spss非线性回归分析

课程名称 实用统计软件 实验项目名称 非线性回归分析 实验成绩 指导老师（签名 ） 日期 2011-9-23 一实验目的1掌握非线性回归的基本原理和算法；2能够用SPSS软件应用非线性回归模型解决实际问题。二. 实验内容与要求 1根据数据 金属强度测试.sav利用曲线参数估计法分析金属强度（y）与温度（x）之间的关系。2实现书上 P189 中的研究问题。第一步要选中所有的模型，然后根据R-square 和拟合曲线标准选择模型！并且要预测到2010年的数据！三实验步骤1模型选择（标准：R-square 以及拟合曲线的比较）2所选择模型的拟合优度（R-square、拟合曲线）3所选择模型的回归方程（回归系数的估计值）4所选择模型的检验问题（模型方差分析表：模型显著性F检验、回归系数非零T检验）5保存关心的统计数据（预测值、残差值、预测值的置信区间）具体操作参见课件 非线性回归分析.PPT四. 实验结果（数据与图形）与分析1.Model Summary and Parameter EstimatesDependent Variable:强度EquationModel SummaryParameter EstimatesR SquareFdf1df2Sig.Constantb1b2b3Linear.67412.39116.013.719-.002Logarithmic.92573.71216.0002.518-.424Inverse.983346.05116.000-.09155.466Quadratic.94441.91025.0011.171-.0068.416E-6Cubic.993186.30234.0001.485-.0123.409E-5-3.144E-8Compound.992760.86116.0001.324.991Power.93281.77216.0002.136E3-1.833S.69313.53516.010-3.356200.730Growth.992760.86116.000.281-.009Exponential.992760.86116.0001.324-.009Logistic.992760.84016.000.7551.009The independent variable is 温度.图中看出Cubic，Compound，Growth，Exponential和Logistic较高，其中Cubic最高，所以选择三次函数拟合。观察得，图形更接近Cubic和Exponential两种曲线。Cubic函数在500处为0，有明显差异。ANOVASum of SquaresdfMean SquareFSig.Regression14.368114.368760.861.000Residual.1136.019Total14.4827The independent variable is 温度.CoefficientsUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta温度-.009.000-.996-27.584.000(Constant)1.324.12810.382.000The dependent variable is ln(强度).CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BCorrelationsBStd. ErrorBetaLower BoundUpper BoundZero-orderPartialPart1(Constant).719.1444.982.002.3661.072温度-.002.001-.821-3.520.013-.003.000-.821-.821-.821a. Dependent Variable: 强度0.366,1.072-0.003,02.Model Summary and Parameter EstimatesDependent Variable:社会消费品零售总额EquationModel SummaryParameter EstimatesR SquareFdf1df2Sig.Constantb1b2b3Linear.836137.490127.000-1.372E42.325E3Logarithmic.52730.083127.000-2.442E41.854E4Inverse.1846.104127.0202.764E4-4.756E4Quadratic.987953.866226.0006.756E3-1.639E3132.133Cubic.9951.816E3325.000230.765768.904-65.2004.385Compound.9955.654E3127.0001.368E31.152Power.856160.241127.000446.2581.322S.43120.448127.0009.905-4.068Growth.9955.654E3127.0007.221.142Exponential.9955.654E3127.0001.368E3.142Logistic.9967.339E3127.000.001.856Logistic，Cublic，Compound，Growth，Exponential拟合度较高。观察得，Cublic和Logistic曲线更接近观察值。Model Summary and Parameter EstimatesDependent Variable:社会消费品零售总额EquationModel SummaryParameter EstimatesR SquareFdf1df2Sig.Constantb1b2b3Cubic.9951.816E3325.000230.765768.904-65.2004.385CoefficientsUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBetaCase Sequence2324.553198.246.91411.726.000(Constant)-13724.6833404.981-4.031.000CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BBStd. ErrorBetaLower BoundUpper