Free Essay

Mathematical Methods of Optimal Planing

In: Other Topics

Submitted By easyessay
Words 254
Pages 2
МІНІСТЕРСТВО ОСВІТИ I НАУКИ УКРАЇНИ
НАЦІОНАЛЬНИЙ УНІВЕРСИТЕТ “ЛЬВІВСЬКА ПОЛІТЕХНІКА”

Кафедра прикладної математики

Звіт про виконання лабораторної роботи №1 з курсу “Математичні методи оптимального планування” на тему:
“Обчислення МНК-оцінки класичної лінійної регресійної моделі на відрізку”
Варіант №9

Виконав:
Прийняв:

Львів-2014

Постановка задачі
Розглядається класична лінійна регресійна модель з поліноміальною функцією регресії 5-го порядку , ; , — вектор похибок, компоненти якого мають нормальний розподіл , тобто , . — сукупність точок, в яких проводяться спостереження. Значення параметрів регресії . Потрібно передбачити вивід проміжних даних: матрицю плану , матрицю , МНК-оцінку . Порівняти значення функції регресії для вхідних параметрів і знайдених параметрів .
Хід роботи
Для виконання роботи використовую пакет прикладних програм Maple. 1. Сукупність точок спостережень задаю двома способами:
а) набір точок відрізку , що задовольняє умову :
>
>
>
>
>
>
>
>
>
>
б) рівномірно розподілений набір точок на відрізку :
>
>

Для задання матриці плану експерименту

використовую таку конструкцію:
>
2. Моделюю вектор похибок , , де має – нормальний розподіл:
>
3. Обчислюю вектор результатів спостережень , використовуючи формулу :
>
>
>
4. Обчислюю МНК-оцінку для вектора наступним чином :
У випадку а) отримую такий результат:
>
>
>

У випадку б) отримую такий результат:
>
>
>

5. Порівнюю функції і . Для побудови графіків використовую таку функцію Maple: plot ({f(v), h(v)}, v=a..b), де f , h – функції, a, b – межі зміни v.
а)
>

б)
>

Висновок:під час виконання лабораторної роботи я обчислив вектор результатів спостережень , МНК-оцінку для вектора , дисперсію МНК-оцінки , а також оцінку дисперсії . Порівняв значення функції регресії для вхідних параметрів і знайдених параметрів .

Similar Documents

Premium Essay

Supply Chain

...all, I would like to give special thanks to my supervisor Mikael R¨nnqvist o for giving support, inspiration and guidance. Your positive attitude and enthusiasm have meant much to me. I would also like to thank my co-supervisor Jan Lundgren for your support, encouragement and guidance in writing. Thanks to Dick Carlsson at S¨dra Cell AB for very good cooperation and friendo ship. I am grateful to Torbj¨rn Larsson, for always taken time for discussions cono cerning both research and teaching. I appreciate my friendship with Maud G¨the-Lundgren. o Thanks to Mathias Henningsson for good cooperation in teaching and J¨rgen o Blomvall for helping me with computer problems. Thanks to Kaj Holmberg for interesting discussions about decomposition methods. Thanks to Oleg Burdakov and Sven Erlander for encouragement. The group of PhD students has been important for me. Thanks to Maria Daneva, Elina R¨nnberg, Per-˚ke Andersson and Kristian Lundberg for supo A porting me and for all fun discussions. Thanks also to my former colleagues, I miss you all. Thanks to David Bredstr¨m for generating the routes in the second paper. o Thanks also to Anders Folkesson, Kent Hjelm, and Bertil Thunstr¨m at Sydved o Energileveranser AB for good cooperation. Thanks to Pamela Vang and Bj¨rn Lidestam for helping me improving the o English. Thanks to Monika Gustafsson and the other administrative staff who always are willing to provide. Many thanks to...

Words: 10305 - Pages: 42

Premium Essay

Distribution Channel

...Proposing a Research Agenda for Swedish Sawmill Distribution Channel Challenges Åsa Gustafsson asa.gustafsson@lnu.se Lars-Olof Rask lars-olof.rask@lnu.se School of Engineering Linnaeus University, Växjö, Sweden Abstract Purpose; The purpose of this study is to identify distribution channel research needs given the variety of distribution channel challenges among Swedish sawmill companies. Design / methodology / approach; Explorative case study research Findings: The paper proposes a typology of sawmill distribution channel challenges, as well as aligns research needs with distribution channel type. The typology is based on i) number of sawmill units within the firm, in combination with ii) distribution channel heterogeneity. Significant management decisions and research needs are identified for the different types. Research limitations / implications; This research makes tentative statements regarding typology of sawmill distribution channel challenges and potential research needs in the Swedish sawmill industry with regards to the respective typology. However, further research is needed in order to validate these results. What is original/value of paper: This paper focus on the sawmill industry distribution channels, which is a neglected but important area for sawmill’s competitive advantage. The paper also contributes to research by applying contingency theory and typology as an approach to deal with the variety of sawmills distribution channel challenges. Keywords; Typology...

Words: 4034 - Pages: 17

Free Essay

S2S Business Model

...support the social processes of constructing shared vision. These operate on the layer of participants' cognitive processes, to integrate the different participants' views into a unified, shared framework that heightens understanding and commitment. Example scenario planning projects from two industries, electric utilities and software research, are summarized to demonstrate lessons learned that enhance the facilitation of scenarios as a group process. Introduction Scenarios are a commonly used management technique. There is wide variation in the details of their application. This paper briefly summarizes the growing attention to vision as a necessary component of leadership in organizations, and then describes the Scenarios-toStrategies method (S2S) and its benefits. Features of the S2S are presented in contrast with another approach that is here labeled 'Level One Scenarios'. An example of a Level One Scenario approach is available as a...

Words: 9260 - Pages: 38

Free Essay

Nit-Silchar B.Tech Syllabus

...NATIONAL INSTITUTE OF TECHNOLOGY SILCHAR Bachelor of Technology Programmes amï´>r¶ JH$s g§ñWmZ, m¡Úmo{ à VO o pñ Vw dZ m dY r V ‘ ñ Syllabi and Regulations for Undergraduate PROGRAMME OF STUDY (wef 2012 entry batch) Ma {gb Course Structure for B.Tech (4years, 8 Semester Course) Civil Engineering ( to be applicable from 2012 entry batch onwards) Course No CH-1101 /PH-1101 EE-1101 MA-1101 CE-1101 HS-1101 CH-1111 /PH-1111 ME-1111 Course Name Semester-1 Chemistry/Physics Basic Electrical Engineering Mathematics-I Engineering Graphics Communication Skills Chemistry/Physics Laboratory Workshop Physical Training-I NCC/NSO/NSS L 3 3 3 1 3 0 0 0 0 13 T 1 0 1 0 0 0 0 0 0 2 1 1 1 1 0 0 0 0 4 1 1 0 0 0 0 0 0 2 0 0 0 0 P 0 0 0 3 0 2 3 2 2 8 0 0 0 0 0 2 2 2 2 0 0 0 0 0 2 2 2 6 0 0 8 2 C 8 6 8 5 6 2 3 0 0 38 8 8 8 8 6 2 0 0 40 8 8 6 6 6 2 2 2 40 6 6 8 2 Course No EC-1101 CS-1101 MA-1102 ME-1101 PH-1101/ CH-1101 CS-1111 EE-1111 PH-1111/ CH-1111 Course Name Semester-2 Basic Electronics Introduction to Computing Mathematics-II Engineering Mechanics Physics/Chemistry Computing Laboratory Electrical Science Laboratory Physics/Chemistry Laboratory Physical Training –II NCC/NSO/NSS Semester-4 Structural Analysis-I Hydraulics Environmental Engg-I Structural Design-I Managerial Economics Engg. Geology Laboratory Hydraulics Laboratory Physical Training-IV NCC/NSO/NSS Semester-6 Structural Design-II Structural Analysis-III Foundation Engineering Transportation Engineering-II Hydrology &Flood...

Words: 126345 - Pages: 506

Premium Essay

Management

...Subject: Management Concepts and Organizational Behaviour Subject: Management Concepts and Organizational Behaviour ------------------------------------------------- Subject Code: MC-101 Author: Dr. Karam Pal ------------------------------------------------- Lesson No: 01 Vetter: Prof. Harbhajan Bansal ------------------------------------------------- Subject Code: MC-101 Author: Dr. Karam Pal ------------------------------------------------- Lesson No: 01 Vetter: Prof. Harbhajan Bansal INTRODUCTION TO MANAGEMENT Objective: The objectives of this lesson are to enable to define management; to describe the nature and scope of management; to know the difference between management and administration; to understand various levels of management; and to describe the various skills that are necessary for successful managers. Lesson Structure: 1.1 Introduction 1.2 Definition of Management 1.3 Characteristics of Management 1.4 Management Functions/ the Process of Management 1.5 N ature of Management 1.6 Management Vs. Administration 1.7 Levels of Management 1.8 Managerial Skills 1.9 The Manager and his job 1.10 Principles of Management 1.11 Significance of Management 1.12 Summary 1.13 Self Assessment Questions 1.14 Suggested Readings 1.1 INTRODUCTION A business develops in course of time with complexities. With increasing complexities managing the business has become a difficult...

Words: 50220 - Pages: 201

Free Essay

Machine Learning

...Foundations of Machine Learning Adaptive Computation and Machine Learning Thomas Dietterich, Editor Christopher Bishop, David Heckerman, Michael Jordan, and Michael Kearns, Associate Editors A complete list of books published in The Adaptive Computations and Machine Learning series appears at the back of this book. Foundations of Machine Learning Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar The MIT Press Cambridge, Massachusetts London, England c 2012 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email special sales@mitpress.mit.edu or write to Special Sales Department, The MIT Press, 55 Hayward Street, Cambridge, MA 02142. A This book was set in L TEX by the authors. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Mohri, Mehryar. Foundations of machine learning / Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. p. cm. - (Adaptive computation and machine learning series) Includes bibliographical references and index. ISBN 978-0-262-01825-8 (hardcover : alk. paper) 1. Machine learning. 2. Computer algorithms. I. Rostamizadeh, Afshin. II...

Words: 137818 - Pages: 552

Premium Essay

Scp and Sap Apo

...Supply Chain Management and Advanced Planning Hartmut Stadtler ´ Christoph Kilger (Eds.) Supply Chain Management and Advanced Planning Concepts, Models, Software and Case Studies Third Edition With 173 Figures and 56 Tables 12 Professor Dr. Hartmut Stadtler FG Produktion und Supply Chain Management FB Rechts- und Wirtschaftswissenschaften TU Darmstadt Hochschulstraûe 1 64289 Darmstadt Germany stadtler@bwl.tu-darmstadt.de Dr. Christoph Kilger j&m Management Consulting AG Kaiserringforum Willy-Brandt-Platz 5 68161 Mannheim Germany christoph.kilger@jnm.de Cataloging-in-Publication Data Library of Congress Control Number: 2004110194 ISBN 3-540-22065-8 Springer Berlin Heidelberg New York ISBN 3-540-43450-X 2nd edition Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com ° Springer Berlin ´ Heidelberg 2000, 2002, 2005 Printed...

Words: 180845 - Pages: 724

Premium Essay

Application of Qualitative and Quantitave Techniques of Management

...APPLICATIONS OF QUALITATIVE AND QUANTITATIVE TECHNIQUES OF MANAGEMENT IN ADMINISTRATIVE/ACADEMIC DECISION-MAKING IN INSTITUTIONS OF HIGHER EDUCATION IN VIRGINIA by Carlos A. Valero Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION in Educational Administration APPROVED: ______________________ Don G. Creamer, Chairman __________________________________ ____________________________ Karl T. Hereford _________________________ Stephen R. Parson January, 1997 Blacksburg, Virginia David J. Parks ____________________ John W. Dickey APPLICATIONS OF QUALITATIVE AND QUANTITATIVE TECHNIQUES OF MANAGEMENT IN ADMINISTRATIVE/ACADEMIC DECISION-MAKING IN INSTITUTIONS OF HIGHER EDUCATION IN VIRGINIA by Carlos A. Valero Educational Administration Don G. Creamer, Chair Abstract The purpose of this study was to examine the status and extent to which administrators of colleges and universities in the state of Virginia apply qualitative and quantitative techniques of management in planning, directing, reporting, and controlling activities for enhancing their administrative and academic decision-making capability. The study was directed to the top and operative organizational levels in two categories of administrators (nonacademic and academic) to determine the types of managerial techniques used, degrees of familiarity with these techniques, frequency of...

Words: 49968 - Pages: 200

Free Essay

Maglev

...m and mud weight is 1.2 gm/cc. b) Calculate mud weight if mud gradient is 0.87 psi/ft. ′ c) Calculate volume bbl/meter for drill pipe O.D. = 5′ inch and I.D. = 4.276 inch. 2 2 2 10 8 8 16 d) Draw circulation system on a drilling rig. 3. a) Discuss IADC classification of a bit in details. b) Discuss different factors affecting rate of penetration in details. 4. Write short note on : i) Coring ii) Fishing tools iii) BOP iv) Directional well P.T.O. [3963] – 103 -2- *3963103* SECTION – II 5. a) Discuss different types of casings and function of the casings in brief. b) Discuss different types of well completion techniques. 6. a) Discuss primary cementation process with suitable sketch. b) Discuss different perforation methods in brief. 7. a) What are different types of packer ? Discuss any one in brief. b) Draw well head assembly for A, B and C section. 8. Write short note on : i) Drill stem test ii) SSSV iii) X – Mas tree iv) Squeeze cementation. ––––––––––––––––– 8 10 10 6 8 8 16 B/I/11/120 *3963108* [3963] – 108 T.E. (Petroleum)...

Words: 172166 - Pages: 689

Free Essay

Industrial Engineering

...part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher. This McGraw-Hill Create text may include materials submitted to McGraw-Hill for publication by the instructor of this course. The instructor is solely responsible for the editorial content of such materials. Instructors retain copyright of these additional materials. ISBN-10: 1121789048 ISBN-13: 9781121789043 McGraw-Hill Create™ Review Copy for Instructor Espinoza. Not for distribution. Contents 1. Preface 1 2. Methods, Standards, and Work Design: Introduction 7 Problem-Solving Tools 27 3. Tex 29 4. Operation Analysis 79 5. Manual Work Design 133 6. Workplace, Equipment, and Tool Design 185 7. Work Environment Design 239 8. Design of Cognitive Work 281 9. Workplace and Systems Safety 327 10. Proposed Method Implementation 379 11. Time Study 413 12. Performance Rating and Allowances 447 13. Standard Data and Formulas 485 14. Predetermined Time Systems 507 15. Work Sampling 553 16. Indirect and Expense Labor Standards 585 17. Standards Follow-Up and Uses 611 18. Wage Payment 631 19. Training and Other Management Practices 655 20. Appendix 1: Glossary 685 21. Appendix 2: Helpful Formulas 704 22. Appendix 3: Special Tables 706 23. Index 719 iii McGraw-Hill Create™ Review Copy for Instructor Espinoza. Not for distribution. Credits 1. Preface:...

Words: 294686 - Pages: 1179

Premium Essay

E-Book Supply Chain Management

...Introduction to Supply Chain Management Technologies Second Edition Introduction to Supply Chain Management Technologies Second Edition David Frederick Ross CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4398-3753-5 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval...

Words: 158845 - Pages: 636

Premium Essay

Marketing

...MASARYKOVA UNIVERZITA Ekonomicko-správní fakulta Studijní obor: Podnikové hospodářství Kombinované studium [pic] PROPOSAL OF A MARKETING STRATEGY Návrh marketingové strategie Diploma thesis /Diplomová práce Vedoucí diplomové práce/Supervisor: Autor/Author: Ing. Klára KAŠPAROVÁ Mgr. Jana LUDÍKOVÁ Brno, červen 2008 Brno, June 2008 |Jméno a příjmení autora: |Jana Ludíková | |Author´s name: | | |Název diplomové práce: |Návrh marketingové strategie | |Title of the diploma thesis: | | |Název práce v angličtině: |Proposal of a Marketing Strategy | |English title of the diploma thesis: | | |Katedra: |podnikového hospodářství | |Departement |of corporate economy | |Vedoucí diplomové...

Words: 32039 - Pages: 129

Premium Essay

Phd Thesis

...Towards a conceptual framework for strategic cost management - The concept, objectives, and instruments - Von der Fakultät für Wirtschaftswissenschaften der Technischen Universität Chemnitz genehmigte Dissertation zur Erlangung des akademischen Grades Doctor rerum politicarum (Dr. rer. pol.) vorgelegt von Ibrahim Abd El Mageed Ali El Kelety geboren am 11.01.1965 in El Menoufia - Ägypten eingereicht am: 14. Juni 2006 Gutachter: Prof. Dr. Uwe Götze Prof. Dr. Dr. h.c. Jürgen Bloech Prof. Dr. Peter Schuster Tag der mündlichen Prüfung: 18. Juli 2006 Acknowledgement To the Almighty God “ALLAH” Who have granted me all these graces to fulfill this work and Who supported me in all my life. To Him I extend my heartfelt thanks. It is a pleasure to express my sincere and deepest heartfelt gratitude to my “Doktorvater“ Prof. Dr. Uwe Götze for his kind supervision, continuous encouragement, valuable enthusiastic discussion and unfailing advice throughout the present work, as well as financial support during my latest period of study in Germany. He assisted in all matters, provided solutions to different problems. Prof. Dr. Uwe Götze supported and helped me during my learning period in Germany and writing this thesis. I am very lucky being one of his students. I would like to express my deep thanks to Prof. Dr. Dr. h.c. Jürgen Bloech - Georg-August University of Göttingen - for his kind acceptance to act as an examiner. I would also like to express my sincere thanks to Prof. Dr. Peter...

Words: 197356 - Pages: 790

Premium Essay

Cataolog

...ork2012 - 2013 Catalog A Message from the President “Sullivan University is truly a unique and student success focused institution.” I have shared that statement with numerous groups and it simply summarizes my basic philosophy of what Sullivan is all about. When I say that Sullivan is “student success focused,” I feel as President that I owe a definition of this statement to all who are considering Sullivan University. First, Sullivan is unique among institutions of higher education with its innovative, career-first curriculum. You can earn a career diploma or certificate in a year or less and then accept employment while still being able to complete your associate, bachelor’s, master’s or doctoral degree by attending during the day, evenings, weekends, or online. Business and industry do not expand or hire new employees only in May or June each year. Yet most institutions of higher education operate on a nine-month school year with almost everyone graduating in May. We remained focused on your success and education, and continue to offer our students the opportunity to begin classes or to graduate four times a year with our flexible, year-round full-time schedule of classes. If you really want to attend a school where your needs (your real needs) come first, consider Sullivan University. I believe we can help you exceed your expectations. Since words cannot fully describe the atmosphere at Sullivan University, please accept my personal invitation to visit and experience...

Words: 103133 - Pages: 413

Premium Essay

Kelly & Nokes

...Now the perfect companion for anyone sitting the PMI’s PMBOK exams THE DEFINITIVE 2ND EDITION PROJECT MANAGEMENT THE FAST TRACK TO GETTING THE SEBASTIAN NOKES AND SEAN KELLY GUIDE TO JOB DONE ON TIME AND ON BUDGET the definitive guide to project management In an increasingly competitive world, we believe it’s quality of thinking that gives you the edge – an idea that opens new doors, a technique that solves a problem, or an insight that simply makes sense of it all. The more you know, the smarter and faster you can go. That’s why we work with the best minds in business and finance to bring cutting-edge thinking and best learning practice to a global market. Under a range of leading imprints, including Financial Times Prentice Hall, we create world-class print publications and electronic products bringing our readers knowledge, skills and understanding, which can be applied whether studying or at work. To find out more about Pearson Education publications, or tell us about the books you’d like to find, you can visit us at www.pearsoned.co.uk the definitive guide to project management the fast track to getting the job done on time and on budget Second Edition SEBASTIAN NOKES AND SEAN KELLY PEARSON EDUCATION LIMITED Edinburgh Gate Harlow CM20 2JE United Kingdom Tel: +44(0)1279 623623 Fax: +44(0)1279 431059 Website: www.pearsoned.co.uk First published 2003 Second edition published in Great Britain 2007 © Aldersgate Partners LLP 2003 © Casnus Limited...

Words: 144594 - Pages: 579