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南昌工程学院毕业设计(论文)理学系系（院）信息与计算科学专业论文题目多元回归模型及其在工业生产总值预测中的应用研究学生姓名班级学号指导教师-1-多元回归模型及其在工业生产总值预测中的应用研究Multipleregressionmodelanditsapplicationinindustrialproductionprediction总计论文26页表格7个插图2副-2-摘要经济指标预测是一项具有挑战性的研究工作。本文利用多元回归模型研究经济指标影响因素，并为资源优化配置提供一定参考意见。以中国各省制造业工业生产总值为研究对象，依据背景知识选取七个自变量：朔料制品、水泥、玻璃、原煤、生铁、粗钢、钢筋、盘条，建立多元线性回归模型。再通过观测获取n组观测数据，应用最小二乘法求出回归参数估计值。运用回归方程的显著性检验，回归系数的显著性检验，多重共线性检验，异方差检验等检验方法法删除不符合线性关系的自变量或得到更符合实际关系的多元线性模型。关键词：工业生产总值，多元回归模型，资源优化配置，经济预测。-3-AbstractEconomicindexpredictionisachallengingresearchwork.Inthispaper,usingmultivariateregressionmodeloffactorsinfluencingeconomicindex,andoptimalallocationofresourcestoprovideacertainreference.InChinamanufacturingindustrygrossindustrialproductionastheresearchobject,basedonthebackgroundknowledgeofselectedsevenvariables:Schaumburgmaterialproducts,cement,glass,coal,pigiron,crudesteel,rebar,wirerod,establishedamultiplelinearregressionmodel.ThroughobservationtoobtaintheNgroupsofobservationdata,theapplicationoftheleastsquaresmethodtogetregressionparameterestimation.Applicationofsignificancetestofregressionequationthesignificancetestofregressioncoefficients,themulticollinearityofinspection,testingforheteroscedasticitytestmethodtodeletenotconsistentwiththelinearrelationshipbetweenvariablesorgetmoreaccordwithrealrelationshipinthemultivariatelinearmodel.Keyword:Grossindustrialproduction；multipleregressionmodel；optimizetheallocationofresources；economicforecasting.-4-目录摘要.............................................................................................................错误!未定义书签。Abstract.........................................................................................................................错误!未定义书签。第一章引言............................................................................................................................................-5-1.1工业生产总值简介...........................................................................................................................-5-1.2回归分析思想...............................................................................................................................-6-第二章多元线性回归模型....................................................................................................................-7-第三章多元线性回归的参数估计........................................................................................................-8-3.1参数的最小二乘估计.......................................................................................................................-8-3.2最小二乘估计的性质...............................................................................................................-10-第四章模型的检验及修正..................................................................................................................-10-4.1回归方程的显著性.....................................................................................................................-11-4.2回归系数的显著性.....................................................................................................................-12-4.3多重共线性检验.......................................................................................................................-12-4.4异方差检验...............................................................................................................................-14-4.5异方差的修正方法......................................................................................................................-16-第五章回归拟合度..............................................................................................................................-17-5.1决定系数.....................................................................................................................................-17-5.2决定系数的性质和修正决定系数.............................................................................................-18-第六章工业生产总值预测模型分析................................................................................................-20-6.1SPSS简介..................................................................................................................................-20-6.2模型建立和数据搜集..................................................................................................................-20-6.3基于SPSS的回归分析实现........................................................................................................-22-6.4统计检验......................................................................................................................................-22-6.5异方差检验及修正......................................................................................................................-23-6.6模型意义.....................................................................................................................................-25-结论..........................................................................................................................................-27-参考文献.......................................................................................................