Modeling the Relationship between Software Effort and Size Using Deming Regression
|
|
|
- Asher Gilmore
- 5 years ago
- Views:
Transcription
1 Modeling the Relationship between Software Effort and Size Using Deming Regression Nikolaos Mittas Makrina Viola Kosti Basiliki Argyropoulou Lefteris Angelis Programming Languages & Software Engineering Lab Department of Informatics Aristotle University of Thessaloniki, Greece {nmittas, mkosti, vargyrop, PROMISE 2010, September 12-13, Timisoara, Romania 1
2 Presentation Outline!! Motivation and Objectives "! Research questions!! Definitions and Description!! Methodology of Experimentation "! Dataset "! Evaluation method!! Results and Conclusions!! Directions of Future Research PROMISE 2010, September 12-13, Timisoara, Romania 2
3 The Research Problem in Software Cost Estimation (SCE)!! Accurate prediction of software cost needed!! Plethora of prediction methods "! Expert judgment to statistical models and machine learning techniques!! The General Research problem "! Identification of the best prediction technique for a certain dataset!! Findings from literature contradictory - no global answer "! Lack of standardization in SCE methodologies, measurement, reporting techniques, terminology, etc "! Accuracy depends on dataset PROMISE 2010, September 12-13, Timisoara, Romania 3
4 Motivation!! Regression Analysis (RA) (especially Ordinary Least Squares OLS)! Well-known modeling technique: "! Various forms of regression for modeling the relationship between effort and size!! Despite the popularity of OLS in SCE! Several restrictions: "! OLS it is assumed that the values of the independent variable (i.e. size) are measured without errors!! The assumption of error-free measurement is not so realistic in SCE: "! Software size is the result of a counting and estimating process derived from a tool or an expert (Source Lines of Code (SLOC) or Function Points (FP)) PROMISE 2010, September 12-13, Timisoara, Romania 4
5 Related Work!! Literature Regression forms "! Miyazaki et al.(1991)!! Regression based on relative errors "! Chen & Stromberg (1997)!! Heteroscedasticity (LMS, Least Median of Squares LTS, Least Trimmed Squares ) "! Pickard et al. (1999)!! RR, Robust Regression LAD, Least Absolute Deviation!! Inaccuracy of measurement "! Miyazaki et al.(1994) "! Foss et al. (2001) PROMISE 2010, September 12-13, Timisoara, Romania 5
6 Proposed Model!! Deming regression! Improvement of the process for modeling the relationship between effort and size!! Deming regression! General class of errors-in-variables models: "! Appropriate in situations where random errors exist in the measurements of both the independent and the dependent variable PROMISE 2010, September 12-13, Timisoara, Romania 6
7 Modeling the SCE Procedure!! SCE is the procedure of predicting the cost of a new project!! Let: "! Y "! X! Real random dependent variable representing the cost of projects! Real random variable representing the size of projects!! Goal to find a regression function "!! i! Real random error PROMISE 2010, September 12-13, Timisoara, Romania 7
8 Parametric Estimation Technique!! Ordinary Least Squares (OLS) Regression!! Objective: "! Minimization of the overall Sum of Squared Residuals (SSR)!! Final estimation of constant (! 0 ) and slope (! 1 ) where PROMISE 2010, September 12-13, Timisoara, Romania 8
9 Proposed Model!!Deming Regression: "! A form of errors-in-variables model "! Takes into account:!!the error arising from the dependent variable (effort) (similarly OLS)!!The error in measurement of the independent variable (size) PROMISE 2010, September 12-13, Timisoara, Romania 9
10 Theoretical Model (1/2)!! Notation "! (X i,y i )! True unknown observations "! (x i,y i )! Erroneously measured observations "! (! i," i )! Error terms!! Constant ratio # of error variances!! Deming Regression Model PROMISE 2010, September 12-13, Timisoara, Romania 10
11 Theoretical Model (2/2)!! Deming Regression!! Objective: "! Minimization of the overall weighted Sum of Squared Residuals (SSR) PROMISE 2010, September 12-13, Timisoara, Romania 11
12 Estimation of Coefficients!! Final estimation of constant (! 0 ), slope (! 1 ) and X where PROMISE 2010, September 12-13, Timisoara, Romania 12
13 Methodology (Datasets)!! Desharnais "! 77 completed software projects from a Canadian Software house "! The project size measured with FPs!! COCOMO81 "! COCOMO81! Public domain database "! The project size is measured with SLOCs!! Maxwell "! 62 projects from a commercial Finnish bank "! The project size measured with FPs!! Nasa93 "! 93 projects from different centers "! The project size measured with SLOCs For better fitting, size and effort were logarithmically transformed PROMISE 2010, September 12-13, Timisoara, Romania 13
14 Methodology (Accuracy measures)!! The predictive accuracy of the cost model is usually based on local measures of error "! Absolute Error (AE) "! The Magnitude of Relative Error (MRE)!! The global accuracy measures are: "! Mean and Median Magnitude of Relative Error (MMRE, MdMRE) "! Mean and Median of Absolute Error (MAE, MdAE) "! Percentage of projects with MRE!25% (pred25) PROMISE 2010, September 12-13, Timisoara, Romania 14
15 Methodology (Graphical Comparison)!! Graphical analysis through Regression Errror Characteristic (REC) curves!! 2-dimensional plot: "! x-axis! the error tolerance of a predefined accuracy measure "! y-axis! the accuracy of a prediction model!! Trade-off between accuracy and tolerance: "! The accuracy of a model increases as the error tolerance becomes higher "! e=0! only the predictions that are identical to actual values considered accurate PROMISE 2010, September 12-13, Timisoara, Romania 15
16 Desharnais Dataset Deming (solid line) vs. OLS (dashed line) PROMISE 2010, September 12-13, Timisoara, Romania 16
17 Accuracy Measures (Desharnais)!Deming outperforms for all accuracy measures!the improvement ranges from 67.60% (MdMRE) up to % (pred25)!the Wilcoxon test statistically signifies the difference for AEs!Error reduction achieved by Deming
18 COCOMO81 Dataset Deming (solid line) vs. OLS (dashed line) PROMISE 2010, September 12-13, Timisoara, Romania 18
19 Accuracy Measures (COCOMO81)!Deming outperforms for all accuracy measures!the improvement ranges from 51.20% (MAE) up to % (pred25)!the Wilcoxon test statistically signifies the difference for AEs!AE distribution of OLS! High variability!rec curve for Deming dominates
20 Maxwell Dataset Deming (solid line) vs. OLS (dashed line) PROMISE 2010, September 12-13, Timisoara, Romania 20
21 Accuracy Measures (Maxwell)!Deming outperforms for all accuracy measures!the improvement ranges from 46.52% (MdAE) up to % (pred25)!the Wilcoxon test statistically signifies the difference for AEs!AE distribution of OLS! High variability with a long upper tail!rec curve for Deming dominates! Solid line climbs rapidly to 1
22 NASA93 Dataset Deming (solid line) vs. OLS (dashed line) PROMISE 2010, September 12-13, Timisoara, Romania 22
23 Accuracy Measures (NASA93)!Deming outperforms for all accuracy measures!the improvement ranges from 42.59% (MdAE) up to 93.58% (pred25)!the Wilcoxon test statistically signifies the difference for AEs!AE distribution of OLS! Slightly higher variability!rec curve for Deming dominates
24 Conclusions (1/2)!! Study of modeling the relationship between effort and size!! Main idea: "! OLS is applied under the assumption that the observed values of the variables are measurements which coincide with the true values "! Not realistic assumption in SCE! Heterogeneous projects with respect to:!! Nature!! The way they were measured PROMISE 2010, September 12-13, Timisoara, Romania 24
25 Conclusions (2/2)!! Goal of this paper: "! Application of Deming regression "! Alternative robust technique! Beneficial:!! Counting process of the size is characterized by uncertainty due to: #! Subjective decisions of the practitioners #! Tools!! Significant improvement compared to OLS: "! Several accuracy measures "! Graphical inspection (REC curves, boxplots) "! Statistical tests (Wilcoxon matched paired) PROMISE 2010, September 12-13, Timisoara, Romania 25
26 Future Work (1/2)!! Method deserves a deeper and thorough study!! Construction of Prediction Intervals (PI)! optimistic and pessimistic guess for the true magnitude of the cost: "! Researchers suggest that PI! Realistic estimate accounting for both uncertainty and risk "! Under the assumption of error in measurement! Point estimate is meaningless:!! Expresses not the response to the true size value, but the response to the measured value PROMISE 2010, September 12-13, Timisoara, Romania 26
27 Future Work (2/2)!! Introduction of more explanatory (or independent) variables in the model! Increase the percent of variability of the effort that is explained by the cost function!! Examination of the performance of the comparative models to different situations: "! Systematic treatment trough simulation "! Errors of the independent variable ranges from a small amount into a high source of variability PROMISE 2010, September 12-13, Timisoara, Romania 27
28 PROMISE 2010, September 12-13, Timisoara, Romania 28
Case Study on Software Effort Estimation
International Journal of Information and Electronics Engineering, Vol. 7, No. 3, May 217 Case Study on Software Estimation Tülin Erçelebi Ayyıldız and Hasan Can Terzi Abstract Since most of the projects
Econometrics I Lecture 3: The Simple Linear Regression Model
Econometrics I Lecture 3: The Simple Linear Regression Model Mohammad Vesal Graduate School of Management and Economics Sharif University of Technology 44716 Fall 1397 1 / 32 Outline Introduction Estimating
Introduction to Linear regression analysis. Part 2. Model comparisons
Introduction to Linear regression analysis Part Model comparisons 1 ANOVA for regression Total variation in Y SS Total = Variation explained by regression with X SS Regression + Residual variation SS Residual
Revisiting Software Development Effort Estimation Based on Early Phase Development Activities
Revisiting Software Development Effort Estimation Based on Early Phase Development Activities Masateru Tsunoda Toyo University Saitama, Japan tsunoda@ieee.org Koji Toda Fukuoka Institute of Technology
Chapter 1 - Lecture 3 Measures of Location
Chapter 1 - Lecture 3 of Location August 31st, 2009 Chapter 1 - Lecture 3 of Location General Types of measures Median Skewness Chapter 1 - Lecture 3 of Location Outline General Types of measures What
Machine Learning Linear Classification. Prof. Matteo Matteucci
Machine Learning Linear Classification Prof. Matteo Matteucci Recall from the first lecture 2 X R p Regression Y R Continuous Output X R p Y {Ω 0, Ω 1,, Ω K } Classification Discrete Output X R p Y (X)
Preliminary Causal Analysis Results with Software Cost Estimation Data
Preliminary Causal Analysis Results with Software Cost Estimation Data Anandi Hira, Barry Boehm University of Southern California Robert Stoddard, Michael Konrad Software Engineering Institute Motivation
Practical Statistics for the Analytical Scientist Table of Contents
Practical Statistics for the Analytical Scientist Table of Contents Chapter 1 Introduction - Choosing the Correct Statistics 1.1 Introduction 1.2 Choosing the Right Statistical Procedures 1.2.1 Planning
BNAD 276 Lecture 10 Simple Linear Regression Model
1 / 27 BNAD 276 Lecture 10 Simple Linear Regression Model Phuong Ho May 30, 2017 2 / 27 Outline 1 Introduction 2 3 / 27 Outline 1 Introduction 2 4 / 27 Simple Linear Regression Model Managerial decisions
Robustness and Distribution Assumptions
Chapter 1 Robustness and Distribution Assumptions 1.1 Introduction In statistics, one often works with model assumptions, i.e., one assumes that data follow a certain model. Then one makes use of methodology
DEMAND ESTIMATION (PART III)
BEC 30325: MANAGERIAL ECONOMICS Session 04 DEMAND ESTIMATION (PART III) Dr. Sumudu Perera Session Outline 2 Multiple Regression Model Test the Goodness of Fit Coefficient of Determination F Statistic t
NRC Workshop - Probabilistic Flood Hazard Assessment Jan 2013
Regional Precipitation-Frequency Analysis And Extreme Storms Including PMP Current State of Understanding/Practice Mel Schaefer Ph.D. P.E. MGS Engineering Consultants, Inc. Olympia, WA NRC Workshop - Probabilistic
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Exploring Data: Distributions Look for overall pattern (shape, center, spread) and deviations (outliers). Mean (use a calculator): x = x 1 + x
Cost Analysis and Estimating for Engineering and Management
Cost Analysis and Estimating for Engineering and Management Chapter 6 Estimating Methods Ch 6-1 Overview Introduction Non-Analytic Estimating Methods Cost & Time Estimating Relationships Learning Curves
Regression Analysis. BUS 735: Business Decision Making and Research. Learn how to detect relationships between ordinal and categorical variables.
Regression Analysis BUS 735: Business Decision Making and Research 1 Goals of this section Specific goals Learn how to detect relationships between ordinal and categorical variables. Learn how to estimate
FORECASTING STANDARDS CHECKLIST
FORECASTING STANDARDS CHECKLIST An electronic version of this checklist is available on the Forecasting Principles Web site. PROBLEM 1. Setting Objectives 1.1. Describe decisions that might be affected
Hierarchical models for the rainfall forecast DATA MINING APPROACH
Hierarchical models for the rainfall forecast DATA MINING APPROACH Thanh-Nghi Do dtnghi@cit.ctu.edu.vn June - 2014 Introduction Problem large scale GCM small scale models Aim Statistical downscaling local
Parametric Estimating Nonlinear Regression
Parametric Estimating Nonlinear Regression The term nonlinear regression, in the context of this job aid, is used to describe the application of linear regression in fitting nonlinear patterns in the data.
Econometric Forecasting Overview
Econometric Forecasting Overview April 30, 2014 Econometric Forecasting Econometric models attempt to quantify the relationship between the parameter of interest (dependent variable) and a number of factors
Preliminary Causal Analysis Results with Software Cost Estimation Data. Anandi Hira, Bob Stoddard, Mike Konrad, Barry Boehm
Preliminary Causal Analysis Results with Software Cost Estimation Data Anandi Hira, Bob Stoddard, Mike Konrad, Barry Boehm Parametric Cost Models COCOMO II Effort =2.94 Size E 17 i=1 EM i u Input: size,
MS&E 226: Small Data
MS&E 226: Small Data Lecture 3: More on linear regression (v3) Ramesh Johari ramesh.johari@stanford.edu 1 / 59 Recap: Linear regression 2 / 59 The linear regression model Given: n outcomes Y i, i = 1,...,
Inference for Regression Inference about the Regression Model and Using the Regression Line, with Details. Section 10.1, 2, 3
Inference for Regression Inference about the Regression Model and Using the Regression Line, with Details Section 10.1, 2, 3 Basic components of regression setup Target of inference: linear dependency
Note on Bivariate Regression: Connecting Practice and Theory. Konstantin Kashin
Note on Bivariate Regression: Connecting Practice and Theory Konstantin Kashin Fall 2012 1 This note will explain - in less theoretical terms - the basics of a bivariate linear regression, including testing
Basic Business Statistics 6 th Edition
Basic Business Statistics 6 th Edition Chapter 12 Simple Linear Regression Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of a dependent variable based
Accounting for measurement uncertainties in industrial data analysis
Accounting for measurement uncertainties in industrial data analysis Marco S. Reis * ; Pedro M. Saraiva GEPSI-PSE Group, Department of Chemical Engineering, University of Coimbra Pólo II Pinhal de Marrocos,
Class time (Please Circle): 11:10am-12:25pm. or 12:45pm-2:00pm
Name: UIN: Class time (Please Circle): 11:10am-12:25pm. or 12:45pm-2:00pm Instructions: 1. Please provide your name and UIN. 2. Circle the correct class time. 3. To get full credit on answers to this exam,
Lecture 3: Statistical Decision Theory (Part II)
Lecture 3: Statistical Decision Theory (Part II) Hao Helen Zhang Hao Helen Zhang Lecture 3: Statistical Decision Theory (Part II) 1 / 27 Outline of This Note Part I: Statistics Decision Theory (Classical
Part 8: GLMs and Hierarchical LMs and GLMs
Part 8: GLMs and Hierarchical LMs and GLMs 1 Example: Song sparrow reproductive success Arcese et al., (1992) provide data on a sample from a population of 52 female song sparrows studied over the course
Chapter 8 Handout: Interval Estimates and Hypothesis Testing
Chapter 8 Handout: Interval Estimates and Hypothesis esting Preview Clint s Assignment: aking Stock General Properties of the Ordinary Least Squares (OLS) Estimation Procedure Estimate Reliability: Interval
Regression Analysis: Basic Concepts
The simple linear model Regression Analysis: Basic Concepts Allin Cottrell Represents the dependent variable, y i, as a linear function of one independent variable, x i, subject to a random disturbance
1 A Non-technical Introduction to Regression
1 A Non-technical Introduction to Regression Chapters 1 and Chapter 2 of the textbook are reviews of material you should know from your previous study (e.g. in your second year course). They cover, in
Chapter 9 Regression with a Binary Dependent Variable. Multiple Choice. 1) The binary dependent variable model is an example of a
Chapter 9 Regression with a Binary Dependent Variable Multiple Choice ) The binary dependent variable model is an example of a a. regression model, which has as a regressor, among others, a binary variable.
Introduction Robust regression Examples Conclusion. Robust regression. Jiří Franc
Robust regression Robust estimation of regression coefficients in linear regression model Jiří Franc Czech Technical University Faculty of Nuclear Sciences and Physical Engineering Department of Mathematics
Evaluation. Andrea Passerini Machine Learning. Evaluation
Andrea Passerini passerini@disi.unitn.it Machine Learning Basic concepts requires to define performance measures to be optimized Performance of learning algorithms cannot be evaluated on entire domain
Prediction of Bike Rental using Model Reuse Strategy
Prediction of Bike Rental using Model Reuse Strategy Arun Bala Subramaniyan and Rong Pan School of Computing, Informatics, Decision Systems Engineering, Arizona State University, Tempe, USA. {bsarun, rong.pan}@asu.edu
The OLS Estimation of a basic gravity model. Dr. Selim Raihan Executive Director, SANEM Professor, Department of Economics, University of Dhaka
The OLS Estimation of a basic gravity model Dr. Selim Raihan Executive Director, SANEM Professor, Department of Economics, University of Dhaka Contents I. Regression Analysis II. Ordinary Least Square
Evaluation requires to define performance measures to be optimized
Evaluation Basic concepts Evaluation requires to define performance measures to be optimized Performance of learning algorithms cannot be evaluated on entire domain (generalization error) approximation
Reducing Computation Time for the Analysis of Large Social Science Datasets
Reducing Computation Time for the Analysis of Large Social Science Datasets Douglas G. Bonett Center for Statistical Analysis in the Social Sciences University of California, Santa Cruz Jan 28, 2014 Overview
Turning a research question into a statistical question.
Turning a research question into a statistical question. IGINAL QUESTION: Concept Concept Concept ABOUT ONE CONCEPT ABOUT RELATIONSHIPS BETWEEN CONCEPTS TYPE OF QUESTION: DESCRIBE what s going on? DECIDE
Unsupervised Anomaly Detection for High Dimensional Data
Unsupervised Anomaly Detection for High Dimensional Data Department of Mathematics, Rowan University. July 19th, 2013 International Workshop in Sequential Methodologies (IWSM-2013) Outline of Talk Motivation
Correlation and Regression
Correlation and Regression October 25, 2017 STAT 151 Class 9 Slide 1 Outline of Topics 1 Associations 2 Scatter plot 3 Correlation 4 Regression 5 Testing and estimation 6 Goodness-of-fit STAT 151 Class
Regression Analysis: Exploring relationships between variables. Stat 251
Regression Analysis: Exploring relationships between variables Stat 251 Introduction Objective of regression analysis is to explore the relationship between two (or more) variables so that information
Introduction to Course
.. Introduction to Course Oran Kittithreerapronchai 1 1 Department of Industrial Engineering, Chulalongkorn University Bangkok 10330 THAILAND last updated: September 17, 2016 COMP METH v2.00: intro 1/
Lecture 16 - Correlation and Regression
Lecture 16 - Correlation and Regression Statistics 102 Colin Rundel April 1, 2013 Modeling numerical variables Modeling numerical variables So far we have worked with single numerical and categorical variables,
Nonlinear Regression Functions
Nonlinear Regression Functions (SW Chapter 8) Outline 1. Nonlinear regression functions general comments 2. Nonlinear functions of one variable 3. Nonlinear functions of two variables: interactions 4.
Mining Big Data Using Parsimonious Factor and Shrinkage Methods
Mining Big Data Using Parsimonious Factor and Shrinkage Methods Hyun Hak Kim 1 and Norman Swanson 2 1 Bank of Korea and 2 Rutgers University ECB Workshop on using Big Data for Forecasting and Statistics
The Model Building Process Part I: Checking Model Assumptions Best Practice
The Model Building Process Part I: Checking Model Assumptions Best Practice Authored by: Sarah Burke, PhD 31 July 2017 The goal of the STAT T&E COE is to assist in developing rigorous, defensible test
Learning Classification with Auxiliary Probabilistic Information Quang Nguyen Hamed Valizadegan Milos Hauskrecht
Learning Classification with Auxiliary Probabilistic Information Quang Nguyen Hamed Valizadegan Milos Hauskrecht Computer Science Department University of Pittsburgh Outline Introduction Learning with
Sociology 6Z03 Review I
Sociology 6Z03 Review I John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review I Fall 2016 1 / 19 Outline: Review I Introduction Displaying Distributions Describing
The Prediction of Monthly Inflation Rate in Romania 1
Economic Insights Trends and Challenges Vol.III (LXVI) No. 2/2014 75-84 The Prediction of Monthly Inflation Rate in Romania 1 Mihaela Simionescu Institute for Economic Forecasting of the Romanian Academy,
9/26/17. Ridge regression. What our model needs to do. Ridge Regression: L2 penalty. Ridge coefficients. Ridge coefficients
What our model needs to do regression Usually, we are not just trying to explain observed data We want to uncover meaningful trends And predict future observations Our questions then are Is β" a good estimate
Econometrics of Panel Data
Econometrics of Panel Data Jakub Mućk Meeting # 2 Jakub Mućk Econometrics of Panel Data Meeting # 2 1 / 26 Outline 1 Fixed effects model The Least Squares Dummy Variable Estimator The Fixed Effect (Within
The Model Building Process Part I: Checking Model Assumptions Best Practice (Version 1.1)
The Model Building Process Part I: Checking Model Assumptions Best Practice (Version 1.1) Authored by: Sarah Burke, PhD Version 1: 31 July 2017 Version 1.1: 24 October 2017 The goal of the STAT T&E COE
Simple Linear Regression
Simple Linear Regression Christopher Ting Christopher Ting : christophert@smu.edu.sg : 688 0364 : LKCSB 5036 January 7, 017 Web Site: http://www.mysmu.edu/faculty/christophert/ Christopher Ting QF 30 Week
Intermediate Econometrics
Intermediate Econometrics Markus Haas LMU München Summer term 2011 15. Mai 2011 The Simple Linear Regression Model Considering variables x and y in a specific population (e.g., years of education and wage
COMPARING PARAMETRIC AND SEMIPARAMETRIC ERROR CORRECTION MODELS FOR ESTIMATION OF LONG RUN EQUILIBRIUM BETWEEN EXPORTS AND IMPORTS
Applied Studies in Agribusiness and Commerce APSTRACT Center-Print Publishing House, Debrecen DOI: 10.19041/APSTRACT/2017/1-2/3 SCIENTIFIC PAPER COMPARING PARAMETRIC AND SEMIPARAMETRIC ERROR CORRECTION
Small Sample Corrections for LTS and MCD
myjournal manuscript No. (will be inserted by the editor) Small Sample Corrections for LTS and MCD G. Pison, S. Van Aelst, and G. Willems Department of Mathematics and Computer Science, Universitaire Instelling
HOOKE S LAW FORCE AND STRETCH OF A SPRING
HOOKE S LAW FORCE AND STRETCH OF A SPRING NAME DATE PERIOD Hooke's Law Lab Report 1 of 5 PURPOSE: The purpose of this experiment was to determine the relationship between the stretch of a spring and the
Fundamentals of data, graphical, and error analysis
Fundamentals of data, graphical, and error analysis. Data measurement and Significant Figures UTC - Physics 030L/040L Whenever we take a measurement, there are limitations to the data and how well we can
Transition Passage to Descriptive Statistics 28
viii Preface xiv chapter 1 Introduction 1 Disciplines That Use Quantitative Data 5 What Do You Mean, Statistics? 6 Statistics: A Dynamic Discipline 8 Some Terminology 9 Problems and Answers 12 Scales of
ON USING BOOTSTRAP APPROACH FOR UNCERTAINTY ESTIMATION
The First International Proficiency Testing Conference Sinaia, România 11 th 13 th October, 2007 ON USING BOOTSTRAP APPROACH FOR UNCERTAINTY ESTIMATION Grigore Albeanu University of Oradea, UNESCO Chair
Statistics for Managers using Microsoft Excel 6 th Edition
Statistics for Managers using Microsoft Excel 6 th Edition Chapter 13 Simple Linear Regression 13-1 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of
Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
What is Multiple Linear Regression Several independent variables may influence the change in response variable we are trying to study. When several independent variables are included in the equation, the
Big Data Analytics. Special Topics for Computer Science CSE CSE Feb 24
Big Data Analytics Special Topics for Computer Science CSE 4095-001 CSE 5095-005 Feb 24 Fei Wang Associate Professor Department of Computer Science and Engineering fei_wang@uconn.edu Prediction III Goal
Introduction to Statistical Data Analysis III
Introduction to Statistical Data Analysis III JULY 2011 Afsaneh Yazdani Preface Major branches of Statistics: - Descriptive Statistics - Inferential Statistics Preface What is Inferential Statistics? The
Statistics: A review. Why statistics?
Statistics: A review Why statistics? What statistical concepts should we know? Why statistics? To summarize, to explore, to look for relations, to predict What kinds of data exist? Nominal, Ordinal, Interval
Regression. Simple Linear Regression Multiple Linear Regression Polynomial Linear Regression Decision Tree Regression Random Forest Regression
Simple Linear Multiple Linear Polynomial Linear Decision Tree Random Forest Computational Intelligence in Complex Decision Systems 1 / 28 analysis In statistical modeling, regression analysis is a set
Regression Analysis for Data Containing Outliers and High Leverage Points
Alabama Journal of Mathematics 39 (2015) ISSN 2373-0404 Regression Analysis for Data Containing Outliers and High Leverage Points Asim Kumer Dey Department of Mathematics Lamar University Md. Amir Hossain
Week 3: Simple Linear Regression
Week 3: Simple Linear Regression Marcelo Coca Perraillon University of Colorado Anschutz Medical Campus Health Services Research Methods I HSMP 7607 2017 c 2017 PERRAILLON ALL RIGHTS RESERVED 1 Outline
Contents. Acknowledgments. xix
Table of Preface Acknowledgments page xv xix 1 Introduction 1 The Role of the Computer in Data Analysis 1 Statistics: Descriptive and Inferential 2 Variables and Constants 3 The Measurement of Variables
Regression Analysis. BUS 735: Business Decision Making and Research
Regression Analysis BUS 735: Business Decision Making and Research 1 Goals and Agenda Goals of this section Specific goals Learn how to detect relationships between ordinal and categorical variables. Learn
Class 7. Prediction, Transformation and Multiple Regression.
Class 7. Prediction, Transformation and Multiple Regression. 1 Today s material Prediction Transformation Multiple regression Robust regression Bootstrap 2 Prediction Two types corresponding to the data
Course Goals and Course Objectives, as of Fall Math 102: Intermediate Algebra
Course Goals and Course Objectives, as of Fall 2015 Math 102: Intermediate Algebra Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them. Represent
Multivariate Lineare Modelle
0-1 TALEB AHMAD CASE - Center for Applied Statistics and Economics Humboldt-Universität zu Berlin Motivation 1-1 Motivation Multivariate regression models can accommodate many explanatory which simultaneously
Bagging During Markov Chain Monte Carlo for Smoother Predictions
Bagging During Markov Chain Monte Carlo for Smoother Predictions Herbert K. H. Lee University of California, Santa Cruz Abstract: Making good predictions from noisy data is a challenging problem. Methods
Chapter 5: Ordinary Least Squares Estimation Procedure The Mechanics Chapter 5 Outline Best Fitting Line Clint s Assignment Simple Regression Model o
Chapter 5: Ordinary Least Squares Estimation Procedure The Mechanics Chapter 5 Outline Best Fitting Line Clint s Assignment Simple Regression Model o Parameters of the Model o Error Term and Random Influences
Single and multiple linear regression analysis
Single and multiple linear regression analysis Marike Cockeran 2017 Introduction Outline of the session Simple linear regression analysis SPSS example of simple linear regression analysis Additional topics
Applied Statistics and Econometrics
Applied Statistics and Econometrics Lecture 6 Saul Lach September 2017 Saul Lach () Applied Statistics and Econometrics September 2017 1 / 53 Outline of Lecture 6 1 Omitted variable bias (SW 6.1) 2 Multiple
Midwest Big Data Summer School: Introduction to Statistics. Kris De Brabanter
Midwest Big Data Summer School: Introduction to Statistics Kris De Brabanter kbrabant@iastate.edu Iowa State University Department of Statistics Department of Computer Science June 20, 2016 1/27 Outline
Electricity Demand Probabilistic Forecasting With Quantile Regression Averaging
Electricity Demand Probabilistic Forecasting With Quantile Regression Averaging Bidong Liu, Jakub Nowotarski, Tao Hong, Rafa l Weron Department of Operations Research, Wroc law University of Technology,
Accouncements. You should turn in a PDF and a python file(s) Figure for problem 9 should be in the PDF
Accouncements You should turn in a PDF and a python file(s) Figure for problem 9 should be in the PDF Please do not zip these files and submit (unless there are >5 files) 1 Bayesian Methods Machine Learning
Optimal Transport in Risk Analysis
Optimal Transport in Risk Analysis Jose Blanchet (based on work with Y. Kang and K. Murthy) Stanford University (Management Science and Engineering), and Columbia University (Department of Statistics and
y Xw 2 2 y Xw λ w 2 2
CS 189 Introduction to Machine Learning Spring 2018 Note 4 1 MLE and MAP for Regression (Part I) So far, we ve explored two approaches of the regression framework, Ordinary Least Squares and Ridge Regression:
Algebra I. CORE TOPICS (Key Concepts & Real World Context) UNIT TITLE
CHAPTER 1 Using variables Exponents and Order of Operations Exploring real numbers Adding real numbers Subtracting real numbers Multiplying and dividing real numbers The Distributive Property Properties
Available online at ScienceDirect. Procedia Engineering 119 (2015 ) 13 18
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 119 (2015 ) 13 18 13th Computer Control for Water Industry Conference, CCWI 2015 Real-time burst detection in water distribution
7.0 Lesson Plan. Regression. Residuals
7.0 Lesson Plan Regression Residuals 1 7.1 More About Regression Recall the regression assumptions: 1. Each point (X i, Y i ) in the scatterplot satisfies: Y i = ax i + b + ɛ i where the ɛ i have a normal
Visualization of distance measures implied by forecast evaluation criteria
Visualization of distance measures implied by forecast evaluation criteria Robert M. Kunst kunst@ihs.ac.at Institute for Advanced Studies Vienna and University of Vienna Presentation at RSS International
Inference for Regression
Inference for Regression Section 9.4 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 13b - 3339 Cathy Poliak, Ph.D. cathy@math.uh.edu
Forecast performance in times of terrorism
Forecast performance in times of terrorism FBA seminar at University of Macau Jonathan Benchimol 1 and Makram El-Shagi 2 This presentation does not necessarily reflect the views of the Bank of Israel December
Decision Tree Learning
Decision Tree Learning Berlin Chen Department of Computer Science & Information Engineering National Taiwan Normal University References: 1. Machine Learning, Chapter 3 2. Data Mining: Concepts, Models,
Finite Population Correction Methods
Finite Population Correction Methods Moses Obiri May 5, 2017 Contents 1 Introduction 1 2 Normal-based Confidence Interval 2 3 Bootstrap Confidence Interval 3 4 Finite Population Bootstrap Sampling 5 4.1
Relevance Vector Machines for Earthquake Response Spectra
2012 2011 American American Transactions Transactions on on Engineering Engineering & Applied Applied Sciences Sciences. American Transactions on Engineering & Applied Sciences http://tuengr.com/ateas
Developing a Military Aircraft Cost Estimating Model in Korea. June, 2013
Developing a Military Aircraft Cost Estimating Model in Korea June, 2013 Professor Sung Jin Kang, Ph. D. Dong Kyu Kim, KNDU Henry Apgar, MCR 1 / 43 Contents 1. Introduction 2. Development Process 3. R&D
IDENTIFYING MULTIPLE OUTLIERS IN LINEAR REGRESSION : ROBUST FIT AND CLUSTERING APPROACH
SESSION X : THEORY OF DEFORMATION ANALYSIS II IDENTIFYING MULTIPLE OUTLIERS IN LINEAR REGRESSION : ROBUST FIT AND CLUSTERING APPROACH Robiah Adnan 2 Halim Setan 3 Mohd Nor Mohamad Faculty of Science, Universiti
Lecture 7: Dynamic panel models 2
Lecture 7: Dynamic panel models 2 Ragnar Nymoen Department of Economics, UiO 25 February 2010 Main issues and references The Arellano and Bond method for GMM estimation of dynamic panel data models A stepwise
Christopher Dougherty London School of Economics and Political Science
Introduction to Econometrics FIFTH EDITION Christopher Dougherty London School of Economics and Political Science OXFORD UNIVERSITY PRESS Contents INTRODU CTION 1 Why study econometrics? 1 Aim of this
Preface Introduction to Statistics and Data Analysis Overview: Statistical Inference, Samples, Populations, and Experimental Design The Role of
Preface Introduction to Statistics and Data Analysis Overview: Statistical Inference, Samples, Populations, and Experimental Design The Role of Probability Sampling Procedures Collection of Data Measures
Empirical Bayesian Kriging
Empirical Bayesian Kriging Implemented in ArcGIS Geostatistical Analyst By Konstantin Krivoruchko, Senior Research Associate, Software Development Team, Esri Obtaining reliable environmental measurements
Power and nonparametric methods Basic statistics for experimental researchersrs 2017
Faculty of Health Sciences Outline Power and nonparametric methods Basic statistics for experimental researchersrs 2017 Statistical power Julie Lyng Forman Department of Biostatistics, University of Copenhagen
SUPERVISED LEARNING: INTRODUCTION TO CLASSIFICATION
SUPERVISED LEARNING: INTRODUCTION TO CLASSIFICATION 1 Outline Basic terminology Features Training and validation Model selection Error and loss measures Statistical comparison Evaluation measures 2 Terminology