(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 415841, 10601]*) (*NotebookOutlinePosition[ 416930, 10634]*) (* CellTagsIndexPosition[ 416886, 10630]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Curve fitting How-to", "Title"], Cell["by W. Garrett Mitchener", "Author"], Cell[TextData[{ "This worksheet goes over traditional linear and non-linear least squares \ curve fitting and different ways to do it in ", StyleBox["Mathematica. ", FontSlant->"Italic"], "It also goes over maximum likelihood curve fitting. Along the way, it \ shows different functions for finding maxima and minima of expressions." }], "Abstract"], Cell[CellGroupData[{ Cell["Least squares and linear regression", "Section"], Cell[TextData[{ "Let's say you have some data ", Cell[BoxData[ \(TraditionalForm\`{\((x\_1, y\_1)\), \ \((x\_2, y\_2)\) ... }\)]], " and you want to fit a curve to it so that you can say ", Cell[BoxData[ \(TraditionalForm\`y = f(x) + noise\)]], ". 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