regression 过非线性回归：程。²：它们以 Logistic 模型

2、为代表，包应变量为分类资料的回归括二分类（Binary Logistic）、无序多分类（Multinomial Logistic）和有序多分类（Ordinal Logistic）的 Logistic 过程以及 Probit（概率回归分析用于分析剂量-反应）过程。²其它回归过程线性回归假设被的各种情况而推出的一些“补Weight Estimation 过程、Two-Stage Least-Squares充”，过程和Optimal Scaling 过程，这些有其特定用途，不能随意使用。QIU YulanShanghai Jiao Tong University School of Med

3、icineLinear 过程主要用于拟合多元线性回归模型。引例：某地一年级 12名女大学生体重与肺活量数据如下，见数据文件corr.sav，请据此计算肺活量对体重的直线回归方程。424246464650505052525858体重肺活量 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操作步骤如下：AnalyzeRegressionLinearDependent 框：lungIndependent 框：weightF 应变

4、量为 lungF 自变量为 weight界面说明：【主框】1、Dependent 框：用于选入回归分析的应变量，只能选入一个。2、Block：由 Previous和 Next按两个按成，用于将下面Independent 框中选入的自变量分组。由于多元回归分析中自变量的入选方式有前进、后退、逐步等，如果对不同的自变量选入的不同，则用该按将自变量分组选入即可。3、Independent 框：用于选入回归分析的自变量，它们进入模型的使用 Block 按钮进行不同的定义。可QIU YulanShanghai Jiao Tong University School of MedicineOK4、Meth

5、od下拉列表：用于选择对自变量的选入，该选项对当前Independent 框中的所有变量均有效。Enter：强行进入法，候选自变量全部纳入模型，不做任何筛选，默认选项。²QIU YulanShanghai Jiao Tong University School of Medicine²Stepwise：逐步法，根据在 Options 框中设定的纳入和排除标准进行变量筛选。Remove：强制剔除法，只出不进。²²²Backward：法，只出不进。Forward：向前法，只进不出。5、Selection Variable 框：进入一个筛选变量，并利

6、用右侧的 Rules立一个选择条件，这样只有满足该条件的义仅在当前回归过程有效。才会进入回归分析，该定6、Case Labels 框：选择一个变量，它的取值将作为每条的。典ID 号的变量。最小二乘法的回归分析。型的情况是使用7、WLS Weight：进行QIU YulanShanghai Jiao Tong University School of Medicine【子框】用于选择所需要的描述统计量。1、Regression Coefficients 复选框组：定义回归系数的输出情况。Estimates回归系数 B 及其标准误，t 值和 p 值，标准化回归系数 Beta；Confidence

7、Intervals回归系数的 95%区间。QIU YulanShanghai Jiao Tong University School of MedicineStatistics2、Residuals 复选框组：用于选择输出残差信息。3、Mfit：模型拟合过程中进入、的变量列表，一些拟合优度的检数 R，决定系数 R2 和调整的 R2，标准误及方差分析表。验，复相4、R squared change：显示模型拟合过程中 R2、F 值和 P 值的改变情况5、Descriptives：提供一些变量描述，给出一个自变量间的相关矩阵。6、Part and partial Correlations：显示自变

8、量间的相关、部分相关和偏相数。效例数、均数、标准差等，还7、Collinearity diagnostics：给出一些用于共线性的统计量。QIU YulanShanghai Jiao Tong University School of Medicine【子框】1、Stepping Method Criteria 单选或 F 值来设置。：设置纳入和排除标准，可按 P 值2、Include const3、Missing Values 单选quation：用于决定是否在模型中常数项。：用于选择对值的处理方式。QIU YulanShanghai Jiao Tong University School

9、of MedicineOptions结果解释：拟合过程中变量进入/模型的情况：QIU YulanShanghai Jiao Tong University School of MedicineVariables Entered/Remov ebdMVariables EnteredVariables RemovedMethod1weighta.Entera. All requested variables entered.b. Dependent Variable: lung拟合模型的拟合优度情况简报：QIU YulanShanghai Jiao Tong University School

10、of MedicineMSummaryMRR SquareAdjusted R SquareStd. Error of the Estimate1.741a.550.504.29385a. Predictors: (Constant), weight模型假设检验结果：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回归系数的检验结果：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结果：QIU YulanShanghai Jiao Tong University School of MedicineVariables Entered/Remov eadMVariables EnteredVariables RemovedMeth

13、od12体重指数瘦素.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: 脂联素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), 体重指数b. Predictors: (Constant), 体重指数, 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), 体重指数b. Predictors: (Constant), 体重指数, 瘦素c. Dependent Variable: 脂联素QIU YulanShanghai Jiao Tong University School of Medicinea. Dependent Variable: 脂联素Coefficie

16、ntsaMUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BCorrelationsBStd. ErrorBetaLower BoundUpper BoundZero-orderPartialPart1(Constant)体重指数76.802-2.3288.976.358-.7768.556-6.505.000.00058.415-3.06195.189-1.595-.776-.776-.7762(Constant) 体重指数瘦素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: 脂联素QIU YulanShanghai Jiao Tong University School of MedicineExcluded VariablecsPartialCollinearity St