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河北工程大学本科毕业设计（论文）1摘要许多现象往往不是简单的与某一因素有关而是要受多个因素的影响，此时就需要用两个或两个以上的影响因素作为自变量来解释因变量的变化，这就是多元回归亦称多重回归。当多个自变量与因变量之间是线性关系时，所进行的回归分析就是多元性回归。本文的研究主要从四个部分来进行。第一章从基础内容和研究对象着手，对主要研究内容进行了简单的阐述。第二章对多元线性回归的基础进行了详细分析。第三章介绍了中国经济的现状。最后通过多元线性回归模型对我国工业生产总值进行了分析。总的来说，本文在2007年全国各省市主要工业产品的产量与工业总产值的具体数据下，选用塑料、水泥、钢筋、平板玻璃、粗钢、盘条以及原煤等工业产品的产量作为研究对象，建立多元线性回归模型，并对模型做出参数估计.在此基础上对模型做出一定的解释，对于预测工业总产值具有一定的理论指导和现实意义。关键词：多元线性回归模型工业生产总值假设检验预测河北工程大学本科毕业设计（论文）2AbstractManyphenomenaareoftennotsimplyassociatedwithanumberoffactorsbutwithvarieties.Atthispointweneedtousetwoormorefactorsasindependentvariablestoexplainchangesinthedependentvariable.Thisisalsoknownasmultipleregression.Whenmorethanoneindependentvariableandthedependentvariablearelinearrelationship,theregressionanalysisiscarriedoutbydiversityregression.Themainresearchworkofthisthesisisdividedintofourparts.Inthefirstchapter,thethesisproceedfromthebasiccontentandobjectofstudyandelaboratemaincontentsimply.Inthesecondchapter,multiplelinearregressionmodelisanalyzeddetail.Inthethirdchapter,thethesisintroducesstatusquoofchina.Andatlast,grossindustrialproductionisanalyzedbymultiplelinearregressionmodelinthisarticle.Overall,thisarticleusethespecificdataoftheoutputofmajorindustrialproductsandindustrialoutputinnationwideprovincesin2007,andselecttheoutputofplastics,cement,steel,plateglass,crudesteel,wirerodandrawcoalasstudyobjecttoestablishmultiplelinearregressionmodel,andthenmakethemodelparameterestimation.Basedonthis，wemakesomeexplanationstothemodel.Alloftheseareofmomentouscurrentsignificanceandfar-reachinghistoricalsignificancetotheforecastofindustrialproduction.KeyWords:MultiplelinearregressionmodelGrossindustrialproductionHypotheticaltestPrediction河北工程大学本科毕业设计（论文）3目录摘要.............................................................................................................................................1Abstract.......................................................................................................................................21绪论........................................................................................................................................42多元线性回归分析基础........................................................................................................52.1多元线性回归定义......................................................................................................52.2多元线性回归模型........................................................................................................62.2.1模型的建立及矩阵表示.....................................................................................62.2.2模型的假设........................................................................................................72.3多元线性回归参数估计..............................................................................................72.3.1最小二乘估计和正规方程组............................................................................72.3.2最小二乘估计的矩阵形式................................................................................82.4回归拟合度评价和决定系数......................................................................................92.4.1离差分解和决定系数........................................................................................92.4.2决定系数的性质及修正可决系数..................................................................102.5统计检验....................................................................................................................112.5.1回归参数的显著性检验（t检验）.................................................................112.5.2回归方程的显著性检验（F检验）................................................................122.5.3多重共线性检验..............................................................................................122.5.4异方差检验.......................................................................................................133中国经济现状......................................................................................................................153.1中国经济现状.............................................................................................................153.2工业生产总值的概述................................................................................................154工业生产总值的多因素模型分析......................................................................................154.1建立多因素分析模型.................................................................................................164.2数据收集.....................................................................................................................164.3统计检验....................................................................................................................194.4计量经济学检验及模型修正....................................................................................204.4.1异方差检验......................................................................................................214.4.2自相关检验......................................................................................................215结论.........................................