随机权函数非线性回归模型的异方差统计分析

在回归分析中，随机误差是否存在方差齐性是理论与实际工作者都十分关心的问题，方差齐性假设并不总是正确的，在线性和非线性回归中关于异方差的诊断问题已有许多讨论（[1],[2],[4],[5]）。本文在韦博成（1995）讨论了加权非线性回归模型的基础上，用随机系数的方法，讨论随机权函数非线性回归模型中的异方差检验问题，得到了方差齐性检验的似然比统计量和score统计量，同时，当模型存在异方差时，本文给出了估计方差的一种方法。     

随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

大学英语CET-4教学效果评价

对参加华中农业大学2002年CET-4考试的学生随机抽样,获取了具有代表性的某些班级学生CET-4考试成绩,运用协方差分析方法,得到了对指导学生CET-4考试的教师的教学效果的合理评价.为教学管理部门提供分析问题的方法和理论依据.     

基于Adaptive-Lasso的本科成绩统计分析

本文主要研究了合肥工业大学数学学院数学专业学生的本科成绩状况,应用多元线性统计方法,探讨了前期所有课程成绩对后期成绩的影响.首先对前期课程进行主成分分析,并采用逐步回归方法建立了后期成绩与主成分之间的回归模型.其次,采用Adaptive-Lasso方法建立后期成绩与前期课程成绩间的Adaptive-Lasso回归模型.最后,对以上模型进行对比分析.研究表明,基于Adaptive-Lasso方法的主成分回归模型能很好地拟合后期成绩,并对后期成绩情况给出合理的解释.     

具有线性趋势回归信度模型的自相关性的score检验

回归信度模型在保险研究中具有重要的作用。本文讨论了具有线性趋势回归信度模型自相关性的score检验问题。首先推导出模型中自相关存在性检验的score检验统计量,然后利用Monte-Carlo方法模拟了此种检验统计量的功效。最后利用文中所得到的检验方法对旅客意外身体伤害保险数据进行了实例分析。     

电子监控探测人物身高的分析

依据重庆市公安局刑警大队提供的监控数据,分析监控器摄象时影响身高的因素,利用多元回归的原理建立了三个预测身高的回归模型,并对其作出了优劣评价,最终确定出犯罪嫌疑人实际身高与其在照片上的像高、电子监控器距地面的高度、人与监控器的垂直和偏离距离四个因素的最优回归模型.该最优模型的可决系数R2=0.9931,预测身高与实际身高有97.89%的误差点在±0.02m范围内,73.09%在±0.01m范围内.并对最优模型中的预测身高与实际身高进行配对样本的t检验,两者间无显著性差异.     

引入跳跃和结构转换的中国股市已实现波动率预测研究:基于拓展的HAR-RV模型

结合日内跳跃识别方法和马尔可夫机制转换模型,对已实现波动率异质自回归模型(HARRV)进行拓展,以刻画连续波动、跳跃波动以及不同方向跳跃波动对未来波动影响的差异和波动的结构转换特征,并运用该模型对上证综指和深证成指高频数据进行实证分析。研究结果表明:在短期内,连续波动和跳跃波动对未来波动影响具有显著的差异;负向跳跃和正向跳跃往往同时发生且幅度相当,但负向跳跃波动对未来波动的影响更大;在不同波动状态下,历史波动对未来波动的影响存在较为明显的差异。MCS检验结果显示,区分跳跃波动方向和考虑波动的结构转换特征可以显著提升模型的样本内和样本外的预测能力。     

旅游动机对大学生租车出行选择行为的影响

为研究大学生群体租车意愿以及出行方式选择行为的影响.本研究采用自主设计调查问卷,以宁夏银川市大学生为研究对象,获取大学生旅游出行特征数据.首先对问卷中23项旅游动机项进行因子分析提取公因子;然后对因子得分进行聚类分析将大学生群体划分为4类;再者进行相关性分析,筛选与大学生出行选择行为密切相关的影响因素;最后基于MNL模型构建涵盖旅游动机的大学生旅游租车出行方式选择行为度量模型.研究结果表明,旅游动机对大学生旅游租车意愿有显著影响,且不同出行方式间影响程度存在差异.该模型预测精度较高,对大学生群体旅游产品的研发具有指导意义,为进一步研究游客出行决策行为提供了理论依据.     

基于重复测量数据的Poisson回归模型的偏大离差的Score检验

Poisson回归模型广泛应用于分析计数型数据 ,Dean&Lawless(1989)和Dean(1992 )讨论了非重复测量得到的计数型数据的偏大离差存在性的检验问题 .本文分别利用随机系数模型和对数非线性模型讨论了基于重复测量得到的计数型数据的偏大离差的检验问题 ,得到了检验的score统计量 .     

基于多元线性回归模型的东北地区需水量分析

多元线性回归模型在社会、经济、技术以及众多自然科学研究领域中已被广泛使用,某个地区需水量应与该地区多种因素有关,故选取东北地区的GDP、水库蓄水总量、人均可支配收入、城市绿地面积和工业用水量等5个因素,借助MATLAB软件阐明了多元线性回归模型在东北地区需水量分析中的应用.并通过皮尔森相关性检验、拟合优度检验、F检验、t检验和残差分析的方法对模型进行优化,得到了准确可靠的多元线性回归模型,此模型具有拟合程度高、简易、直观等优势,为多元线性回归模型在需水量分析中的应用提供了有力参考.     

基于改进的BP网络对CET-4累计通过率时间序列的预测

时间序列并非总呈自相关性.与[4]不同,对本文中的CET-4累计通过率时间序列建立线性及二阶自回归模型,仿真计算失效.改进的BP网络,适用所有的一维时间序列.本文采用二步预测法,与其它采用BP网络对时间序列预测不同的是,本文不仅预测下一年的时间序列值,还将整个预测模型仿真出来,画出三维图形,从而为教务政策的制订提供直观易看、合理、客观的依据.     

基于演化博弈的大学生诚信考试研究

为研究一些要素对大学生诚信考试问题中主体行为演化的影响,借助演化博弈理论这一前沿研究工具,建立了监考教师与考生交互过程的演化模型,研究了各种情形下监考教师和学生行为交互系统均衡点的存在性和稳定性,并用数值仿真展示了决策参数的不同取值和初始条件的改变对演化结果的影响.研究发现:这些影响二者行为的要素作用的大小会影响均衡点的个数及其稳定性,均衡点的稳定性会在源点、汇点和鞍点之间变化,分析表明大学生从不诚信考试中获得的收益过高,对教师不认真监考监督、处罚不力,都可能使系统的演化向不良状态进化,并最终"锁定"于这一状态,并讨论了系统向良好状态演化和跳出不良"锁定"的条件.分析对大学生考试制度的创新和设计指明了方向.     

我国高等学校生师数动态关系的统计分析

对我国高等学校1978年-2009年在校大学生、在岗教师、生师比值等时序数据进行单位根检验、结构突变的单位根检验、协整检验等,得出我国高等院校在校大学生数与在岗教师数、生师数比值是结构突变的趋势平稳序列,在校大学生数与在岗教师数之间无协整关系.在岗教师数相对于在校大学生人数的增长滞后3-4年.     

历届全国大学生数学建模竞赛专科组赛题的模糊综合评价

建立了在针对每一个待评方案的决策者数量不相等的情况下的多层次多属性模糊综合群决策模型,在对历届全国大学生数学建模竞赛专科组24个赛题进行重点调查的基础上,应用该模型对这些赛题进行了综合评价,评价结果验证了模型的有效性和可行性.     

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours,motivation, and metacognition

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students’ self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students’ homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students’ mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).     

Assessment of numeracy in sports and exercise science students at an Australian university

The effect of high school study of mathematics on numeracy performance of sports and exercise science (SES) students is not clear. To investigate this further, we tested the numeracy skills of 401 students enrolled in a Bachelor of Health Sciences degree in SES using a multiple-choice survey consisting of four background questions and 39 numeracy test questions. Background questions (5-point scale) focused on highest level of mathematics studied at high school, self-perception of mathematics proficiency, perceived importance of mathematics to SES and likelihood of seeking help with mathematics. Numeracy questions focused on rational number, ratios and rates, basic algebra and graph interpretation. Numeracy performance was based on answers to these questions (1 mark each) and represented by the total score (maximum = 39). Students from first (n = 212), second (n = 78) and third (n = 111) years of the SES degree completed the test. The distribution of numeracy test scores for the entire cohort was negatively skewed with a median (IQR) score of 27(11). We observed statistically significant associations between test scores and the highest level of mathematics studied (P < 0.05), being lowest in students who studied Year 10 Mathematics (20 (9)), intermediate in students who studied Year 12 General Mathematics (26 (8)) and highest in two groups of students who studied higher-level Year 12 Mathematics (31 (9), 31 (6)). There were statistically significant associations between test scores and level of self-perception of mathematics proficiency and also likelihood of seeking help with mathematics (P < 0.05) but not with perceived importance of mathematics to SES. These findings reveal that the level of mathematics studied in high school is a critical factor determining the level of numeracy performance in SES students.     

Collaborative Workshops and Student Academic Performance in Introductory College Mathematics Courses: A Study of a Treisman Model Math Excel Program

High failure rates in introductory college mathematics courses, particularly among underrepresented groups of students, have been of concern for many years. One approach to the problem experiencing some success has been Treisman's Emerging Scholars workshop model. The model involves supplemental workshops in which students solve problems in collaborative learning groups. This study reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses (college algebra, precalculus, differential calculus, and integral calculus) at Oregon State University over five academic terms. Regression analyses revealed a significant effect on achievement (.671 grade points on a 4‐point scale) favoring Math Excel students. Even after adjusting for prior mathematics achievement using linear regression with SAT‐M as predictor, Math Excel groups' grade averages were over half a grade point better than predicted (significant at the .001 level). This study provides supporting evidence that programs like Math Excel can help students in making a successful transition to college mathematics study.     

Active learning: a case study of student engagement in college Calculus

This paper presents a case study for strategic engagement of students in a Calculus course in order to produce increased learning in the classroom. Since it has been shown that active learning can promote greater comprehension for students in science, technology, engineering, and mathematics (STEM) courses, the researcher utilized many types of active learning techniques to enhance classroom instruction. The key components implemented are presented as a model of enhanced learning through developed classroom engagement. This course redesign model entitled, Strategic Engagement for Increased Learning (SEIL), has the potential to (1) contribute to the body of knowledge on ways to improve mathematics skills for college students, (2) identify successful teaching strategies and technologies that will promote the retention of STEM students, (3) increase the success rate of students taking Calculus, and (4) help produce more STEM graduates needed for the STEM workforce in the United States of America.     

Students’ ways of understanding a proof

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.