摘 要

伴随着社会的发展，人们生活水平不断提高，交通运输也越来越成为人们生活中不可缺少的一部分。长江水运是我国至关重要的运输渠道，它每年的航运带来巨大的经济效益，所以它的预测模型为更好的发挥长江航运的优势有着极其重要的意义。

在论文里建立了预测模型并根据模型预测未来5年的载货量，同时研究一些会对长江航运造成影响的因素等。本人选取了2003—2014年以来，长江航运载货量、、居民消费水平、城镇居民人均可支配收入、长江流域11个省的人口总数作为本次研究对象。先是利用非线性回归和分段回归模型对长江载货量进行预测并对两种模型进行比较，接着是利用主成分分析对影响长江载货量的因素进行分析，最后是建立模型，并与回归模型进行比较。

研究最终的结果表明长江载货量显现着逐年增长的趋势，而且受到经济因素以及长江流域的人口总数的影响。

关键词：非线性回归；分段回归；主成分分析；模型

Abstract

With the development of society, people's living standard continuous improvement , transportation has increasingly become an indispensable part of life.Yangtze River is of vital transport channels, shipping annually bring huge economic benefits, so its predictive model to better play the advantages of the Yangtze River shipping has an extremely important significance.

In the thesis, the prediction model and predict the next five years based on the model of cargo capacity, it also studied a number of factors will affect the Yangtze River shipping et al. This paper selected the Yangtze River shipping cargo capacity, the level of consumption of urban residents per capita disposable income of the total population of the Yangtze River Valley in 11 provinces from 2003 to 2014 as study. First, it uses nonlinear regression and segmented regression model to predict the amount of cargo on the Yangtze River and compare models Which is better. Second followed by principal component analysis of factors affecting the Yangtze River cargo capacity for analysis. Finally building model and with the regression model are compared to regression models.

The final study results show that the Yangtze River cargo volume increased year by year show the trend and by economic factors and the population as well as the Yangtze River Region.

Key words: Nonlinear regression; Piecewise regression Principal; Componen

Analysis; Model.

目 录

摘要.................................................................................................................................................I

Abstract.........................................................................................................................................II

第1章 绪论...................................................................................................................................1

1.1 研究目的及意义..............................................................................................................1

1.2 背景分析..........................................................................................................................1

1.3 国内外现状综述及评价........................................................................................... ......2

1.3.1 国外现状.. .............................................................................................................2

1.3.2 国内现状 ...............................................................................................................3

第2章 回归建模以及结果分析 ...................................................................................................5

2.1 建模准备 ..........................................................................................................................5

2.1.1 数据获取 ...............................................................................................................5

2.1.2 显著性检验...........................................................................................................5

2.1.3 最小二乘估计.......................................................................................................6

2.2 一元非线性回归理论基础与模型以及实例分析........................................................6

2.2.1 一元非线性回归模型...........................................................................................7

2.2.2 一元非线性回归实例分析...................................................................................8

2.3 分段回归理论基础与模型以及实例分析......................................................................8

2.3.1 分段回归模型.......................................................................................................9

2.3.2 分段回归实例分析...............................................................................................9

2.4 回归模型的对比............................................................................................................10

第3章 主成分分析模型以及结果分析 .....................................................................................12

3.1 建模准备 ........................................................................................................................12

3.2 主成分分析的相关问题 ................................................................................................12

3.2.1 由协方差.矩阵或由相关矩阵出发求解主成分 ................................................12

3.2.2 主成分的获取 .....................................................................................................12

3.3 主成分分析的基本理论及模型....................................................................................13

3.4 主成分分析实例分析....................................................................................................14

第4章 模型及分析........................................................................................................19

4.1 建模准备 ........................................................................................................................19

4.2 差分方式的选择 ............................................................................................................20