毕业设计(论 文)
数理统计在经济和管理中的应用
院 别 专业名称 班级学号 学生姓名 指导教师
数学与统计学院 数学与应用数学
7110418 何 俊 李晓奇
2015年06月08日
东北大学秦皇岛分校毕业设计（论文） 第 I 页
数理统计在经济和管理中的应用
摘 要
步入21世纪，社会经济和管理水平飞速发展，在经济和管理领域问题的研究中，我们除了要学习些量化的研究方法，还要掌握定性与定量有机结合的研究技能，而数理统计这门学科正是为此而开设的。随着概率论的不断发展，对数理统计的研究逐渐发展成为新的一个数学分支，对数理统计的研究主要是从怎样有效地搜集和整理分析受到随机变量干扰的数据方面入手，进而对所考虑分析的问题作出合理的推断或预测，为作出某种决策提供可靠的意见和有力的支持。
目前，随着统计方法在各个领域中的广泛应用，数理统计这门学科已发展成为具有多个分支的大家族。随着社会经济的多元化、金融交易的多样化、国际市场间资本移动的迅猛增长、以及电子商务的出现，数理统计及其应用将会继续发展和扩大。
本文选取了数理统计中的两个极为重要的理论：假设检验理论和回归分析理论进行着重介绍，对其中的一些应用思想方法进行了剖析和解释，并以工厂的生产管理和国民经济的核算为例，介绍了这两种理论思想在其中的具体应用，并进行MATLAB和SPSS软件实现，为数理统计在经济和管理领域中应用提供了参考案例。
关键词：回归分析，假设检验，MATLAB，SPSS
东北大学秦皇岛分校毕业设计（论文） 第 II 页
The Application of Mathematical Statistics in the Economic and Management
Author: He Jun Tutor: Li Xiao-qi
Abstract
The 21st century, the social economic and management level rapidly developing, in the study of economics and management issues, we in addition to learning some quantitative research methods, but also grasp the organic combination of qualitative and quantitative research skills, and mathematical statistics and that is why the subject. With the continuous development of probability theory, mathematical statistics research has gradually developed into a new branch of mathematics, mathematical statistics research mainly from how to effectively collect and organize the analysis of the data of disturbance by random variables, and then to consider the analysis of the problem to make reasonable inference or forecast, the opinions of the to make some decisions to provide reliable and strong support.
Now, with the statistical method is widely used in various fields, mathematical statistics discipline has developed into a large family has multiple branches. With the diversification of social economy, the diversification of financial transactions, the rapid growth of capital movement among the international market, and the emergence of electronic commerce, mathematical statistics and its application will continue to develop and expand.
This paper selected two very important theory in the mathematical statistics: the theory of hypothesis testing and regression analysis theory focuses on some of these applications thinking were analyzed and interpreted, and the accounting of factory production management and the national economy as example, describes the specific application in which these two theories of thought, and the MATLAB and SPSS software, several statistics in the field of economics and management provide a reference case.
Key Words: Regression analysis, Hypothesis testing, SPSS, MATLAB
东北大学秦皇岛分校毕业设计（论文） 第 III 页
目 录
1 绪 论 .................................................................................................................................... 1
1.1 课题背景及意义 ......................................................................................................... 1 1.2 国内外研究现状 ......................................................................................................... 1 1.3 论文的内容 ................................................................................................................. 2 2 数理统计基础 ...................................................................................................................... 3
2.1 统计数据的整理与描述 ............................................................................................. 3
2.1.1 母体与子样 ........................................................................................................ 3 2.1.2 统计量 ................................................................................................................ 3 2.2 几种重要的概率分布 ................................................................................................. 4
2.2.1 正态分布 ............................................................................................................ 4 2.2.2 ?2分布 ............................................................................................................... 6 2.2.3 t分布 .................................................................................................................. 7 2.2.4 F分布 ................................................................................................................. 7 2.2.5 自由度 .................................................................................................................. 8 2.3 参数估计 ..................................................................................................................... 8
2.3.1 点估计 ................................................................................................................ 8 2.3.2 区间估计 ............................................................................................................ 9 2.3.3 两种参数估计方法 ............................................................................................ 9 2.3.4 估计量的评判标准 .......................................................................................... 10
3 假设检验理论 .................................................................................................................... 12
3.1 假设检验的基本原理和问题的提出 ....................................................................... 12 3.2 假设检验的步骤 ....................................................................................................... 12
3.2.1 提出原假设和备择假设 .................................................................................. 13 3.2.2 确定并计算适当的统计检验量 ...................................................................... 14 3.2.3 给定显著性水平 .............................................................................................. 15 3.2.4 做出统计决策并解释 ...................................................................................... 15 3.3 置信区间 ................................................................................................................... 16 4 回归分析理论 .................................................................................................................... 18
东北大学秦皇岛分校毕业设计（论文） 第 IV 页
4.1 什么是回归分析 ....................................................................................................... 18 4.2 回归模型 ................................................................................................................... 18
4.2.1 数学模型简述 .................................................................................................. 18 4.2.2 回归参数的最小二乘估计 .............................................................................. 19 4.3 回归方程的假设检验与自变量的选择 ................................................................... 19
4.3.1 回归方程的线性假设检验 .............................................................................. 19 4.3.2 自变量的选择 .................................................................................................. 20 4.4 基本回归诊断 ..................................................................................................... 20 4.4.1 残差诊断 .......................................................................................................... 21 4.4.2 共线性诊断 ...................................................................................................... 21
5 数理统计在经济和管理中的应用实例 ............................................................................ 22
5.1 假设检验在生产管理中的MATLAB实现 ............................................................. 22 5.2 回归分析模型在国民经济核算中的应用及SPSS求解 ........................................ 23 结 论 .................................................................................................................................. 29 致 谢 .................................................................................................................................. 30 参考文献 .................................................................................................................................. 31 附 录 .................................................................................................................................. 32