主成份分析因子分析毕业论文终稿

主成份分析因子分析毕业论文终稿

学科分类号110 黑龙江科技大学

本科学生毕业论文

题目主成分与因子分析对黑龙江

省城市经济发展水平的评价

The principal components and factor analysis

of urban economic development level

evaluation of heilongjiang province

姓名

学号

院（系）理学院

专业、年级数学与应用数学

指导教师

2014年6月12日

摘要

经济是指一个国家国民经济的总称。我们要提高某地方人民的生活水平，要更好更快地发展某个地区，就必须充分了解这个地区现有的经济发展状况。因此，现有的经济发展状况研究对将来的发展有着非常重要的指导意义。

主成分分析也称主分量分析，就是设法将原来指标重新组合成一组新的互相无关的几个综合指标来代替原来指标。因子分析是主成分分析的推广和发展，它也是将具有错综复杂关系的变量综合为数量较少的几个因子，以再现原始变量与因子的相互关系，同时根据不同因子还可以对变量进行分类。主成分分析与因子分析都是多元分析中处理降维的一种统计方法。本文通过学习与查阅相关资料找到黑龙江省12个地级市的10个具有代表性指标，运用spss统计分析软件对这些指标进行主成分分析和因子分析得到特征值、方差贡献率及公共因子等相关数据。并利用这些数据对12个市经济水平划分等级。

关键词主成分分析因子分析经济spss统计分析软件

I

Abstract

Economy refers to the floorboard of the national economy of a country. We will improve the level of a local people's life, to somewhere better and faster development, we must fully understand the current situation of economic development. Therefore, the existing research on the development of future economic development has a very important guiding significance.

Principal component analysis (also called principal component analysis, is to try the original index combined into a new set of several comprehensive index instead of the original index has nothing to do with each other, at the same time, according to the actual need to recommend a few less comprehensive response as much as possible the original information of indicators. Is a generalization of the principal component analysis and factor analysis, it is also will have the intricate relationship between variables comprehensive to a small number of several factors, and to recreate the relationship of the original variables and factor, at the same time according to different factors can also categorize variables,. Principal component analysis and factor analysis is a multivariate analysis of a statistical method of dealing with the dimension reduction. In this article, through learning and access to relevant data found nine representative indexes of 12 cities in heilongjiang province, using the SPSS statistical analysis software to the indicators of principal component analysis and factor analysis of the characteristic value, the variance contribution rate and public factor and related data. And using the data of 13 cities economic grade level.

Key words Principal component analysis Factor analysis Economic SPSS statistical analysis softwar

II

目录

摘要.......................................................................................................................... I Abstract..................................................................................................................... II

第1章绪论 (1)

1.1 选题的背景和提出 (1)

(1)

(2)

1.2 选题的意义和目的 (3)

(3)

(3)

1.3 主成分分析和因子分析的发展及应用 (4)

(4)

(4)

1.4 本文主要研究内容 (5)

第2章主成分与因子分析 (6)

2.1 主成分分析的内容 (6)

(6)

(6)

(8)

2.2 主成分分析的求解方法和数学模型 (8)

2.3 主成分分析的基本步骤 (11)

2.4 因子分析的内容 (13)

(13)

(13)

III