6 Regression tutorial solution

合集下载

SPSS菜单命令详解剖析

purchase：选
Compare effectiveness of campaigns(control Package Test)：比较活动效果〔把握包装检验〕
Apply scores from a model File：应用来自模型文件的得分
1.6.9 Graphs菜单
Chart Builder 图形生成器
Graphboard Template Chooser 图形模板选择
1Bar
条形图
3-D Bar
三维条形图
Line
线图
Area
面积图
Pie
饼图
High-Low 凹凸图
Box Plot
箱图
Error Bar
误差条图
Population Pyramid 人口金字塔图
Scatter/Dot 散点图
Histogram 直方图
状态栏显示工具条栏显示菜单编辑器字体显示/隐蔽格线显示/隐蔽变量值标签标记错误数据查看自变量变量定义窗口和数据编辑
窗口转换
1.6.5 Data菜单
Define Variable Properties
定义变量属性
Set Measurement Level for Unknown 设置未知测量级别
SPSS帮助主题用户指南统计辅导学习统计训练指导语句命令参考
研发中心关于SPSS版本信息算法 SPSS官方主页版本更新检查
1.7 SPSS中英文界面的转换
当首次安装软件时，SPSS界面为英文显示，此时可以承受如下方法将其转换为中文界面。
1. 选择菜单栏中的【Edit(编辑)】菜单中的【Option(选项)】命令。
数据汇总正交设计复制数据集分割文件选择观测量观ompute Variable Count Values within Cases Shift Values Recode into Same Variables Recode into Different Variables Automatic Recode Visual Binning Optimal Binning

【荐】一款可以替代spss的免费开源软件——JASP

【荐】一款可以替代spss的免费开源软件——JASPJASP 介绍JASP 开发团队的主要目标是使统计工具的使用者通过简单易用的工具获取尽量多的统计结果。

为了实现此目标，跨平台且界面友好的统计软件JASP 软件应运而生。

JASP 是一款开源且免费的统计软件，并且提供充分的社区支持。

JASP 本着免费 - 友好 - 弹性（Free - Friendly - Flexible）的原则，为使用者提供易用的统计分析体验。

软件本身提供所有常用的统计方法，同时这些方法支持频率论和贝叶斯理论两种理论下的计算。

事实上，JASP 的重要功能即在于使用者可以轻易使用贝叶斯方法进行统计计算。

对于高级的统计方法（如多层线性回归、结构方程模型、网络模型、Meta 分析等）也能提供简单易用的交互方式，使得用户可以能够轻易使用这些方法完成自己的研究。

JASP 软件也易于输出结果，它支持在 Word 中拷贝 APA 格式的表格，软件中的输出结果也可以根据输入选项动态调整。

用户可以直观地在软件中调整输出格式，并将结果放到自己的论文当中。

对于科研人员来说，也不必顾虑使用 JASP 是否会影响文章的审核与出版。

JASP 的底层基于R 进行开发，R 本身作为常用的统计分析工具在学术界受到广泛的认同，而JASP 项目本身也得到了包括European Research Council 等项目基金的赞助以及University of Amsterdam 等高校的支持。

故 JASP 可靠性较高，可以作为科研工作当中的数据分析工具使用。

JASP 教学视频中文化项目由于 JASP 项目的目标是开发一款免费且易于使用的统计软件，而这个目标与 PsychoR 团队“用数据科学拓展心理学的未来”的愿景相一致，因此 PsychoR 团队希望通过一些工作，推广 JASP 软件在国内的使用。

在Open Science Club （/）的胡传鹏博士的引荐下，我们与 JASP TEAM 取得了联系，将官方的一系列教学视频进行了中文化，并将在接下来的一段时间内逐步放出。

SPSS基本界面

第一章SPSS基本界面第一节SPSS for windows的特点SPSS（statistics package for social science）for windows是最初的SPSS／pc+ for dos发展到SPSS 6.0、7.0、8.0、9.0、10.0 、11.0for windows，从7.0版本开始，均基于windows95系统。

从而具有以下特点：一、使用简单，便于学习。

二、完全的windows风格界面，输入数据文件以后，只需用鼠标结合简单的数据输入便可进行操作。

三、统计功能强大，使用方便。

四、可以与其他很多软件进行数据传输。

五、具有丰富的图表表达功能。

六、便捷的数据输入。

第二节SPSS for windows的运行环境一、SPSS for windows的安装。

二、SPSS for windows启动与退出：（一）启动方法（二）退出方法三、主环境的介绍：（一）打开SPSS后出现提示对话框,各选项的含义1、Run the tutorial运行图解帮助。

2、Type in data输入数据。

3、Run an existing query。

运行已经存在的数据库文件图1－1选择对话框4、Open an existing data source打开已经存在的SPSS数据文件，可以在列表中双击“More Files…”然后在打开的对话框中进行选择，打开更多的数据文件。

5、Create new query using Database Wizard用Database Wizard应用程序创建新的数据库文件。

6、Open another type of file7、Don′t show this dialog in the future复选框，选择该项，以后打开SPSS不再显示本对话框。

（二）数据编辑器：1、Data view：数据编辑窗口。

2、Variable view：定义变量窗口。

机器学习与数据挖掘笔试面试题

What is a decision tree? What are some business reasons you might want to use a decision tree model? How do you build a decision tree model? What impurity measures do you know? Describe some of the different splitting rules used by different decision tree algorithms. Is a big brushy tree always good? How will you compare aegression? Which is more suitable under different circumstances? What is pruning and why is it important? Ensemble models: To answer questions on ensemble models here is a :
Why do we combine multiple trees? What is Random Forest? Why would you prefer it to SVM? Logistic regression: Link to Logistic regression Here's a nice tutorial What is logistic regression? How do we train a logistic regression model? How do we interpret its coefficients? Support Vector Machines A tutorial on SVM can be found and What is the maximal margin classifier? How this margin can be achieved and why is it beneficial? How do we train SVM? What about hard SVM and soft SVM? What is a kernel? Explain the Kernel trick Which kernels do you know? How to choose a kernel? Neural Networks Here's a link to on Coursera What is an Artificial Neural Network? How to train an ANN? What is back propagation? How does a neural network with three layers (one input layer, one inner layer and one output layer) compare to a logistic regression? What is deep learning? What is CNN (Convolution Neural Network) or RNN (Recurrent Neural Network)? Other models: What other models do you know? How can we use Naive Bayes classifier for categorical features? What if some features are numerical? Tradeoffs between different types of classification models. How to choose the best one? Compare logistic regression with decision trees and neural networks. and What is Regularization? Which problem does Regularization try to solve? Ans. used to address the overfitting problem, it penalizes your loss function by adding a multiple of an L1 (LASSO) or an L2 (Ridge) norm of your weights vector w (it is the vector of the learned parameters in your linear regression). What does it mean (practically) for a design matrix to be "ill-conditioned"? When might you want to use ridge regression instead of traditional linear regression? What is the difference between the L1 and L2 regularization? Why (geometrically) does LASSO produce solutions with zero-valued coefficients (as opposed to ridge)? and What is the purpose of dimensionality reduction and why do we need it? Are dimensionality reduction techniques supervised or not? Are all of them are (un)supervised? What ways of reducing dimensionality do you know? Is feature selection a dimensionality reduction technique? What is the difference between feature selection and feature extraction? Is it beneficial to perform dimensionality reduction before fitting an SVM? Why or why not? and Why do you need to use cluster analysis? Give examples of some cluster analysis methods? Differentiate between partitioning method and hierarchical methods. Explain K-Means and its objective? How do you select K for K-Means?

Matlab的第三方工具箱大全

Matlab的第三方工具箱大全(按住CTRL点击连接就可以到达每个工具箱的主页面来下载了)Matlab Toolboxes∙ADCPtools - acoustic doppler current profiler data processing∙AFDesign - designing analog and digital filters∙AIRES - automatic integration of reusable embedded software∙Air-Sea - air-sea flux estimates in oceanography∙Animation - developing scientific animations∙ARfit - estimation of parameters and eigenmodes of multivariate autoregressive methods∙ARMASA - power spectrum estimation∙AR-Toolkit - computer vision tracking∙Auditory - auditory models∙b4m - interval arithmetic∙Bayes Net - inference and learning for directed graphical models∙Binaural Modeling - calculating binaural cross-correlograms of sound∙Bode Step - design of control systems with maximized feedback∙Bootstrap - for resampling, hypothesis testing and confidence interval estimation ∙BrainStorm - MEG and EEG data visualization and processing∙BSTEX - equation viewer∙CALFEM - interactive program for teaching the finite element method∙Calibr - for calibrating CCD cameras∙Camera Calibration∙Captain - non-stationary time series analysis and forecasting∙CHMMBOX - for coupled hidden Markov modeling using max imum likelihood EM ∙Classification - supervised and unsupervised classification algorithms∙CLOSID∙Cluster - for analysis of Gaussian mixture models for data set clustering∙Clustering - cluster analysis∙ClusterPack - cluster analysis∙COLEA - speech analysis∙CompEcon - solving problems in economics and finance∙Complex - for estimating temporal and spatial signal complexities∙Computational Statistics∙Coral - seismic waveform analysis∙DACE - kriging approximations to computer models∙DAIHM - data assimilation in hydrological and hydrodynamic models∙Data Visualization∙DBT - radar array processing∙DDE-BIFTOOL - bifurcation analysis of delay differential equations∙Denoise - for removing noise from signals∙DiffMan - solv ing differential equations on manifolds∙Dimensional Analysis -∙DIPimage - scientific image processing∙Direct - Laplace transform inversion via the direct integration method∙DirectSD - analysis and design of computer controlled systems with process-oriented models∙DMsuite - differentiation matrix suite∙DMTTEQ - design and test time domain equalizer design methods∙DrawFilt - drawing digital and analog filters∙DSFWAV - spline interpolation with Dean wave solutions∙DWT - discrete wavelet transforms∙EasyKrig∙Econometrics∙EEGLAB∙EigTool - graphical tool for nonsymmetric eigenproblems∙EMSC - separating light scattering and absorbance by extended multiplicative signal correction∙Engineering Vibration∙FastICA - fixed-point algorithm for ICA and projection pursuit∙FDC - flight dynamics and control∙FDtools - fractional delay filter design∙FlexICA - for independent components analysis∙FMBPC - fuzzy model-based predictive control∙ForWaRD - Fourier-wavelet regularized deconvolution∙FracLab - fractal analysis for signal processing∙FSBOX - stepwise forward and backward selection of features using linear regression∙GABLE - geometric algebra tutorial∙GAOT - genetic algorithm optimization∙Garch - estimating and diagnosing heteroskedasticity in time series models∙GCE Data - managing, analyzing and displaying data and metadata stored using the GCE data structure specification∙GCSV - growing cell structure visualization∙GEMANOVA - fitting multilinear ANOVA models∙Genetic Algorithm∙Geodetic - geodetic calculations∙GHSOM - growing hierarchical self-organizing map∙glmlab - general linear models∙GPIB - wrapper for GPIB library from National Instrument∙GTM - generative topographic mapping, a model for density modeling and data visualization∙GVF - gradient vector flow for finding 3-D object boundaries∙HFRadarmap - converts HF radar data from radial current vectors to total vectors ∙HFRC - importing, processing and manipulating HF radar data∙Hilbert - Hilbert transform by the rational eigenfunction expansion method∙HMM - hidden Markov models∙HMMBOX - for hidden Markov modeling using maximum likelihood EM∙HUTear - auditory modeling∙ICALAB - signal and image processing using ICA and higher order statistics∙Imputation - analysis of incomplete datasets∙IPEM - perception based musical analysisJMatLink - Matlab Java classesKalman - Bayesian Kalman filterKalman Filter - filtering, smoothing and parameter estimation (using EM) for linear dynamical systemsKALMTOOL - state estimation of nonlinear systemsKautz - Kautz filter designKrigingLDestimate - estimation of scaling exponentsLDPC - low density parity check codesLISQ - wavelet lifting scheme on quincunx gridsLKER - Laguerre kernel estimation toolLMAM-OLMAM - Levenberg Marquardt with Adaptive Momentum algorithm for training feedforward neural networksLow-Field NMR - for exponential fitting, phase correction of quadrature data and slicing LPSVM - Newton method for LP support vector machine for machine learning problems LSDPTOOL - robust control system design using the loop shaping design procedure LS-SVMlabLSVM - Lagrangian support vector machine for machine learning problemsLyngby - functional neuroimagingMARBOX - for multivariate autogressive modeling and cross-spectral estimation MatArray - analysis of microarray dataMatrix Computation- constructing test matrices, computing matrix factorizations, visualizing matrices, and direct search optimizationMCAT - Monte Carlo analysisMDP - Markov decision processesMESHPART - graph and mesh partioning methodsMILES - maximum likelihood fitting using ordinary least squares algorithmsMIMO - multidimensional code synthesisMissing - functions for handling missing data valuesM_Map - geographic mapping toolsMODCONS - multi-objective control system designMOEA - multi-objective evolutionary algorithmsMS - estimation of multiscaling exponentsMultiblock - analysis and regression on several data blocks simultaneously Multiscale Shape AnalysisMusic Analysis - feature extraction from raw audio signals for content-based music retrievalMWM - multifractal wavelet modelNetCDFNetlab - neural network algorithmsNiDAQ - data acquisition using the NiDAQ libraryNEDM - nonlinear economic dynamic modelsNMM - numerical methods in Matlab textNNCTRL - design and simulation of control systems based on neural networks NNSYSID - neural net based identification of nonlinear dynamic systemsNSVM - newton support vector machine for solv ing machine learning problems NURBS - non-uniform rational B-splinesN-way - analysis of multiway data with multilinear modelsOpenFEM - finite element developmentPCNN - pulse coupled neural networksPeruna - signal processing and analysisPhiVis- probabilistic hierarchical interactive visualization, i.e. functions for visual analysis of multivariate continuous dataPlanar Manipulator - simulation of n-DOF planar manipulatorsPRT ools - pattern recognitionpsignifit - testing hyptheses about psychometric functionsPSVM - proximal support vector machine for solving machine learning problems Psychophysics - vision researchPyrTools - multi-scale image processingRBF - radial basis function neural networksRBN - simulation of synchronous and asynchronous random boolean networks ReBEL - sigma-point Kalman filtersRegression - basic multivariate data analysis and regressionRegularization ToolsRegularization Tools XPRestore ToolsRobot - robotics functions, e.g. kinematics, dynamics and trajectory generation Robust Calibration - robust calibration in statsRRMT - rainfall-runoff modellingSAM - structure and motionSchwarz-Christoffel - computation of conformal maps to polygonally bounded regions SDH - smoothed data histogramSeaGrid - orthogonal grid makerSEA-MAT - oceanographic analysisSLS - sparse least squaresSolvOpt - solver for local optimization problemsSOM - self-organizing mapSOSTOOLS - solving sums of squares (SOS) optimization problemsSpatial and Geometric AnalysisSpatial RegressionSpatial StatisticsSpectral MethodsSPM - statistical parametric mappingSSVM - smooth support vector machine for solving machine learning problems STATBAG - for linear regression, feature selection, generation of data, and significance testingStatBox - statistical routinesStatistical Pattern Recognition - pattern recognition methodsStixbox - statisticsSVM - implements support vector machinesSVM ClassifierSymbolic Robot DynamicsTEMPLAR - wavelet-based template learning and pattern classificationTextClust - model-based document clusteringTextureSynth - analyzing and synthesizing visual texturesTfMin - continous 3-D minimum time orbit transfer around EarthTime-Frequency - analyzing non-stationary signals using time-frequency distributions Tree-Ring - tasks in tree-ring analysisTSA - uni- and multivariate, stationary and non-stationary time series analysisTSTOOL - nonlinear time series analysisT_Tide - harmonic analysis of tidesUTVtools - computing and modifying rank-revealing URV and UTV decompositions Uvi_Wave - wavelet analysisvarimax - orthogonal rotation of EOFsVBHMM - variation Bayesian hidden Markov modelsVBMFA - variational Bayesian mixtures of factor analyzersVMT- VRML Molecule Toolbox, for animating results from molecular dynamics experimentsVOICEBOXVRMLplot - generates interactive VRML 2.0 graphs and animationsVSVtools - computing and modifying symmetric rank-revealing decompositions WAFO - wave analysis for fatique and oceanographyWarpTB - frequency-warped signal processingWAVEKIT - wavelet analysisWaveLab - wavelet analysisWeeks - Laplace transform inversion via the Weeks methodWetCDF - NetCDF interfaceWHMT - wavelet-domain hidden Markov tree modelsWInHD - Wavelet-based inverse halftoning via deconvolutionWSCT - weighted sequences clustering toolkitXMLTree - XML parserYAADA - analyze single particle mass spectrum dataZMAP - quantitative seismicity analysis。

SPSS经典的教程总结

基本用途文件操作文件编辑视图编辑数据操作数据转换统计分析方法直销分析图形编辑实用程序附加程序窗口控制
帮助
1.6.2 File菜单
• New
新建文件
• Open
打开文件
• Open Data base 打开数据库
• Read Text Data 读取文本数据
• Close
关闭文件
•
• •
Recode into Different Vari ables
Automatic Recode
Visual Binning
自动赋值可视离散化最优离散化
• Optimal Binning
• Prepare Data for Modeli 准备建模数据
ng
• Rank Cases
求观测量的秩
第1章统计软件SPSS基础
1.1 SPSS的产生及发展
SPSS是软件英文名称的首字母缩写，全称为： Statistical Package for the Social Sciences，即 “社会科学统计软件包”。它是目前世界上流行的三大统计分析软件之一（SAS、SPSS及SYSTAT）。在我国，SPSS以其强大的统计分析功能、方便的用户操作界面、灵活的表格式报告及其精美的图形展现，受到了社会各界统计分析人员的喜爱。
• 选择菜单栏中的【File(文件)】→【Open(打开)】 →【Syntax(语法)】命令，打开一个保存的语句文件。
1.5.4 脚本编辑窗口
选择菜单栏中的【File(文件)】→【New(新建)】→ 【Script(脚本)】命令，新建一个SPSS的脚本编辑窗口，如下图所示。
选择菜单栏中的【File(文件)】→【Open(打开)】 →【Script(脚本)】命令，打开一个保存的脚本语言文件。

Origin6.0绘图分析软件—操作方法与实例分析第三章

Origin6.0绘图分析软件 Origin6.0绘图分析软件
—操作方法与实例分析
第三章数据管理
数列变换数列或工作表的排序频率计数规格化数据选择数据范围绘图屏蔽掉不必要的数据点线性拟合
数列变换
1.导入数据（例1） 2.在Set Column Value对话框内编辑数学运算式，变换数列
Error：拟合误差 R：相关系数 SD：标准差 N：参与拟合数据点个数 P：相关系数为0的概率
N
SD =
∑[ y
i =1
i
− ( A + Bxi )]2 N −2
相关系数是衡量两个变量之间相关相关密切程度的统计指标。
(2)数据点未被屏蔽时，线性拟合
屏蔽单数据点取消屏蔽改变屏蔽点颜色
Mean：平均值 SD：标准差
Size：本列数据个数
SD =
( X i − X )2 ∑
i =1
N
N −1
1 X= N
N
∑X
i =1
i
Back！
规格化数据
功能：把数列（或其中的一段）的各数值都除以一个因子。功能
命令：选中数列； Analysis|Normalize 或右键菜单Normalize命令
D = ∑[ f (xi , a1,...,as ) − yi )2 为最小，这种方法称为最小二乘法。
i=1 n
(1)数据点被屏蔽时，线性拟合
FLUOR Linear Fit of TUTORIAL2_FLUOR
0.60 0.55 0.50 12.1 12.0 11.9 11.8 11.7 11.6 11.5 0.25 11.4 0.20 11.3 20 22 24 26 28 30 32 34 36 38

Andrew Ng机器学习课程目录(带翻译)

I. Introduction (Week 1)一、引言（第1周）•Welcome (7 min)•欢迎（7分钟）•What is Machine Learning? (7 min)•机器学习是什么？（7分钟）•Supervised Learning (12 min)•监督学习（12分钟）•Unsupervised Learning (14 min)•无监督学习（14分钟）II. Linear Regression with One Variable (Week 1)二、一元线性回归（第1周）•Model Representation (8 min)•模型表示（8分钟）•Cost Function (8 min)•成本函数（8分钟）•Cost Function - Intuition I (11 min)•成本函数的直观理解I（11分钟）•Cost Function - Intuition II (9 min)•成本函数的直观理解II（9分钟）•Gradient Descent (11 min)•梯度下降（11分钟）•Gradient Descent Intuition (12 min)•梯度下降的直观理解（12分钟）•Gradient Descent For Linear Regression (10 min) •梯度下降的线性回归（10分钟）•What's Next (6 min)•接下来的内容（6分钟）III. Linear Algebra Review (Week 1, Optional)三、线性代数回顾（第1周，可选）•Matrices and Vectors (9 min)•矩阵和向量（9分钟）•Addition and Scalar Multiplication (7 min)•加法和标量乘法（7分钟）•Matrix Vector Multiplication (14 min)•矩阵向量乘法（14分钟）•Matrix MatrixMultiplication (11 min)•矩阵乘法（11分钟）•Matrix Multiplication Properties (9 min)•矩阵乘法的性质（9分钟）•Inverse and Transpose (11 min)•逆、转置（11分钟）IV. Linear Regression with Multiple Variables (Week 2)四、多变量线性回归（第2周）•Multiple Features (8 min)•多特征（8分钟）•Gradient Descent for Multiple Variables (5 min)•梯度下降的多变量（5分钟）•Gradient Descent in Practice I - Feature Scaling (9 min) •梯度下降法实践1-特征尺度（9分钟）•Gradient Descent in Practice II - Learning Rate (9 min)•梯度下降法实践2-学习速率（9分钟）•Features and Polynomial Regression (8 min)•特征和多项式回归（8分钟）•Normal Equation (16 min)•正规方程（16分钟）•Normal Equation Noninvertibility (Optional) (6 min)•正规方程不可逆性（可选）（6分钟）V. Octave Tutorial (Week 2)五、Octave教程（第2周）•Basic Operations (14 min)•基本操作（14分钟）•Moving Data Around (16 min)•移动数据（16分钟）•Computing on Data (13 min)•计算数据（13分钟）•Plotting Data (10 min)•绘图数据（10分钟）•Control Statements: for, while, if statements (13 min)•控制语句：for，while，if语句（13分钟）•Vectorization (14 min)•矢量化（14分钟）•Working on and Submitting Programming Exercises (4 min) •工作和提交的编程练习（4分钟）VI. Logistic Regression (Week 3)六、Logistic回归（第3周）•Classification (8 min)•分类（8分钟）•Hypothesis Representation (7 min)•假说表示（7分钟）•Decision Boundary (15 min)•决策边界（15分钟）•Cost Function (11 min)•成本函数（11分钟）•Simplified Cost Function and Gradient Descent (10 min) •简化的成本函数和梯度下降（10分钟）•Advanced Optimization (14 min)•Multiclass Classification: One-vs-all (6 min)•多类分类：一个对所有（6分钟）VII. Regularization (Week 3)七、正则化（第3周）•The Problem of Overfitting (10 min)•过拟合的问题（10分钟）•Cost Function (10 min)•成本函数（10分钟）•Regularized Linear Regression (11 min)•正则线性回归（11分钟）•Regularized Logistic Regression (9 min)•正则化的逻辑回归模型（9分钟）VIII. Neural Networks: Representation (Week 4)第八、神经网络：表述（第4周）•Non-linear Hypotheses (10 min)•非线性假设（10分钟）•Neurons and the Brain (8 min)•神经元和大脑（8分钟）•Model Representation I (12 min)•模型表示1（12分钟）•Model Representation II (12 min)•模型表示2（12分钟）•Examples and Intuitions I (7 min)•例子和直观理解1（7分钟）•Examples and Intuitions II (10 min)•例子和直观理解II（10分钟）•Multiclass Classification (4 min)•多类分类（4分钟）IX. Neural Networks: Learning (Week 5)九、神经网络的学习（第5周）•Cost Function (7 min)•成本函数（7分钟）•Backpropagation Algorithm (12 min)•反向传播算法（12分钟）•Backpropagation Intuition (13 min)•反向传播算法直观理解（13分钟）•Implementation Note: Unrolling Parameters (8 min) •实现注意：展开参数（8分钟）•Gradient Checking (12 min)•梯度检测（12分钟）•Random Initialization (7 min)•随机初始化（7分钟）•Putting It Together (14 min)•Autonomous Driving (7 min)•自主驾驶（7分钟）X. Advice for Applying Machine Learning (Week 6)十、应用机器学习的建议（第6周）•Deciding What to Try Next (6 min)•决定下一步做什么（6分钟）•Evaluating a Hypothesis (8 min)•评估一个假设（8分钟）•Model Selection and Train/Validation/Test Sets (12 min)•模型的选择和培训/测试集（12分钟）•Diagnosing Bias vs. Variance (8 min)•诊断偏差和方差（8分钟）•Regularization and Bias/Variance (11 min)•正则化和偏差/方差（11分钟）•Learning Curves (12 min)•学习曲线（12分钟）•Deciding What to Do Next Revisited (7 min)•决定下一步做什么（7分钟）XI. Machine Learning System Design (Week 6)十一、机器学习系统的设计（第6周）•Prioritizing What to Work On (10 min)•优先要做什么（10分钟）•Error Analysis (13 min)•误差分析（13分钟）•Error Metrics for Skewed Classes (12 min)•误差度量的偏斜类别（12分钟）•Trading Off Precision and Recall (14 min)•交易精度和召回（14分钟）•Data For Machine Learning (11 min)•数据的机器学习（11分钟）XII. Support Vector Machines (Week 7)十二、支持向量机（第7周）•Optimization Objective (15 min)•优化目标（15分钟）•Large Margin Intuition (11 min)•大边界的直观理解（11分钟）•Mathematics Behind Large Margin Classification (Optional) (20 min) •数学背后的大边界分类（可选）（20分钟）•Kernels I (16 min)核函数1（16分钟）•Kernels II (16 min)•核函数2（16分钟）•Using An SVM (21 min)•使用支持向量机（21分钟）XIII. Clustering (Week 8)十三、聚类（第8周）•Unsupervised Learning: Introduction (3 min)•无监督的学习：简介（3分钟）•K-Means Algorithm (13 min)•k-均值算法（13分钟）•Optimization Objective (7 min)•优化目标（7分钟）•Random Initialization (8 min)•随机初始化（8分钟）•Choosing the Number of Clusters (8 min)•选择簇的数量（8分钟）XIV. Dimensionality Reduction (Week 8)十四、降维（8周）•Motivation I: Data Compression (10 min)•动机1：数据压缩（10分钟）•Motivation II: Visualization (6 min)•动机2：可视化（6分钟）•Principal Component Analysis Problem Formulation (9 min)•主成分分析问题（9分钟）•Principal Component Analysis Algorithm (15 min)•主成分分析算法（15分钟）•Choosing the Number of Principal Components (11 min)•从主成分选择数（11分钟）•Reconstruction from Compressed Representation (4 min)•重建的压缩表示（4分钟）•Advice for Applying PCA (13 min)•主成分分析法的应用建议（13分钟）XV. Anomaly Detection (Week 9)十五、异常检测（第9周）•Problem Motivation (8 min)•问题的动机（8分钟）•Gaussian Distribution (10 min)•高斯分布（10分钟）•Algorithm (12 min)•算法（12分钟）•Developing and Evaluating an Anomaly Detection System (13 min) •开发和评价一个异常检测系统（13分钟）•Anomaly Detection vs. Supervised Learning (8 min)•异常检测与监督学习（8分钟）•Choosing What Features to Use (12 min)•选择使用什么特征（12分钟）•Multivariate Gaussian Distribution (Optional) (14 min)•多元高斯分布（可选）（14分钟）•Anomaly Detection using the Multivariate Gaussian Distribution (Optional) (14 min) 使用多变量的高斯分布进行异常检测（可选）（14分钟）XVI. Recommender Systems (Week 9)十六、推荐系统（第9周）•Problem Formulation (8 min)•问题（8分钟）•Content Based Recommendations (15 min)•基于内容的推荐（15分钟）•Collaborative Filtering (10 min)•协同过滤（10分钟）•Collaborative Filtering Algorithm (9 min)•协同过滤算法（9分钟）•Vectorization: Low Rank Matrix Factorization (8 min)•矢量化：低秩矩阵分解（8分钟）•Implementational Detail: Mean Normalization (9 min)•推行工作上的细节：均值归一化（9分钟）XVII. Large Scale Machine Learning (Week 10)十七、大规模机器学习（第10周）•Learning With Large Datasets (6 min)大型数据集的学习•（6分钟）•Stochastic Gradient Descent (13 min)•随机梯度下降（13分钟）•Mini-Batch Gradient Descent (6 min)•迷你批处理梯度下降（6分钟）•Stochastic Gradient Descent Convergence (12 min)•随机梯度下降法收敛（12分钟）•Online Learning (13 min)•在线学习（13分钟）•Map Reduce and Data Parallelism (14 min)•减少图和数据并行（14分钟）XVIII. Application Example: Photo OCR十八、应用实例：照片的OCR•Problem Description and Pipeline (7 min)•问题描述和传播途径（7分钟）•Sliding Windows (15 min)•滑动窗口（15分钟）•Getting Lots of Data and Artificial Data (16 min)•获取数据和大量人造数据（16分钟）•Ceiling Analysis: What Part of the Pipeline to Work on Next (14 min)•上限分析：哪部分管道的接下去做（14分钟）XIX. Conclusion十九、结论•Summary and Thank You (5 min)•总结和致谢（5分钟）。

A Tutorial on Support Vector Regression

as at as possible. In other words, we do not care about errors as long as they
are less than ", but will not accept any deviation larger than this. This may be
Introduction 1
Abstract
In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for regression and function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modi cations and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization and capacity control from a SV point of view.
1 Introduction
The purpose of this paper is twofold. It should serve as a self-contained introduction to Support Vector regression for readers new to this rapidly developing eld of research. On the other hand, it attempts to give an overview of recent developments in the eld.

对Cpk和非正态,misclassification rate的辨识

对Cpk,Non-normal, control chart Misclassification的再认识作者：Hetairae1.Most data is non-normal if you have enough samples, and metrology is very preciseand accurate. Its like most p-values, easily overwhelmed by lots of data.如果你的样品数越多，大多的数据是非正态，由于对正态的衡量是非常精确的，就象P值，很容易被否决2. And if it’s based on SPC chart data, watch out for sampling plans as automaticgaging has given us lots of autocorrelated data which show up as run rule violations and can lead to SPC overcontrol.如果基于SPC control chart,从自动化测量的数据有很多呈现出自相关，用SPC control chart去分析，违反受控。

3.And remember for capability studies use the RAW data not the SPC Stats data....inmy opinion...since spec limits are about individual parts usually. But differentindustries have very different metrology and "critical" variables that are monitored.Talk to industry-specific experts before you waste time with fitting distributions to get a Cpk or Ppk index. Many industries avoid spec limits and use TARGETS and Cpm measures of Taguchi-style capability. Stay on target. Continuously tighten variation.在用原始数据而非SPC受控数据计算Cpk时，通常spc 控制线是经对单个数据，而不同的行业都有不同的衡量度量和关键变量；在你拟合分布以获取Cpk、Ppk之间同行业专家交谈。

计算机专业单词(完整版)

计算机专业单词(完整版)zoom v.变焦距zip 邮递区号zone 区zap v.迅速离去，击溃throughout prep.贯穿，整，遍through prep.通过，直通three a.三(的)throw 废弃thread 线程whichever a.无论哪个withdraw 撤回without prep.没有，在..以外think v.考虑，以为，判断will 将wick 油心width 宽度within prep.在..以内thesaurus 词库week 周whenever ad.随时when 当well n.好，良好wait 等待weight 权way n.路线，途径，状态whereas conj.面，其实，既然ware n.仪器，商品work 工作third a.第三，三分之一Word n.著名文字编辑软件watch n.监视，观测whatever pron.无论什么watt 瓦want v.需要，应该，缺少warn vt.警告，警戒，预告view 显示方式visibility 可见性volt 伏verification 验证variety n.变化，种类，品种validity 有效性vocabulary 词汇表verb 动词volatility 变更率void 空vice n.缺点，毛病，错误violation 违反validation 验证twist 扭曲twice n.两次，两倍于tool 工具two n.二，两，双TRUE a.真，实，选中trunk 总线treat v.处理，加工tree 树trend 趋势trace 跟踪train 字列tray 托盘traversal 遍历traditional a.传统的，惯例的try 尝试trap 自陷transmitter 发送器transmit 发送transmission 传输transducer 变换器transformation 变换transceiver 收发器transparent 透明transportable 可传送的transport 传送transparency 透明性transliterate 直译translate 翻译translation 翻译transcribe 转录transfer 传送transformer 变压器transform 变换transaction 事务transition 转移translator 转换器track 磁道touch 接触topology 拓扑学tube 管子tutorial 指导的this 此tip 倾斜tilt 倾斜tick 滴答teach v.教，讲授team n.队，小组choose v.挑选，选择，选定chunk n.厚块，大部分chip 芯片check 检查change 更改chained 链接chain 链choice 选项child 儿子节点chart 图表charge 费用char 字符tone n.音调，音色，色调though conj.虽然，尽管test 测试then 然后tell n.讲，说，教，计算text 文本technology n.工艺，技术，制造学tape 磁带take v.取，拿thereafter ad.此后，据此toward prep.朝(着..方向) tachometer 转速计together ad.一同，共同，相互today n.今天turn v.圈，匝termination 端接terminology 术语term 项top 顶部talk v.通话，谈话tornado n.旋风，龙卷风type 类型times n.次数time 时间Tile 阶式task 任务tag 标记tab 跳位、标签switch 开关swap 交换swab 棉签string 字符串stream 流stroke 笔划strong a.强的strike v.敲，击stride 跨越stuff n.装入stub 抽头still a.静 v.平静step 步骤state 状态stage 阶段stay v.停止，停留statistics 统计学statistical 统计的stability 稳定性stop 停止store 存储style 形式start 开始star n.星形，星号stand v.处于(状态)，保持stamp n.图章stack 堆栈such a.这样的，如此sun n.太阳，日sum 和数substitution 替代subheading 次标题subscriber 用户submit 提交submission 提交subdirectory 子目录spool 假脱机spring 弹簧spread v.展开，传播sprite 子画面split 分割spill v.漏出，溢出，漏失specific 特定speech n.说话，言语，语音speed 速度specification 规范spell v.拼写space 空间spare 备用specifically ad.特别地，逐一地spontaneous 自发的smooth v.平滑的smudge 污迹small 小slow a.慢速的slave 从属slot 槽slice 片slide 滑动导轨slash 斜线square n.方形的screw 螺钉screen 屏幕scroll 滚动scratch 擦除scrap 报废skulk 躲藏skew 偏斜skip 跳跃skill n.技巧scheme n.方案，计划，图scope 作用域scale 比例尺Scout 检索程序scan 扫描situation n.情况，状况，势态sit v.位于，安装since prep.自从...以来synchronization 同步化syntactical 语法的syndetic 连接的simulation 模拟simultaneous 同时的six n.六(个)(的)significant a.有效的，有意义的significance 有效serialize 串行化severe 严重severity 严重性synergic 协作的symmetric 对称selector 选择器select 选择selection 选择sequentially ad.顺序地security 安全性secure 安全的cedilla 变音符seek 查找see 查看so pron.如此,这样set 设置suspension n.暂停，中止，挂起suspend 暂停sensitivity 灵敏度sense 检测send 发送cell 单元successive a.逐次的，相继的successful 成功的successor 后续succession n.逐次性，连续性save 保存same a.同样的，相同的sale n.销售，销路safe a.安全的，可靠的say v.说，显示，假定segmentation 分段substantially ad.实质上，本质上substantial a.实质的，真正的subscribe 签署surrounding a.周围的，环绕的suppressed vt.抑制，取消suppress 抑制suppression 抑制supplier 供应商supply vt.电源，供给supposed a.假定的，推测的suppose v.假定，推测support 支持semantic 语义solution n.解，解法，解答sufficient 足够的suggestion n.暗示，提醒suggest vt.建议，提议，暗示subordinate 附属serve 服务certification 确证search 搜索survey 勘测soft a.软的sort 分类source 源sound n.声音，音响size 大小site 位置sign 正负号scientific 科学的side 一边citation 引用root 根route 路径room n.房间，空间rule n.规则，法则，尺routine 例行程序run 运行responsibility 责任restricted a.受限制的，受约束的restrict vt.约束，限制restriction 限制restore 复原respectively ad.分别地respect n.遵守，关系response 响应respond v.回答，响应ring 环reliability 可靠性real 实rear 背面regeneration 重新生成redefine vt.重新规定(定义) rid 资源标识符result 结果resume 继续resistance 阻抗residual 残留的reserve vt.保留，预定，预约resolve 分辨reside vi.驻留review 复查revoke 取消reversal 反向reverse 反向revise 修订retrieval 检索retrieve 检索retrace 重新跟踪retainer 定位器retain vt.保持，维持returned a.退回的return 返回reciprocal 倒数recipient 收件人receiving 接收receiver 接收者received a.被接收的，公认的receive 接收receipt 收据resource 资源replacement n.替换，置换，更新replaceable 可置换的replace 置换reply 回答repeating n.重复，循环repeatedly ad.重复地repeated a.重复的repeater 中继器repeat 重复repetitive a.重复的repair 修理repository 仓库report 报告removal 除去remove 除去remote 远程remember v.存储，记忆，记住remainder 余数remain vi.剩下，留下，仍然remark 评语release 释放related a.相关的relationship 关系relation 关系request 请求requirement 需求require 需求recovery 恢复recoverable a.可恢复的，可回收的recover 恢复reclaim 收回recursive a.递归的，循环的recall vt.撤消，复活，检索recorder 记录器regression 回归regardless a.不注意的，不考虑的regard vt.考虑，注意，关系refresh 刷新reflect 反映reflection 反射referral 工作分派refer 参考reject 拒绝redundant a.冗余的redundancy 冗余reduction n.减化，还原，减少reduce 减少reactivate v.使恢复活动reach v.范围，达到范围reproduce 复制relocation 浮动reel 卷reinstate vt.复原，恢复rearrange v.重新整理，重新排序redirect 重定向redirection 重定向read 读rework 重做rewind 回绕restructure vt.调整，重新组织reset 复位receptacle 插座resend 再送replan 重新计划repaint vt.重画rename 重新命名relocate 浮动reload vt.再装入reusable 可再用的reflow v.回流，逆流reentrant 可重入的reenter v.重新进入redo 重做redraw vt.再拉redisplay 再显示reservation 保留resolution 分辨率revolutionize vt.变革，彻底改革roll 卷动row 行rest n.剩余，休息representation 表示法representative a.典型的，表示的represent v.表示，表现，代表replication 复制rent n.裂缝requisition 请求reconciliation 对帐recommend vt.推荐，建议rectangular a.矩形的rate 速率range 范围rail 导轨regulation 规则registration 登记round 舍入right 右write 写入wrap 环绕rank 排序RAM 随机存取存储器rack 机架update 更新up 向上unavailable a.不能利用的unattended 无人照管unattached 不连接的undefined a.未定义的understanding n.了解的，聪明的understand v.懂，明白(了)，理解underscore 下划线underline 下划线underlying a.基础的，根本的unwanted a.不需要的，多余的unrecognized a.未被认出的unnecessary a.不必要的，多余的unmarked a.没有标记的unlink 解链unload 卸出unfortunately ad.不幸，遗憾地unbind 切断push 按pool 池proof 证明print 打印preserve vt.保存，维持prevent v.防止，预防precision 精度precedence 优先级prefer vt.更喜欢，宁愿predict vt.预测，预言prerequisite 先决条件preemption 抢先preceding a.先的，以前的precede v.先于presentation 呈示press 按preparation 准备productivity 生产力provide 提供protect vt.保护protection 保护procedural a.程序上的procedure 过程proceed 继续proprietary a.专有的promote 促进professional 专业人员project 项目projection 投影production 生产produce v.生产，制造prompt 提示price n.价格priority 优先级pragmatics 语用学pulse 脉冲puck 球publication 出版物plug 插头plane 位面plot 绘图plant 工厂plan 计划pitch 音调pin 针pick 检料peer 同级postpone 延迟poll 轮询Paste 粘贴选项pace 调步pane 屏面position 位置particularly ad.特别，格外，尤其particular a.特定的，特别的potentially ad.可能地，大概地percentage 百分率peripheral 外围的parentheses 括号parenthesis n.括弧，圆括号parameter 参数performance 性能perform 实行personnel 人员permutation 排列purge 清除pertain vi.附属，属于，关于permit 允许persistence 持续性permission 许可权possibility n.可能性pop 弹出polymorphism 多形性point 点pause 暂停portability 可移植性port 端口pipe 管道path 路径part 部件parse 语法分析pass v.传送，传递，遍(数) participant 参与者partition 分区patch 修补password 口令pack 压缩pagination 页调整pad 填充overwrite 覆盖override 覆盖null 空的notation 记数法numerical 数字的numeration 记数numeric 数字的new 新的negotiation 协商negate vt.否定,求反,“非”mnemonic 助记的note 注意node 节点nest 嵌套noise 噪声knob 握柄navigation n.导航move 移动must 必须month 月份multiplication 乘法multiplicand 被乘数multiplicity 复合度motif n.主题，要点，特色miscellaneous 多种的mistake 错误mismatch n.失配，不匹配mix 混合剂means n.方法，手段mean 平均mode 方式materialization 具体化manipulator 操纵元maintainable 可维护的memorandum 便笺maintain 维护main 主mail 邮件make vt.制造，形成materialize 具体化material 资料manipulate 操作machine 机器majority 多数merge 合并modulation 调制modification 修改more 尚有mouse 鼠标mount 装载mile 英里microcomputer 微型计算机microprocessor 微处理器millimeter 毫米migrate 移植migration 移植mask 掩码marked a.有记号的mach n.马赫(速度单位) mark 标记math n.数学match 匹配map 映象manufacturing 制造manufacturer 制造商manufacture vt.制造(业)，工业mantissa 尾数macroinstruction 宏指令loop 循环lux 勒克司locator 定位器locale 场所list 列表link 连接limitation 限制leaves 叶leave 脱离leaf 叶localization 本地化load 装入locate 找出location 位置left 向左laboratory 实验室lost 丢失long 长型lock 加锁logged a.记录的，浸透的log 记录launch 启动light 指示灯line 行librarian 库管理器lag 延迟quit 退出quote 报价quotation 引语quartet 四位字节quark 夸克Coulomb 库仑crew 组员cryptographic 密码cryptography 密码术creation n.创造，创作creator 建立者create 建立craze n.开裂cross 跨crop v.切，剪切criteria 标准criterion n.标准，判据，准则crank 曲柄crash 崩溃cut 剪下coalesce 结合coordinator 协调程序clip 裁剪click 单击clear 清除closed a.关闭的，闭迹Close 关闭clock 时钟clause 子句class 类clerk 职员clamp 夹queue 队列kit 组件kill 杀死（进程）keep 保持key 键coax 同轴coefficient 系数code 代码coordinate 坐标consideration n.考虑，研究，讨论configuration 配置convenient a.方便的，便利的convenience n.方便，便利conventional a.常规的，习惯的convention 约定converted 转换的convert 转换conversion 转换controller 控制器controlled a.受控制的，受操纵的control 控制contractor 承包方continuously ad.连续不断地continued 接上页continue 继续contiguous 相连的contention 争用contextual 上下文的container 容器contain 包含constraint 约束consult v.咨询，顾问consume v.消耗，使用consistent 一致的consistency 一致性consist vi.符合，包括considered a.考虑过的，被尊重的consider 考虑console 控制台consent 插座consecutive 连续的consolidate 合并concurrent 同时的concordance 重要语汇索引conflicting 冲突confuse vt.使混乱，干扰configure 配置confirm 确认conform vi.遵从，符合conjunction 与congestion 拥塞conductor 导线conditional 条件的condition 条件condense 压缩compressor 压缩器consumable 消费品compress 压缩comprise vt.包括，由...组成composing 组成completely ad.十分，完全，彻底complete 完成completion 完成complexity 复杂程度computer 计算机compute 计算compose 组成component 部件compare 比较compiler 编译器compile 编译compatible 兼容的comparison 比较combine 组合case n.情况，场合capability 能力cage 盒子corrupt v.有毛病的corona 电晕correctly 正确correct 正确correction n.校正，修正capacity 能力capacitor 电容connective 连接词connected 连接connector 连接器connect 连接connection 连接communicate 通信communication n.通信commitment 落实commit 落实commercial a.商业的，经济的commodity 商品command 命令collision 冲突collection 堆集collapse 崩溃cost 成本corresponding 相应的correspond vi.通信(联系) conversational 会话式conversation 对话concentration 集中confidential 机密confirmation 确认concatenate 并置concatenation 并置compilation 编译composition 组合combination 组合compression 压缩collator 整理器collate 整理collation 整理cause 原因course n.过程，航向，课程call 调用chord 弦cord n.绳子，电线core 核心counterclockwise 反时针方向count 计数cast 强制转型card 卡cassette 盒式磁带catch 捕捉cascade 级联carousel n.圆盘传送带characteristic 特性caption 图表说明calculation n.计算，统计，估计cache 高速缓存cash n.现金CAD 计算机辅助设计use 使用utilization 使用率university n.(综合性)大学utility 实用程序unique 唯一的year 年iteration 迭代establishment 建立establish 建立especially ad.特别(是)，尤其escape 跳出invocation 调用environmental a.周围的，环境的introduction 介绍interrelated 相关的intervene vi插入，干涉intervention 介入intercept 拦截intersection 逻辑乘interrupt 中断interaction 交互intermittent 间歇性的intermediate 中间的interlink 相互链接interleave 交错interlace 交错interlock 互锁interference 干扰interfere vi.干涉，干扰，冲突interchange 交换international 国际的instrumentation 仪表化installation 安装insulation 绝缘insufficient a.不足的，不适当的incremental 增量的incompatible 不兼容incorrect 不正确inexperienced a.不熟练的，外行的information 信息individually ad.个别地，单独地individual 个别的indirectly ad.间接地indirect 间接的indirection 间接independently 各自地independent 独立indentation 缩排inaccessible 不可存取的invoke 调用investigate 审查invent vt.创造，想象invariant 不变量invert 翻转inverse 逆矩阵involve vt.涉及，卷入，占用environ vt.围绕，包围environment 环境intensity 亮度intense a.强烈的，高度的intend vt.打算，设计intelligent 智能的intelligence 智能integrity 完整性interpreter 解释器interpret v.解释internal 内部的intern 保留区entirely ad.完全地，彻底地entire a.总体instruct 指示instruction 指令instead ad.(来)代替，当作install 安装instantiate 实例化inspection 检查insert 插入insertion n.插入，嵌入，插页encipher 加密器inside n.内部的enroll 报名inquiry 查询increase v.增加，增大encoder 编码器encode 编码inclusion 包含inclusive a.包括的，内含的include 包括enclose vt.封闭，密封，包装enclosure 安装箱incorporate 合并encounter 遇到inhibit 禁止inheritance 继承inherit 继承enhance 增强ensure 保证insure v.保证，保障infinity 无穷大inform 通知industrial 工业的induction 归纳法indent 缩排indention 缩排indefinitely ad.无限地，无穷地inactive 非活动的inaccuracy 不准确度implementation 实现implication 蕴含式improvement 改进improve 改进imprinting 印刷implosion 内爆implicit 隐式impingement 冲击impedance 阻抗importer 进口服务器import 调入embossment 凸起electronics 电子学electronic 电子的elaboration 加工equivocation 条件信息量总平均值extremely ad.极端地，非常extremity 极限extract 抽取exchange 交换extent 范围extension 扩充extend 扩展express a.快速的expression 表达式exponent 指数explain 说明explanatory a.解释(性)的experience vt.试验exposure 曝光度experiment n.实验，试验(研究) expenditure 支出expect vt.期望，期待，盼望exporter 出口服务器expire v.终止，期满expansion n.展开，展开式expanding a.扩展的，扩充的expander 扩充器expand 扩充exclusive 互斥的exclude 排除exceed 超过except prep.除...之外，除非exception 异常exist 存在exhaust v.取尽，用完example 例子examine v.检验，考试，审查ignore 忽略event 事件evaluate 估计essentially ad.实质上，本来eraser 擦除器erase 擦除enumerator 枚举符initiator 启动程序initiate 启动initially ad.最初，开头initial 初始的enable 允许emulsion 感光乳剂immediate 立即的ellipsis n.省略符号，省略(法) ellipse 椭圆eliminate 消去illegal 非法的equivalent 等价的equivalence 等价equipment 装置equation 方程式efficiently ad.有效地efficiency 效率effective a.有效的effect n.效率，作用，效能edition 版本each 每个equalization 均衡eject 弹出hook 挂钩hub 集线器heuristic 试探的humidity 湿度hit 命中heap 堆阵host 主机hold 保持hole 孔whole 整个Help 帮助hex 十六进制head 磁头horizontal 水平的halt 停机how 如何hide 隐藏hyperbola 双曲线harmonic 谐波hang v.中止，暂停，挂起groove 槽group 组grid 栅极growth 增长grave 雕刻gradation 灰度ground 地grant 授予grantee 接受者gram 克graph 图grab 抓取glyph 图象字符glance n.闪烁go vi.运行，达到gate 门gain 增益guide 指南gap 间隔foot 英尺full 全部sure 确认should 应该freeze v.冻结，结冰free 释放phrase 短语freight 运费frame 帧from 从fragmentation 存储残片shut v.关闭fundamental a.基本的，根本的fluidics 射流技术flush 清仓flow 流动flexibility 灵活性flat 平面的flag 标志fuse 熔凝ship 装运film 薄膜fill 填充fixed 固定的fix 修订shift 移位sheet n.(图)表，纸，片field 字段shield v.屏蔽，罩，防护feed 馈送phone 电话fold 折叠Show 显示fetch 取familiarize vt.使熟悉，使通俗化shell 外壳phase 阶段face n.面，表面shape 形状fail 失败share 共享facility n.设施，装备，便利familiar a.熟悉的，惯用的forget 忽略forbidden 禁用的first 首先forced a.强制的font 字体short 短路force v.力，强度form 表格fault 故障FALSE a.假(布尔值)，错误fork 创建子进程fortuitous 不规则的formation n.构造，结构，形成find 寻找file 文件fast 快速factorial 阶乘facsimile 传真availability 可用性overrun 过速overload 超负荷overlap 重叠overflow 上溢ohm 欧姆opaque 不透明的omit vt.省略，删去，遗漏。

introduction to linear regression analysis 6

introduction to linear regression analysis 6
摘要：
1.线性回归分析简介
2.线性回归分析的基本概念
3.线性回归分析的实际应用
4.线性回归分析的优点和局限性
正文：
线性回归分析是一种常用的统计分析方法，它的主要目的是通过建立一个线性方程来描述两个或多个变量之间的关系。

这种分析方法被广泛应用于各个领域，包括经济学、金融学、社会科学和自然科学等。

线性回归分析的基本概念主要包括两个部分：回归系数和截距。

回归系数表示自变量每变动一个单位时，因变量相应变动的数量；截距则表示当自变量为零时，因变量的取值。

这两个概念一起构成了线性回归方程，是分析的关键。

线性回归分析的实际应用非常广泛。

例如，在经济学中，它可以用来分析价格和销售量之间的关系；在金融学中，它可以用来预测股票价格的走势；在社会科学中，它可以用来研究教育水平和收入之间的关系；在自然科学中，它可以用来预测天气等。

尽管线性回归分析具有很多优点，例如简单、易于理解和操作，但它也有其局限性。

首先，它只能用来描述线性关系，对于非线性关系则无能为力；其次，它的结果受到样本数据的影响，当样本数据存在偏差时，分析结果也可能
出现偏差；最后，它只能预测未来数据的趋势，而无法精确预测具体数值。

总的来说，线性回归分析是一种重要的统计分析方法，它可以帮助我们更好地理解和预测各种现象之间的关系。

regression analysis 公式

regression analysis 公式
回归分析（Regression Analysis）是一种统计方法，用于研究两个或多个变量之间的关系。

它的主要目标是通过建立一个数学模型，根据自变量的变化来预测因变量的值。

回归分析中最常用的公式是简单线性回归模型的形式：
Y = α + βX + ε
其中，Y代表因变量，X代表自变量，α和β分别是截距和斜率，ε是随机误差项。

回归分析的目标是找到最佳拟合线（最小化误差项），使得模型能够最准确地预测因变量的值。

除了简单线性回归，还存在多元线性回归模型，它可以同时考虑多个自变量对因变量的影响。

多元线性回归模型的公式可以表示为：
Y = α + β₁X₁ + β₂X₂ + ... + βₚXₚ + ε
其中，X₁，X₂，...，Xₚ代表不同的自变量，β₁，β₂，...，βₚ代表各自变量的斜率。

通过回归分析，我们可以得到一些关键的统计指标，如回归系数的估计值、回归方程的显著性等。

这些指标可以帮助我们判断自变量对因变量的影响程度，评估模型的拟合优度。

回归分析在许多领域都有广泛的应用，如经济学、社会科学、市场研究等。

它能够揭示变量之间的关联性，为决策提供可靠的预测结果。

总之，回归分析是一种重要的统计方法，通过建立数学模型来研究变量之间的关系。

通过分析回归方程和统计指标，我们可以了解自变量对因变量的影响，并进行预测和决策。

逻辑回归模型书籍 -回复

逻辑回归模型书籍-回复逻辑回归模型是一种常用的统计分析方法，在分类问题中具有广泛的应用。

它通过将数据映射到一个逻辑函数，将观察值分为两个可能的分类之一。

逻辑回归模型的原理和应用被广泛讨论和研究，有很多相关的书籍提供了详细的介绍和教程。

一本值得推荐的逻辑回归模型的书籍是《Logistic Regression Using R: A Comprehensive Tutorial》，作者是卡雷拉-科尔佩恩。

这本书以R语言为工具，系统地介绍了逻辑回归模型的理论与应用。

下面将按照这本书的章节内容，一步一步回答逻辑回归模型的相关问题。

第一章介绍了逻辑回归模型的概念和应用背景。

逻辑回归模型是一种广义线性模型，用于解决分类问题，特别适用于二分类问题。

它通过映射函数将输入和输出之间建立关联，可以预测某个事件发生的概率。

逻辑回归模型在医学、社会科学、市场营销等领域都有重要的应用。

第二章讲解了逻辑回归模型的数学基础。

逻辑回归模型使用的是逻辑函数，也称为sigmoid函数，可以将线性函数的输出限制在0到1之间。

这个函数的性质决定了逻辑回归模型的输出为概率值，在建模中非常重要。

第三章介绍了逻辑回归模型在R语言中的实现。

作者详细讲解了如何使用R语言中的函数对逻辑回归模型进行拟合和预测。

这些函数包括glm()和predict()，可以帮助我们构建模型并进行预测。

第四章讨论了逻辑回归模型的评估方法。

在应用逻辑回归模型时，我们需要对其性能进行评估，以了解预测的准确性。

评估方法包括混淆矩阵、准确率、召回率和AUC曲线等。

作者对这些指标的计算公式和解释进行了详细的说明。

第五章介绍了逻辑回归模型的改进方法。

在实际应用中，我们可能遇到模型拟合不好或过拟合的情况。

作者提供了一些常用的改进方法，如权衡模型复杂度和预测准确性、变量选择和正则化等。

这些方法可以帮助我们提高逻辑回归模型的性能。

第六章讲解了逻辑回归模型在实际数据集上的应用。

作者通过一个真实的案例来演示逻辑回归模型在实际问题中的应用过程。

标准化回归系数python

标准化回归系数python在统计学和机器学习中，标准化回归系数是一种常用的技术，它可以用来比较不同变量对因变量的影响程度。

在Python中，我们可以使用多种库来计算标准化回归系数，其中最常用的是使用scikit-learn库中的线性回归模型。

以下是一个简单的示例代码来计算标准化回归系数：python.import numpy as np.from sklearn.linear_model import LinearRegression.from sklearn.preprocessing import StandardScaler.# 创建一些示例数据。

X = np.array([[1, 2], [2, 4], [3, 6], [4, 8]])。

y = np.array([2, 3, 5, 4])。

# 使用StandardScaler对特征进行标准化。

scaler = StandardScaler()。

X_scaled = scaler.fit_transform(X)。

# 拟合线性回归模型。

model = LinearRegression()。

model.fit(X_scaled, y)。

# 输出标准化回归系数。

print("标准化回归系数，", model.coef_)。

在这个示例中，我们首先导入必要的库，然后创建了一些示例数据。

接下来，我们使用StandardScaler对特征进行标准化处理，然后使用LinearRegression模型拟合数据并输出标准化回归系数。

除了scikit-learn之外，你还可以使用statsmodels库来计算标准化回归系数。

下面是一个使用statsmodels库的示例代码： python.import numpy as np.import statsmodels.api as sm.from sklearn.preprocessing import StandardScaler. # 创建一些示例数据。

SPSS分析技术简介

K-means Cluster原理
K-means Cluster过程
分析实例
一个电信服务提供商希望基于客户使用的服务种类对客户进行细分。如果客户能够按照使用的服务种类进行细分，提供商就可以针对客户的偏好，向其提供不同的服务内容，吸引客户使用更多的服务。
数据的价值和利用
➢ 数据无处不在
➢ 数据包含的信息很多，但是数据中的信息往往是分散的，单个数据很难直接被应用起来
➢ 统计学就是把数据转பைடு நூலகம்为信息的科学
统计学
statistics: the science of collecting, analyzing, presenting, and interpreting data.
利用SPSS整理市场调查数据
利用SPSS分析市场调查数据
单变量分析－－描述统计分析：
变量分布集中趋势：均值、中位数、众数变量分布离散趋势：极差、四分位数、标准差、标准误
双变量分析－－相关分析、列联分析、一元回归分析
多变量分析－－偏相关分析、多元回归分析、聚类分析、因子分析、对应分析等
分析、多元回归等 ▪ 顾客满意度分析－－Logistic回归、对应分析等 ▪ 价格敏感度分析－－交叉分析、多元回归、结合分
析等 ▪ 市场预测分析－－多元回归、时间序列分析等
一个例子——罗斯文商贸公司
▪ 背景介绍：
罗斯文商贸公司是Microsoft数据库产品（Access, SQL Server等)中的一个示例数据库；
在SPSS变量编辑窗口逐个定义变量属性

变量名、变量类型、宽度、小数点位数、变量标签、缺失值
、列宽、对齐方式、测度水平
在数据编辑窗口逐行录入问卷记录

统计建模中的分类响应回归模型及glmcat包的教程说明书

A tutorial on ﬁtting Generalized Linear Models for categoricalresponses with the glmcat packageLorena León ∗Jean Peyhardi †Catherine Trottier ‡AbstractIn statistical modeling,there is a wide variety of regression models for categorical responses.Yet,no software encapsulates all of these models in a standardized format.We introduce and illustrate the utility of glmcat,the R package we developed to estimate generalized linear models implemented under the uniﬁed speciﬁcation (r,F,Z ),where r represents the ratio of probabilities (reference,cumulative,adjacent,or sequential),F the cumulative cdf function for the linkage,and Z the design matrix.We present the properties of the four families of models,which must be investigated when selecting the components r ,F ,and Z .The functions are user-friendly and fairly intuitive;oﬀering the possibility to choose from a large range of models through a combination (r,F,Z ).Introduction to the (r,F,Z)methodology:A generalized linear model is characterized by three components:1)the random component that deﬁnes the conditional cdf of the response variable Y i given the realization of the explanatory variables x i ;2)the systematic component which is determined by the linear predictor η(that speciﬁes the linear entry of the independent variables),and 3)the link function g that relates the expected response and the linear predictor.The random component of a GLM for a categorical response with J categories is the multinomial cdf with vector of probabilities (π1,...,πJ )where πr =1.The linear predictor (η1,...,ηJ −1)can be written as the product of the design matrix Z and the unknown parameter vector β.The link function which characterizes this model is given by the equation g (π)=Zβ,with J −1equations g j =ηj .Peyhardi,Trottier,and Guédon (2015)proposed to write the link function asg j =F −1◦r j ⇔r j =F (ηj )j =1,2,...,J −1(1)where F is a cumulative cdf function and r =(r 1,...,r J −1)is a transformation of the expected value vector.In the following,we will describe in more details the components (r,F,Z)and their modalities.Ratio of probabilities rThe linear predictor is not directly related to the expectation πinstead they are related through a par-ticular transformation r of the vector πwhich is called the ratio.Peyhardi,Trottier,and Guédon (2015)proposed four ratios that gather the alternatives to model categorical response data:Cumulative SequentialAdjacentReference r j (π)π1+...+πjπjπj +...+πJ πjπj +πj +1πj πj +πJ Yordinalnominal∗Universitéde Montpellier,**********************†Universitéde Montpellier,*****************************‡Universitéde Montpellier,**********************************Each component r j(π)can be viewed as a(conditional)probability.For the reference ratio,each category j is compared to the reference category J.For the adjacent ratio,each category j is compared to its adjacent category j+1.For the cumulative ratio,the probabilities of categories are cumulated.For the sequential ratio,each category j is compared to its following category,j+1,...,J.The adjacent,cumulative and sequential ratios all rely on an ordering assumption among categories.The reference ratio is devoted to nominal responses.Cumulative cdf function FThe cumulative cdf functions(distributions)available in glmcat toﬁt the models are:logistic,normal, Cauchy,Student(with any df),Gompertz and Gumbel.The logistic and normal distributions are the sym-metric distributions most commonly used to deﬁne link functions in generalized linear models.However,for speciﬁc scenarios,the use of other distributions may result in a more accurateﬁt.An example is presented by Bouscasse,Joly,and Peyhardi(2019),where the employment of the Student cdf leaded to a betterﬁt for a modeling exercise on travel choice data.For the asymmetric case,the Gumbel and Gompertz distributions are the most commonly used.Design Matrix ZIt is possible to impose restrictions on the thresholds,or on the eﬀects of the covariates,for example,for them to vary or not according to the response categories.•Constraints on the eﬀects:It is plausible for a predictor to have speciﬁc level of impact on the diﬀerent categories of the response. Thus,the J−1linear predictors are of the form:ηj=αj+x′δj withβ=(α1,...,αJ−1,δ′1,...,δ′J−1).And, its associated design matrix is:Z c=1x t......1x t(J−1)×(J−1)(1+p)(2)\end{equation}Another case is to constrain the eﬀects of the covariates to be constant across the response categories.Therefore,there is only a global eﬀect that is not speciﬁc to the response categories,this is known as the parallelism assumption,for which the constrained space is represented by:Z p=1x t......1x t(J−1)×(J−1+p)(3)Theﬁrst case(Z c)is named by Peyhardi,Trottier,and Guédon(2015)as the complete design,whereas the second(Z p)as the parallel design.These two matrices are suﬃcient to deﬁne all the classical models.A third option is to consider both kind of eﬀects,complete and parallel,this in known as partial parallel designZ=1x t k x t l.........1x t k x t l(J−1)×((J−1)(1+K)+L)(4)\end{equation}•Constraints on the intercepts:For the particular case of the cumulative ratio the equidistant constraint considers that the distances between adjacent intercepts are the same for all the pairs(j,j+1),therefore we can write the intercepts asαj=α1+(j−1)θ(5) this restriction implies that only two parameters(α1,theﬁrst threshold,and,θthe spacing)have to be estimated regardless the number of categories.All the classical models for categorical response data,can be written as an(r,F,Z)triplet,as examples:•The multinomimal model≡(Reference,Logistic,Complete)•The odds parallel logit model≡(Cumulative,Logistic,parallel)•The parallel hazard model≡(Sequential,Gompertz,parallel)•The continuation ratio logit model≡(Sequential,Logistic,Complete)•The adjacent logit model≡(Adjacent,Logistic,Complete)Fitting(r,F,Z)with the glmcat packageFamily of reference modelsWe used the223observations of the boy’s disturbed dreams benchmark dataset drawn from a study that cross-classiﬁed boys by their age x and the severity of their disturbed dreams y(Maxwell1961).The data is available as the object DisturbedDreams in the package glmcat.For more information see the manual entry for the DisturbedDreams data:help(DisturbedDreams).#devtools::load_all()library(GLMcat)data("DisturbedDreams")summary(DisturbedDreams)##Age Level##Min.:6.00Not.severe:100##1st Qu.:8.50Severe.1:42##Median:10.50Severe.2:41##Mean:10.96Very.severe:40##3rd Qu.:12.50##Max.:14.50We willﬁt the model(Reference,Logistic,Complete)to the DisturbedDreams data using the function glmcat.We save theﬁtted glmcat model in the object mod_ref_log_c and we print it by simply typing its name:DisturbedDreams$Level<-as.factor(as.character(DisturbedDreams$Level))mod_ref_log_c<-glmcat(formula=Level~Age,ratio="reference",cdf="logistic",ref_category="Very.severe",data=DisturbedDreams)The most common R functions which describe diﬀerent model features are available for the objects in glmcat •The summary of the object:summary(mod_ref_log_c)##Level~Age##ratio cdf nobs niter logLik##Model info:reference logistic2235-277.1345##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-2.454440.84559-2.9030.0037**##(Intercept)Severe.1-0.554640.89101-0.6220.5336##(Intercept)Severe.2-1.124640.91651-1.2270.2198##Age Not.severe0.309990.07804 3.9727.13e-05***##Age Severe.10.059970.085820.6990.4847##Age Severe.20.112280.08684 1.2930.1960##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1•The number or observations:nobs(mod_ref_log_c)##[1]223•The coeﬃcients of the modelcoef(mod_ref_log_c)##[,1]##(Intercept)Not.severe-2.45443827##(Intercept)Severe.1-0.55463962##(Intercept)Severe.2-1.12464112##Age Not.severe0.30998759##Age Severe.10.05997162##Age Severe.20.11228063•The LogLikelihoodlogLik(mod_ref_log_c)##’log Lik.’-277.1345(df=6)•Information criteriaAIC(mod_ref_log_c)##[1]566.2691BIC(mod_ref_log_c)##[1]586.7121It is possible to do predictions in glmcat using the function predict_glmcat.We are going to predict the response for3random observations:#Random observationsset.seed(13)ind<-sample(x=1:nrow(DisturbedDreams),size=3)#Probabilitiespredict(mod_ref_log_c,newdata=DisturbedDreams[ind,],type="prob")##Not.severe Severe.1Severe.2Very.severe##[1,]0.53920490.15833210.17218260.1302804##[2,]0.18322070.27325190.21150460.3320229##[3,]0.29964140.23918790.21100340.2501674#Linear predictorpredict(mod_ref_log_c,newdata=DisturbedDreams[ind,],type="linear.predictor")##Not.severe Severe.1Severe.2##[1,] 1.42040660.195005660.2788668##[2,]-0.5945128-0.19480988-0.4509573##[3,]0.1804562-0.04488083-0.1702558Now we illustrate how to predict in a set of new observations.Suppose we want to predict the severity of dreams for3individuals whose ages are5,9.5and15respectively:#New data#Age<-c(5,9.5,15)#predict(mod_ref_log_c,newdata=Age,type="prob")Assume that we are interested in making the eﬀect of the predictor variable parallel,to that end,we type the name of the predictor variable as the input for the parameter parallel.The model toﬁt corresponds to the triplet(Reference,Logistic,parallel):#DisturbedDreams$Level<-as.factor(as.character(DisturbedDreams$Level))#mod2<-glmcat(#formula=Level~Age,cdf="logistic",#parallel="Age",ref_category="Very.severe",#data=DisturbedDreams#)#summary(mod2)#logLik(mod2)Another variation of the reference model is obtained at changing the cdf function.Let’s nowﬁt the model (Reference,Student(0.5),Complete):#DisturbedDreams$Level<-as.factor(as.character(DisturbedDreams$Level))#mod3<-glmcat(#formula=Level~Age,ref_category="Very.severe",#data=DisturbedDreams,cdf=list("student",0.5)#)#summary(mod3)#logLik(mod3)Family of adjacent modelsThe equivalence between(Adjacent,Logistic,Complete)and(Reference,Logistic,Complete)models is shown by comparing the associated LogLikelihood of both models:logLik(mod_ref_log_c)#recall(ref,logit,com)##’log Lik.’-277.1345(df=6)mod_adj_log_c<-glmcat(formula=Level~Age,ratio="adjacent",data=DisturbedDreams,cdf="logistic")##Warning in glmcat(formula=Level~Age,ratio="adjacent",data=##DisturbedDreams,:The response variable is not defined as an ordered variable.##Recall that the the reference ratio is appropiate for nominal responses,while##for ordinal responses the ratios to use are cumulative,sequential or adjacent.logLik(mod_adj_log_c)##’log Lik.’-279.5628(df=4)summary(mod_adj_log_c)##Level~Age##ratio cdf nobs niter logLik##Model info:adjacent logistic2235-279.5628##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-0.236110.33657-0.7020.48297##(Intercept)Severe.1-1.018750.33535-3.0380.00238**##(Intercept)Severe.2-0.954640.31524-3.0280.00246**##Age0.097300.02405 4.0455.23e-05***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1Remark that despite the fact that the LogLikelihoods are equal,the parameters estimations are diﬀerent (α=α′).Deﬁning the matrix A T as follows:A T=100−1100−11we can check that A T∗α=α′.Note:The adjacent models are stable under the reverse permutation.(Adjacent,Cauchy,Complete)mod_adj_cau_c<-glmcat(formula=Level~Age,ratio="adjacent",cdf="cauchy",categories_order=c("Not.severe","Severe.1","Severe.2","Very.severe"),data=DisturbedDreams)##Warning in glmcat(formula=Level~Age,ratio="adjacent",cdf="cauchy",: ##The response variable is not defined as an ordered variable.Recall that the the ##reference ratio is appropiate for nominal responses,while for ordinal responses ##the ratios to use are cumulative,sequential or adjacent.logLik(mod_adj_cau_c)##’log Lik.’-280.116(df=4)summary(mod_adj_cau_c)##Level~Age##ratio cdf nobs niter logLik##Model info:adjacent cauchy2236-280.116##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-0.180050.28499-0.6320.527526##(Intercept)Severe.1-0.832970.29215-2.8510.004356**##(Intercept)Severe.2-0.783600.26287-2.9810.002874**##Age0.080080.02083 3.8450.000121***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1(Adjacent,Cauchy,Complete)with reversed ordermod_adj_cau_c_rev<-glmcat(formula=Level~Age,ratio="adjacent",cdf="cauchy",categories_order=c("Very.severe","Severe.2","Severe.1","Not.severe"),data=DisturbedDreams)##Warning in glmcat(formula=Level~Age,ratio="adjacent",cdf="cauchy",: ##The response variable is not defined as an ordered variable.Recall that the the ##reference ratio is appropiate for nominal responses,while for ordinal responses ##the ratios to use are cumulative,sequential or adjacent.logLik(mod_adj_cau_c_rev)##’log Lik.’-280.116(df=4)summary(mod_adj_cau_c_rev)##Level~Age##ratio cdf nobs niter logLik##Model info:adjacent cauchy2236-280.116##Estimate Std.Error z value Pr(>|z|)##(Intercept)Very.severe0.783600.26287 2.9810.002874**##(Intercept)Severe.20.832970.29215 2.8510.004356**##(Intercept)Severe.10.180050.284990.6320.527526##Age-0.080080.02083-3.8450.000121***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1The LogLikelihoods of the last two models are the same,this is because the Cauchy cdf is symmetric;for non symmetric distributions this is not longer true.Note that if the Gumbel cdf is used with the reverse order,then,its LogLikelihood is equal to the model using Gompertz as the cdf,this is because the Gumbel cdf is the symmetric of the Gompertz cdf.Otherwise,the parameter estimations are reversed: (Adjacent,Gumbel,parallel)adj_gumbel_p<-glmcat(formula=Level~Age,ratio="adjacent",cdf="gumbel",categories_order=c("Not.severe","Severe.1","Severe.2","Very.severe"),parallel=c("(Intercept)","Age"),data=DisturbedDreams)##Warning in glmcat(formula=Level~Age,ratio="adjacent",cdf="gumbel",:##The response variable is not defined as an ordered variable.Recall that the the##reference ratio is appropiate for nominal responses,while for ordinal responses##the ratios to use are cumulative,sequential or adjacent.logLik(adj_gumbel_p)##’log Lik.’-284.0416(df=2)summary(adj_gumbel_p)##Level~Age##ratio cdf nobs niter logLik##Model info:adjacent gumbel2235-284.0416##Estimate Std.Error z value Pr(>|z|)##(Intercept)-0.280230.20340-1.3780.168##Age0.083850.01909 4.3921.13e-05***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1(Adjacent,Gompertz,parallel)adj_gompertz_rev<-glmcat(formula=Level~Age,ratio="adjacent",cdf="gompertz",categories_order=c("Very.severe","Severe.2","Severe.1","Not.severe"),parallel=c("(Intercept)","Age"),data=DisturbedDreams)##Warning in glmcat(formula=Level~Age,ratio="adjacent",cdf="gompertz",:##The response variable is not defined as an ordered variable.Recall that the the##reference ratio is appropiate for nominal responses,while for ordinal responses##the ratios to use are cumulative,sequential or adjacent.logLik(adj_gompertz_rev)##’log Lik.’-284.0416(df=2)summary(adj_gompertz_rev)##Level~Age##ratio cdf nobs niter logLik##Model info:adjacent gompertz2235-284.0416##Estimate Std.Error z value Pr(>|z|)##(Intercept)0.280230.20340 1.3780.168##Age-0.083850.01909-4.3921.13e-05***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1Family of sequential modelsThe sequential ratio,which assumes a binary process at each transition,higher levels can be reached only if previous levels where reached at a earlier stage.(Sequential,Normal,Complete)seq_probit_c<-glmcat(formula=Level~Age,ratio="sequential",cdf="normal",data=DisturbedDreams)##Warning in glmcat(formula=Level~Age,ratio="sequential",cdf="normal",:##The response variable is not defined as an ordered variable.Recall that the the##reference ratio is appropiate for nominal responses,while for ordinal responses##the ratios to use are cumulative,sequential or adjacent.logLik(seq_probit_c)##’log Lik.’-280.5465(df=4)summary(seq_probit_c)##Level~Age##ratio cdf nobs niter logLik##Model info:sequential normal2236-280.5465##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-1.203130.27969-4.3021.69e-05***##(Intercept)Severe.1-1.413470.28345-4.9876.14e-07***##(Intercept)Severe.2-0.983930.28252-3.4830.000496***##Age0.097520.02414 4.0395.36e-05***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1Family of cumulative models(Cumulative,Logistic,Complete)cum_log_co<-glmcat(formula=Level~Age,cdf="logistic",ratio="cumulative",data=DisturbedDreams)##Warning in glmcat(formula=Level~Age,cdf="logistic",ratio=##"cumulative",:The response variable is not defined as an ordered variable.##Recall that the the reference ratio is appropiate for nominal responses,while##for ordinal responses the ratios to use are cumulative,sequential or adjacent.logLik(cum_log_co)##’log Lik.’-278.4682(df=4)summary(cum_log_co)##Level~Age##ratio cdf nobs niter logLik##Model info:cumulative logistic2236-278.4682##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-2.606390.56166-4.6403.48e-06***##(Intercept)Severe.1-1.781570.54641-3.2600.00111**##(Intercept)Severe.2-0.777140.53923-1.4410.14953##Age0.218750.04949 4.4209.86e-06***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1The function glmcat has special features for the cumulative models.The option for the thresholds to be equidistant is a characteristic of interest for the family of cumulative models:(Cumulative,Logistic,Equidistant)cum_log_co_e<-glmcat(formula=Level~Age,cdf="logistic",ratio="cumulative",data=DisturbedDreams,parallel="Age",threshold="equidistant",)##Warning in glmcat(formula=Level~Age,cdf="logistic",ratio=##"cumulative",:The response variable is not defined as an ordered variable.##Recall that the the reference ratio is appropiate for nominal responses,while##for ordinal responses the ratios to use are cumulative,sequential or adjacent.logLik(cum_log_co_e)##’log Lik.’-278.892(df=3)summary(cum_log_co_e)##Level~Age##ratio cdf nobs niter logLik##Model info:cumulative logistic2236-278.892##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-2.637690.56148-4.6982.63e-06***##(Intercept)distance0.903660.0886010.199<2e-16***##Age0.219950.04947 4.4468.75e-06***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1If we have a preliminary idea of the coeﬃcients of the model,we can specify an initialization vector through the parameter beta_init:cum_log_c<-glmcat(formula=Level~Age,cdf=list("student",0.8),ratio="cumulative",data=DisturbedDreams,control=control_glmcat(beta_init=coef(cum_log_co)))##Warning in glmcat(formula=Level~Age,cdf=list("student",0.8),ratio=##"cumulative",:The response variable is not defined as an ordered variable.##Recall that the the reference ratio is appropiate for nominal responses,while##for ordinal responses the ratios to use are cumulative,sequential or adjacent.logLik(cum_log_c)##’log Lik.’-280.5428(df=4)summary(cum_log_c)##Level~Age##ratio cdf nobs niter logLik##Model info:cumulative student2237-280.5428##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-2.152580.56970-3.7780.000158***##(Intercept)Severe.1-1.391690.52035-2.6750.007483**##(Intercept)Severe.2-0.071410.57835-0.1230.901740##Age0.179090.04957 3.6130.000302***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1The equivalence between the(Cumulative,Gompertz,parallel)and(Sequential,Gompertz,parallel)mod-els has been demonstrated by Lääräand Matthews(1985)and it is hereby tested using the functions:cum_gom_p<-glmcat(formula=Level~Age,cdf="gompertz",ratio="cumulative",data=DisturbedDreams,parallel="Age")##Warning in glmcat(formula=Level~Age,cdf="gompertz",ratio=##"cumulative",:The response variable is not defined as an ordered variable.##Recall that the the reference ratio is appropiate for nominal responses,while##for ordinal responses the ratios to use are cumulative,sequential or adjacent.logLik(cum_gom_p)##’log Lik.’-280.0788(df=4)summary(cum_gom_p)##Level~Age##ratio cdf nobs niter logLik##Model info:cumulative gompertz2236-280.0788##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-1.887810.36046-5.2371.63e-07***##(Intercept)Severe.1-1.335150.35206-3.7920.000149***##(Intercept)Severe.2-0.785510.34252-2.2930.021828*##Age0.124340.03009 4.1333.59e-05***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1seq_gom_p<-glmcat(formula=Level~Age,cdf="gompertz",ratio="sequential",data=DisturbedDreams,parallel="Age")##Warning in glmcat(formula=Level~Age,cdf="gompertz",ratio=##"sequential",:The response variable is not defined as an ordered variable.##Recall that the the reference ratio is appropiate for nominal responses,while##for ordinal responses the ratios to use are cumulative,sequential or adjacent.logLik(seq_gom_p)##’log Lik.’-280.0788(df=4)summary(seq_gom_p)##Level~Age##ratio cdf nobs niter logLik##Model info:sequential gompertz2236-280.0788##Estimate Std.Error z value Pr(>|z|)##(Intercept)Not.severe-1.887810.36046-5.2371.63e-07***##(Intercept)Severe.1-2.191800.36851-5.9482.72e-09***##(Intercept)Severe.2-1.646260.35822-4.5964.31e-06***##Age0.124340.03009 4.1333.59e-05***##---##Signif.codes:0’***’0.001’**’0.01’*’0.05’.’0.1’’1ConclusionThe models for categorical response data have been evolved in diﬀerentﬁelds of research under diﬀerent names.Some of them are fairly similar or are even the same.Until recently,there was no methodology that encompassed these models in a comparable scheme.glmcat is based on the new speciﬁcation of a generalized linear model given by the(r,F,Z)-triplet,which groups together all the proposed methodologies for modelling categorical responses.glmcat oﬀers a full picture of the spectrum of models where the user has three components to combine in order to obtain a model that meets the speciﬁcations of the problem. ReferencesBouscasse,Hélène,Iragaël Joly,and Jean Peyhardi.2019.“A new family of qualitative choice models:An application of reference models to travel mode choice.”Transportation Research Part B:Methodological 121(C):74–91.Läärä,E.,and J.N.S.Matthews.1985.“The equivalence of two models for ordinal data.”Biometrika72(1):206–7.https:///10.1093/biomet/72.1.206.Maxwell,A.E.1961.Analyzing Qualitative Data.Methuen.Peyhardi,J.,C.Trottier,and Y.Guédon.2015.“A new speciﬁcation of generalized linear models for categorical responses.”Biometrika102(4):889–906.https:///10.1093/biomet/asv042.。

用R语言做曲线拟合

Technical note:Curveﬁtting with the R Environment for Statistical ComputingD G RossiterDepartment of Earth Systems Analysis International Institute for Geo-information Science&Earth Observation(ITC)Enschede(NL)December15,2009Contents1Curveﬁtting12Fitting intrinsically linear relations13Fitting linearizable relations14Non-linear curveﬁtting24.1Fitting a power model (2)4.2Fitting to a functional form (4)4.3Fitting an exponential model (6)4.4Fitting a piecewise model (8)References13Index of R concepts14Version1.0Copyright©2009D G Rossiter.All rights reserved.Reproduc-tion and dissemination of the work as a whole(not parts)freely permittedif this original copyright notice is included.Sale or placement on a web sitewhere payment must be made to access this document is strictly prohibited.To adapt or translate please contact the author(http://www.itc.nl/personal/rossiter).1CurveﬁttingThis is a small introduction to curveﬁtting in the R environment for sta-tistical computing and visualisation[2,5]and its dialect of the S language.R provides a sophisticated environment,which gives the user more insightand control than provided by commerical or shareware“push the button”programs such as CurveFit.Note:For an explanation of the R project,including how to obtain andinstall the software and documentation,see Rossiter[7].This also containsan extensive discussion of the S language,R graphics,and many statisticalmethods,as well as a bibliography of texts and references that use R.Note:The code in these exercises was tested with Sweave[3,4]on R version2.10.1(2009-12-14),stats package Version: 2.10.1,running on Mac OS X10.6.2.So,the text and graphical output you see here was automaticallygenerated and incorporated into L A T E X by running actual code through R andits packages.Then the L A T E X document was compiled into the PDF versionyou are now reading.Your output may be slightly diﬀerent on diﬀerentversions and on diﬀerent platforms.2Fitting intrinsically linear relationsRelations that are expected to be linear(from theory or experience)areusuallyﬁt with R’s lm“linear model”method,which by default uses ordinaryleast squares(OLS)to minimize the sum of squares of the residuals.This iscovered in many texts and another tutorial of this series[6].However,linear relations with some contamination(e.g.outliers)may bebetterﬁt by robust regression,for example the lmRob function in the robustpackage.Afterﬁtting a linear model,the analyst should always check the regressiondiagnostics appropriate to the model,to see if the model assumptions aremet.For example,the ordinary least squaresﬁt to a linear model assumes,among others:(1)normally-distributed residuals;(2)homoscedascity(vari-ance of the response does not depend on the value of the predictor);(3)serial independence(no correlation between responses for nearby values ofthe predictor).3Fitting linearizable relationsSome evidently non-linear relations can be linearized by transforming eitherthe response or predictor variables.This should generally be done on thebasis of theory,e.g.an expected multiplicative eﬀect of a causitive variablewould indicate an exponential response,thus a logarithmic transformationof the response variable.An example of a log-linear model is shown in§4.3.4Non-linear curveﬁttingEquations that can not be linearized,or for which the appropriate lineariza-tion is not known from theory,can beﬁtted with the nls method,based onthe classic text of Bates and Watts[1]and included in the base R distribu-tion’s stats package.You must have some idea of the functional form,presumably from theory.You can of course try various forms and see which gives the closestﬁt,butthat may result inﬁtting noise,not model.4.1Fitting a power modelWe begin with a simple example of a known functional form with some noise,and see how close we can come toﬁtting it.Task1:Make a data frame of24uniform random variates(independentvariable)and corresponding dependent variable that is the cube,with noise.Plot the points along with the known theoretical function.•So that your results match the ones shown here,we use the set.seed func-tion to initialize the random-number generator;in practice this is not doneunless one wants to reproduce a result.The choice of seed is arbitrary.Therandom numbers are generated with the runif(uniform distribution,for theindependent variable)and rnorm(normal distribution,for the independentvariable)functions.These are then placed into a two-column matrix withnamed columns with the data.frame function.>set.seed(520)>len<-24>x<-runif(len)>y<-x^3+rnorm(len,0,0.06)>ds<-data.frame(x=x,y=y)>str(ds)'data.frame':24obs.of2variables:$x:num0.14110.49250.09920.04690.1131...$y:num0.025860.05546-0.00480.08050.00764...>plot(y~x,main="Known cubic,with noise")>s<-seq(0,1,length=100)>lines(s,s^3,lty=2,col="green")qq qqq qqqqqqq q qqqq qqqq q qq0.00.20.40.60.8 1.00.00.20.40.60.81.0Known cubic, with noisexySuppose this is a dataset collected from an experiment,and we want todetermine the most likely value for the exponent.In the simplest case,we assume that the function passes through (0,0);we suppose there is a physical reason for that.Task 2:Fit a power model,with zero intercept,to this data.•We use the workhorse nls function,which is analogous to lm for linear models.This requires at least:1.a formula of the functional form;2.the environment of the variable names listed in the formula;3.a named list of starting guesses for these.We’ll specify the power model:y ~I(x^power)and make a starting guess that it’s a linear relation,i.e.that the power is 1.Note:Note the use of the I operator to specify that the ^exponentiation operator is a mathematic operator,not the ^formula operator (factor cross-ing).In this case there is no diﬀerence,because there is only one predictor,but in the general case it must be speciﬁed.We use the optional trace=T argument to see how the non-linear ﬁt con-verges.>m <-nls(y ~I(x^power),data =ds,start =list(power =1),+trace =T)1.539345:10.2639662: 1.8749840.07501804: 2.5846080.0673716: 2.7974050.06735321: 2.8088990.06735321: 2.808956>class(m)[1]"nls"The nls function has returned an object of class nls,for which many further functions are deﬁned.Task3:Display the solution.•The generic summary method specializes to the non-linear model:>summary(m)Formula:y~I(x^power)Parameters:Estimate Std.Error t value Pr(>|t|)power 2.80900.145919.251.11e-15***---Signif.codes:0'***'0.001'**'0.01'*'0.05'.'0.1''1Residual standard error:0.05411on23degrees of freedomNumber of iterations to convergence:5Achieved convergence tolerance:2.163e-07>summary(m)$coefficientsEstimate Std.Error t value Pr(>|t|)power2.8089560.145922419.249661.111061e-15We can see that the estimated power is2.809±0.146The standard error of the coeﬃcient shows how uncertain we are of the solution.Task4:Plot theﬁtted curve against the known curve.•We use the predict method toﬁnd the function value for theﬁtted power function along the sequence[0,0.01,0.02,...,0.99,1],and use these to plot theﬁtted power function.>power<-round(summary(m)$coefficients[1],3)>power.se<-round(summary(m)$coefficients[2],3)>plot(y~x,main="Fitted power model",sub="Blue:fit;green:known") >s<-seq(0,1,length=100)>lines(s,s^3,lty=2,col="green")>lines(s,predict(m,list(x=s)),lty=1,col="blue")>text(0,0.5,paste("y=x^(",power,"+/-",power.se,+")",sep=""),pos=4)qq qqq qqqqqqq q qqqq qqqq q q q0.00.20.40.60.8 1.00.00.20.40.60.81.0Fitted power modelBlue: fit; green: knownxyy =x^ (2.809 +/− 0.146)Despite the noise,the ﬁt is quite close to the known power.Task 5:Determine the quality of the ﬁt.•We compute the residual sum-of-squares (lack of ﬁt)and the complement of its proportion to the total sum-of-squares (coeﬃcient of determination,“R 2”):>(RSS.p <-sum(residuals(m)^2))[1]0.06735321>(TSS <-sum((y -mean(y))^2))[1]2.219379>1-(RSS.p/TSS)[1]0.9696522We can compare this to the lack-of-ﬁt to the known cubic,where the lack of ﬁt is due to the noise:>1-sum((x^3-y)^2)/TSS [1]0.9675771They are hardly distinguishable;the known cubic will not necessarily be better,this depends on the particular simulation.4.2Fitting to a functional formThe more general way to use nls is to deﬁne a function for the right-hand side of the non-linear equation.We illustrate for the power model,but without assuming that the curve passes through (0,0).Task6:Fit a power model and intercept.•First we deﬁne a function,then use it in the formula for nls.The function takes as arguments:1.the input vector,i.e.independent variable(s);2.the parameters;these must match the call and the arguments to thestart=initialization argument,but they need not have the same names.>rhs<-function(x,b0,b1){+b0+x^b1+}>m.2<-nls(y~rhs(x,intercept,power),data=ds,start=list(intercept=0, +power=2),trace=T)0.2038798:020.06829972:-0.01228041 2.553681640.06558916:-0.01466565 2.653907080.06558607:-0.01447859 2.659890000.06558607:-0.01446096 2.660170920.06558607:-0.01446011 2.66018398>summary(m.2)Formula:y~rhs(x,intercept,power)Parameters:Estimate Std.Error t value Pr(>|t|)intercept-0.014460.01877-0.770.449power 2.660180.2317311.489.27e-11***---Signif.codes:0'***'0.001'**'0.01'*'0.05'.'0.1''1Residual standard error:0.0546on22degrees of freedomNumber of iterations to convergence:5Achieved convergence tolerance:5.288e-07>plot(ds$y~ds$x,main="Fitted power model,with intercept",+sub="Blue:fit;magenta:fit w/o intercept;green:known")>abline(h=0,lty=1,lwd=0.5)>lines(s,s^3,lty=2,col="green")>lines(s,predict(m.2,list(x=s)),lty=1,col="blue")>lines(s,predict(m,list(x=s)),lty=2,col="magenta")>segments(x,y,x,fitted(m.2),lty=2,col="red")qq qqq qqqqqqq q qqqq qqqq q qq0.00.20.40.60.8 1.00.00.20.40.60.81.0Fitted power model, with interceptBlue: fit; magenta: fit w/o intercept; green: knownds$xd s $yThis example shows the eﬀect of forcing the equation through a known point,in this case (0,0).Since the model has one more parameter,it will by deﬁnition ﬁt better near the origin.However,in this case it is ﬁtting noise,not structure.Task 7:Compare the ﬁt with the known relation and the power-only model.•>(RSS.pi <-sum(residuals(m.2)^2))[1]0.06558607>(RSS.p)[1]0.06735321>1-(RSS.pi/TSS)[1]0.9704485>1-(RSS.p/TSS)[1]0.9696522>1-sum((x^3-y)^2)/TSS [1]0.9675771Task 8:Compare the two models (with and without intercept)with an Analysis of Variance.•>anova(m.2,m)Analysis of Variance TableModel1:y~rhs(x,intercept,power)Model2:y~I(x^power)Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)1220.0655862230.067353-1-0.00176710.59280.4495The Pr(>F)value is the probability that rejecting the null hypothesis(themore complex model does notﬁt better than the simpler model)would be amistake;in this case since we know there shouldn’t be an intercept,we hopethat this will be high(as it in fact is,in this case).4.3Fitting an exponential modelLooking at the scatterplot we might suspect an exponential relation.Thiscan beﬁt in two ways:linearizing by taking the logarithm of the response;with non-linearﬁt,as in the previous section.Theﬁrst approach works because:y=e a+bx≡log(y)=a+bxTask9:Fit a log-linear model.•The logarithm is not deﬁned for non-positive numbers,so we have to adda small oﬀset if there are any of these(as here).One way to deﬁne this isas the decimal0.1,0.01,0.001...that is just large enough to bring all thenegative values above zero.Here the minimum is:>min(y)[1]-0.06205655and so we should add0.1.>offset<-0.1>ds$ly<-log(ds$y+offset)>m.l<-lm(ly~x,data=ds)>summary(m.l)Call:lm(formula=ly~x,data=ds)Residuals:Min1Q Median3Q Max-1.31083-0.094950.019930.076430.87749Coefficients:Estimate Std.Error t value Pr(>|t|)(Intercept)-2.86980.1458-19.691.85e-15***x 2.93110.261311.221.43e-10***---Signif.codes:0'***'0.001'**'0.01'*'0.05'.'0.1''1Residual standard error:0.3874on 22degrees of freedom Multiple R-squared:0.8512,Adjusted R-squared:0.8445F-statistic:125.9on 1and 22DF,p-value:1.431e-10>plot(ds$ly ~ds$x,xlab ="x",ylab ="log(y+.1)",main ="Log-linear fit")>abline(m.l)>text(0,0.4,pos =4,paste("log(y)=",round(coefficients(m.l)[1],+3),"+",round(coefficients(m.l)[2],3)))q qqqq q qqq q qqq qqqqqqqq q qq0.00.20.40.60.8 1.0−3.0−2.5−2.0−1.5−1.0−0.50.0Log−linear fitxl o g (y +.1)log(y) = −2.87 + 2.931Here the adjusted R 2is 0.844,but this can not be compared to the non-linear ﬁt,because of the transformation.Since this is a linear model,we can evaluate the regression diagnostics:>par(mfrow =c(2,2))>plot(m.l)>par(mfrow =c(1,1))−2.5−1.5−0.5−1.5−0.50.5Fitted valuesR e s i d u a l sq q qqq q q q q q qq q qqq qqqqqq q q Residuals vs Fitted42412q q q q qq q q qq q q q qq qq q q q q qq q−2−1012−3−1123Theoretical QuantilesS t a n d a r d i z e d r e s i d u a l sNormal Q−Q42412−2.5−1.5−0.50.00.51.01.5Fitted valuesS t a n d a r d i z e d r e s i d u a l sq qqqqq q qq qqq q qqqqqqq q q qq Scale−Location424120.000.050.100.15−4−20123LeverageS t a n d a r d i z e d r e s i d u a l sq q q q q qq q q qqqq q q qq qqqq q qCook's distance10.50.51Residuals vs Leverage24412Clearly the log-linear model is not appropriate.The second way is with nls .Task 10:Directly ﬁt an exponential model.•The functional form is y =e a +bx .A reasonable starting point is a =0,b =1,i.e.y =e x .>m.e <-nls(y ~I(exp(1)^(a +b *x)),data =ds,start =list(a =0,+b =1),trace =T)50.47337:015.529667:-1.095364 1.4273970.5618565:-2.280596 2.2984050.1172045:-3.390888 3.4199270.1012589:-3.802324 3.8550690.1011533:-3.766443 3.8120510.1011499:-3.773935 3.8204690.1011498:-3.772497 3.8188490.1011498:-3.772775 3.8191620.1011498:-3.772722 3.819102>summary(m.e)$coefficientsEstimate Std.Error t value Pr(>|t|)a -3.7727220.2516577-14.991484.968731e-13b 3.8191020.280542313.613283.400880e-12>a <-round(summary(m.e)$coefficients[1,1],4)>b <-round(summary(m.e)$coefficients[2,1],4)>plot(y ~x,main ="Fitted exponential function",sub ="Blue:fit;green:known")>s <-seq(0,1,length =100)>lines(s,s^3,lty =2,col ="green")>lines(s,predict(m.e,list(x =s)),lty =1,col ="blue")>text(0,0.5,paste("y =e^(",a,"+",b,"*x)",sep =""),+pos =4)qq qqq qqqqqqq q qqqq qqqq q q q0.00.20.40.60.8 1.00.00.20.40.60.81.0Fitted exponential functionBlue: fit; green: knownxyy =e^ (−3.7727 + 3.8191 * x)Here the goodness-of-ﬁt can be compared directly to that for the power model:>RSS.p [1]0.06735321>(RSS.e <-sum(residuals(m.e)^2))[1]0.1011498>TSS [1]2.219379>1-RSS.p/TSS [1]0.9696522>1-RSS.e/TSS [1]0.9544243The ﬁt is not as good as for the power model,which suggests that the exponential model is an inferior functional form.4.4Fitting a piecewise modelA big advantage of the nls method is that any function can be optimized.This must be continuous in the range of the predictor but not necessariydiﬀerentiable.An example is the linear-with-plateau model sometimes used to predict cropyield response to fertilizers.The theory is that up to some threshold,addedfertilizer linearly increases yield,but once the maximum yield is reached(limited by light and water,for example)added fertilizer makes no diﬀerence.So there are four parameters:(1)intercept:yield with no fertilizer;(2)slope:yield increase per unit fertilizer added;(3)threshold yield:maximumattainable;(4)threshold fertilizer amount:where this yield is attained.Note that one parameter is redundant:knowing the linear part and thethreshold yield we can compute the threshold amount,or with the amountthe yield.Task11:Deﬁne a linear-response-with-plateau function.•We deﬁne the function with three parameters,choosing toﬁt the maxi-mum fertilizer amount,from which we can back-compute the maximum yield(plateau).We use the ifelse operator to select the two parts of the function,depending on the threshold.>f.lrp<-function(x,a,b,t.x){+ifelse(x>t.x,a+b*t.x,a+b*x)+}Task12:Generate a synthetic data set to represent a fertilizer experimentwith0,10,...120kg ha-1added fertilizer,with three replications,withknown linear response y=2+0.5x and maximum fertilizer which givesresponse of70kg ha-1.•In nature there are always random factors;we account for this by addingnormally-distributed noise with the rnorm function.Again we use set.seedso your results will be the same,but you can experiment with other randomvalues.>f.lvls<-seq(0,120,by=10)>a.0<-2>b.0<-0.05>t.x.0<-70>test<-data.frame(x=f.lvls,y=f.lrp(f.lvls,a.0,+ b.0,t.x.0))>test<-rbind(test,test,test)>set.seed<-619>test$y<-test$y+rnorm(length(test$y),0,0.2)>str(test)'data.frame':39obs.of2variables:$x:num0102030405060708090...$y:num 1.92.672.963.773.93...In this example the maximum attainable yield is 5.5,for any fertilizer amount from 70on.No fertilizer gives a yield of 2and each unit of fertilizer added increases the yield 0.05units.The noise represents the intrinsic error in ﬁeld experiments.Note that the amount of fertilizer added is considered exact,since it is under the experimenter’s control.Task 13:Plot the experiment with the known true model.•>plot(test$y ~test$x,main ="Linear response and plateau yield response",+xlab ="Fertilizer added",ylab ="Crop yield")>(max.yield <-a.0+b.0*t.x.0)[1]5.5>lines(x =c(0,t.x.0,120),y =c(a.0,max.yield,max.yield),+lty =2)>abline(v =t.x.0,lty =3)>abline(h =max.yield,lty =3)qq qq qqq q qq q q qq qqqq qqqqq qqqq qqq qqqqq qqqq 02040608010012023456Linear response and plateau yield responseFertilizer addedC r o p y i e l dNote :Although it’s not needed for this example,the replication number should be added to the dataframe as a factor;we use the rep “replicate”function to create the vector of replication numbers,and then as.factor to convert to a factor.The table function gives the count of each replicate:>test$rep <-as.factor(rep(1:3,each =length(test$y)/3))>str(test)'data.frame ':39obs.of 3variables:$x :num 0102030405060708090...$y :num 1.92.672.963.773.93...$rep:Factor w/3levels "1","2","3":1111111111...>table(test$rep)123131313The diﬀerent replications have slightly diﬀerent mean yields,due to random error;we see this with the by function to split a vector by a factor and then apply a function per-factor;in this case mean:>by(test$y,test$rep,mean)test$rep:1[1]4.422042----------------------------------------------------test$rep:2[1]4.488869----------------------------------------------------test$rep:3[1]4.405799Task14:Fit the model to the experimental data.•Now we tryﬁt the model,as if we did not know the parameters.Starting values are from the experimenter’s experience.Here we say zero fertilizer gives no yield,the increment is0.1,and the maximum fertilizer that will give any result is50.>m.lrp<-nls(y~f.lrp(x,a,b,t.x),data=test,start=list(a=0,+b=0.1,t.x=50),trace=T,control=list(warnOnly=T,+minFactor=1/2048))32.56051:0.00.150.08.951927: 2.101938900.0466595660.072510462.265017: 2.090414760.0473510172.644694332.187349: 2.044129920.0496652569.207381932.169194: 2.067272340.0485081370.758438132.149853: 2.055701130.0490866970.046404662.149082: 2.054977930.0491228570.003476142.149081: 2.054893180.0491270969.998453112.149070: 2.054962550.0491236270.003089092.149026: 2.054920240.0491257470.000579142.149018: 2.054909700.0491262669.99995416>summary(m.lrp)Formula:y~f.lrp(x,a,b,t.x)Parameters:Estimate Std.Error t value Pr(>|t|)a 2.0549270.09105522.57<2e-16***b0.0491250.00217722.57<2e-16***t.x70.001112 2.25494231.04<2e-16***---Signif.codes:0'***'0.001'**'0.01'*'0.05'.'0.1''1Residual standard error:0.2443on36degrees of freedomNumber of iterations till stop:10Achieved convergence tolerance:0.1495Reason stopped:step factor0.000244141reduced below'minFactor'of0.000488281>coefficients(m.lrp)ab t.x2.05492700.049125470.0011125The ﬁt is quite close to the known true values.Note that the summary gives the standard error of each parameter,which can be used for simulation or sensitivity analysis.In this case all “true”parameters are well within one standard error of the estimate.Task 15:Plot the experiment with the ﬁtted model and the known model.•>plot(test$y ~test$x,main ="Linear response and plateau yield response",+xlab ="Fertilizer added",ylab ="Crop yield")>(max.yield <-a.0+b.0*t.x.0)[1]5.5>lines(x =c(0,t.x.0,120),y =c(a.0,max.yield,max.yield),+lty =2,col ="blue")>abline(v =t.x.0,lty =3,col ="blue")>abline(h =max.yield,lty =3,col ="blue")>(max.yield <-coefficients(m.lrp)["a"]+coefficients(m.lrp)["b"]*+coefficients(m.lrp)["t.x"])a5.493759>lines(x =c(0,coefficients(m.lrp)["t.x"],120),y =c(coefficients(m.lrp)["a"],+max.yield,max.yield),lty =1)>abline(v =coefficients(m.lrp)["t.x"],lty =4)>abline(h =max.yield,lty =4)>text(120,4,"known true model",col ="blue",pos =2)>text(120,3.5,"fitted model",col ="black",pos =2)qq qq qqq q qq q q qq qqqq qqqqq qqqq qqq qqqqq qqqq 02040608010012023456Linear response and plateau yield responseFertilizer addedC r o p y i e l dknown true modelfitted modelReferences[1]D.M.Bates and D.G.Watts.Nonlinear Regression Analysis and ItsApplications.Wiley,1988.2[2]R Ihaka and R Gentleman.R:A language for data analysis and graphics.Journal of Computational and Graphical Statistics,5(3):299–314,1996.1[3]F Leisch.Sweave User’s Manual.TU Wein,Vienna(A),2.1edition,2006.URL http://www.ci.tuwien.ac.at/~leisch/Sweave.1[4]F Leisch.Sweave,part I:Mixing R and L A T E X.R News,2(3):28–31,December2002.URL /doc/Rnews/.1[5]R Development Core Team.R:A language and environment for statisti-cal computing.R Foundation for Statistical Computing,Vienna,Austria,2004.URL .ISBN3-900051-07-0.1[6]D G Rossiter.Technical Note:An example of data analysis using theR environment for statistical computing.International Institute for Geo-information Science&Earth Observation(ITC),Enschede(NL),0.9edi-tion,2008.URL http://www.itc.nl/personal/rossiter/teach/R/R_corregr.pdf.1[7]D G Rossiter.Introduction to the R Project for Statistical Computingfor use at ITC.International Institute for Geo-information Science&Earth Observation(ITC),Enschede(NL),3.6edition,2009.URL http://www.itc.nl/personal/rossiter/teach/R/RIntro_ITC.pdf.1Index of R Concepts ^formula operator,3 ^operator,3as.factor,13by,14data.frame,2I operator,3ifelse,12lm,1,3lmRob,1mean,14nls,3–6,10,12nls package,2 predict,4rep,13rnorm,2,12robust package,1 runif,2set.seed,2,12stats package,1,2 summary,4table,13。

生物统计学计算机SPSS应用指导

9．数据简化分析（Data Reduction）：因子分析（Factor）。 10. 尺度分析（ Scale ）：可靠性分析（ Reliability Analysis ）、多维尺度分析（Multidimensional Scaling）。 11.非参数检验（Nonparametric Tests）： X2 检验（Chi-Square）、二项式检验（Binomial）。游程检验（Runs）、单样本哥尔莫格罗夫一斯米尔罗夫检验（Kolmogorov－Smirnov， 1-Sample K-S）、两独立样本非参数检验（2 Independent-Samples）、 K 项独立样本非参数检验（K Independent Samples）、两相关样本非多数检验（2 Related Samples）、 K 项相关样本非参数检验（K Related samples）。 12．生存分析（Survival）：寿命表（Life Tables）、Kaplan－Meier 方法（Kaplan－Meter）、 Cox 回归分析（Cox Regression）、Cox w／时间一因变量协变量分析（Cox w/Time－Dep Cox）。 13．多重响应分析（Multiple Response）：确定多重响应分析的设置（Define Sets)、多重频数分析（Frequencies）、多重列联表分析（Crosstabs）。
9. SPSS 10.0 自带 11 种类型 136 个函数，能充分满足各个方面用户的需要。鉴于 SPSS 突出的优越性，熟悉和掌握该软件将对生物统计学的应用带来极大的方便。
第一节 SPSS 系统简介
一．SPSS 的命令类型（一）操作命令一切统计分析都是以数据为基础的,因此统计软件的数据管理能力非常重要。SPSS 中数据文件的管理功能基本上都集中在了”file”菜单上，该菜单的组织结构和 word 极为相似，因此这里我们只介绍比较有特色的几个操作命令： 1. 新建数据文件开始进行一个新的课题，把数据收集上来做统计分析，就需要新建一个数据库，然后将所有的数据输入到计算机里，在 SPSS 中新建一个数据库十分容易，只要进入 SPSS 系统，系统就已经生成了一个空数据文件，即看到的空白的数据管理界面（电子表格）。用户只要按自己的需要定义变量，再输入数据然后存盘就可以了。 2. 打开其他格式的数据文件 SPSS 10.0 的版本可以直接读入许多格式的数据文件，其中包括 Excel 各个版本的数据文件，选择菜单“file”－“open”－“data”或直接单击快捷工具栏上的按钮，系统就会弹出 open file 对话框，单击“文件类型”列表框，在里面能看到直接打开的数据文件格式。选择所需的文件类型，然后选中需要打开的文件，SPSS 就会按要求打开你要使用的数据文件，并自动转数据 SPSS 格式。 SPSS 也可使用数据库查询或文本读入方法打开许多类型的数据文件。（二）统计分析命令 SPSS 统计分析（Analyze）模块，有 13 个主命令，52 个子命令： 1.统计报表（Reports）：成行（在线）分层分析（OLAP Cubes）、个案综合分析（Case Summaries）、按行综合统计报表(Report Summaries in Rows）、按列综合统计报表（Report Summaries in Columns）。 2．描述性统计分析（Descriptive Statistics）：单变量频数分布分析（Frequencies）、描述性分析（Descriptive）、探索性分析（Explore）、列联表分析（Crosstabs）。 3．均数比较分析（Compare Means）；平均数分析（Means）、单样本 t 检验（One-Sample T Test), 独立样本 t 检验（ Independent － Samples T Test ）、配对样本 t 检验（Paried-Samples T Test）。单因素方差分析（One－Way ANOVA）。 4．一般线性模型（General Linear Model）：单变量方差分析（Univariate）、多变量方差分析（Multivariate）、重复测量方差分析（Repeated Measures）、方差分量估计法（Variance Components）。 5．相关分析（Correlate）:双变量相关分析（Bivariate）、偏相关分析（Partial）、距离相关分析（Distances)。 6．回归分析（Regression）：线性回归分析（Linear），曲线参数估计法（Curve Estimation）、二值多元 Logistic 回归分析（ Binary Logistic ）、多项多元 Logistic 回归分析（Multinomial Logistic）、概率单位法（Probit)、非线性回归分析（Nonlinear）、权重估计法（Weight Estimation）、二阶段最小二乘回归分析（2-Stage Least Squares）。