Skinny on Least Squares and Polynomial Curve Fitting

Name: Skinny on Least Squares and Polynomial Curve Fitting
Price: 25.81 USD
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ISBN: 9781483919300

ISBN-10: 1483919307

ISBN-13: 9781483919300

Edition: N/A

Authors: Richard Eckhart

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THE SKINNYThis book gives you the skinny...the inside information, the real facts...about the method of least squares and polynomial curve fitting in a skinny...very thin, compact...format. This is a 'How to...' book presented in a format resembling a cookbook. As a consequence, mathematical derivations, proofs, theory, etc. are relegated to the Appendix.GENERAL BACKGROUND AND REVIEWCurve fitting is generally of interest for one of two reasons:(1) to allow the interpolation of an array or table of data; or(2) to allow the extrapolation of those data.In this book we focus on fitting data with an analytical polynomial in two dimensions, so that the data can either be interpolated or… extrapolated. More specifically, we focus on the method of least squares where it is desired to represent the entire data array with a single smooth analytical function.LEAST SQUARES METHODThe least squares method is not new. The method finds the best line to represent a set of data points such that the sum of the squares of the vertical distances of each data point from the proposed line is a minimum.Discussion of the method is frequently limited to a discussion of the use of least squares for establishing a linear trend or straight-line model of the data. In this book, we show how the least squares criterion can be used to find the best quadratic and cubic polynomial data models in addition to the linear model. Higher-order polynomial models also follow from the development presented here.The method is frequently described or classified as a regression analysis technique. Regression implies the application of statistical methods in its analysis. However, there are no statistical methods applied to the development in this book. Indeed, the mathematical relationships derive from a straight-forward application of differential calculus methods and techniques with no application of any statistical methods.We limit our discussion in this book to systems of two-dimensional data; that is, to systems of data that can be represented on a graph with rectangular coordinates with one independent and one dependent variable.IMPLEMENTATION WITH MICROSOFT(r) EXCELWe demonstrate the implementation of the calculations with Microsoft(r) Excel since Excel is readily available on most PC's as one of the components of the Microsoft(r) Office Suite of applications. We have included screen shots of Excel spreadsheets to show enough detail so that the reader can easily reproduce the calculations. An extensive familiarity with Excel is not required to use this book and to understand the screen shots, although familiarity with some fundamental concepts of Excel is assumed and helpful.TABLE OF CONTENTSChapter 1: IntroductionThe SkinnyGeneral Background and ReviewLeast Squares MethodImplementation with Microsoft(r) Excel Where To Go From HereChapter 2: How To Fit Three or More Points with a Linear PolynomialChapter 3: How To Fit Four or More Points with a Quadratic PolynomialChapter 4: How To Fit Five or More Points with a Cubic PolynomialChapter 5: How To Fit n Points with an (n-1)th Order PolynomialChapter 6: Quality of the Least Squares FitChapter 7: ApplicationsCheck ProcessingStock InvestingPetroleum Fraction Boiling Point CurvesChurch GrowthSteakhouse RestaurantAppendixAppendix 1: Symbols, Nomenclature, Mathematical Notation, Microsoft(r) Excel FunctionsAppendix 2: Development of and Theoretical Basis for the Method of Least SquaresAppendix 3: Summary of Least Squares RelationshipsLinear Least SquaresQuadratic Least SquaresCubic Least SquaresLeast Squares Relationships CharacteristicsAppendix 4: Linear (Straight-Line) Fit of Two PointsAppendix 5: Quadratic Fit of Three PointsAppendix 6: Bibliography, Software, URL'sGlossaryIndex

Book details

List price: $28.75
Publisher: CreateSpace Independent Publishing Platform
Publication date: 6/23/2013
Binding: Paperback
Pages: 148
Size: 8.50" wide x 11.00" long x 0.35" tall
Weight: 0.990
Language: English

Richard A. Eckhart has over 50 years of combined industrial, business, and academic experience. With degrees through the doctoral level in Chemical Engineering from Lehigh University and Penn State University, he has held industrial positions with several well-known corporations including Monsanto, Exxon, Honeywell, Parsons, and SimSci. In addition, he has been on the faculties of a number of colleges and universities including Azusa Pacific University, Penn State, Villanova, UCLA, University of Maryland, California State University-Fullerton, California National University, CALCampus, and Northcentral University in both the online and face-to-face environments.Dr. Eckhart has experience as…