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Curve Fitting Chapter III-8 III-8Curve Fitting Overview.......................................................................................................................................................... 152 Curve Fitting Terminology............................................................................................................................ 152 Overview of Curve Fitting............................................................................................................................. 153 Iterative Fitting......................................................................................................................................... 153 Initial Guesses ................................................................................................................................... 154 Termination Criteria......................................................................................................................... 154 Errors in Curve Fitting..................................................................................................................... 154 Data for Curve Fitting ............................................................................................................................. 154 Curve Fitting Using the Quick Fit Menu..................................................................................................... 155 Limitations of the Quick Fit Menu ........................................................................................................ 155 Using the Curve Fitting Dialog..................................................................................................................... 155 A Simple Case — Fitting to a Built-In Function: Line Fit .................................................................. 156 Choosing the Function and Data.................................................................................................... 157 Two Useful Additions: Holding a Coefficient and Generating Residuals............................... 158 Automatic Guesses Didn’t Work........................................................................................................... 161 Fits with Constants .................................................................................................................................. 163 Fitting to a User-Defined Function........................................................................................................ 163 Creating the Function ...................................................................................................................... 163 Coefficients Tab for a User-Defined Function.............................................................................. 166 Making a User-Defined Function Always Available .................................................................. 167 Removing a User-Defined Fitting Function.................................................................................. 167 User-Defined Fitting Function Details .......................................................................................... 167 Fitting to an External Function (XFUNC) ............................................................................................ 167 The Coefficient Wave .............................................................................................................................. 168 Default................................................................................................................................................ 168 Explicit Wave .................................................................................................................................... 168 New Wave ......................................................................................................................................... 169 Errors.................................................................................................................................................. 169 The Destination Wave............................................................................................................................. 169 No Destination .................................................................................................................................. 169 Auto-Trace......................................................................................................................................... 169 Explicit Destination .......................................................................................................................... 170 New Wave ......................................................................................................................................... 170 Fitting a Subset of the Data .................................................................................................................... 170 Selecting a Range to Fit.................................................................................................................... 170 Using a Mask Wave.......................................................................................................................... 172 Weighting.................................................................................................................................................. 172 Proportional Weighting .......................................................................................................................... 173 Fitting to a Multivariate Function ......................................................................................................... 174 Selecting a Multivariate Function .................................................................................................. 174 Selecting Fit Data for a Multivariate Function ............................................................................. 174 Fitting a Subrange of the Data for a Multivariate Function ....................................................... 175 Model Results for Multivariate Fitting ................................................................................................. 175 Time Required to Update the Display.................................................................................................. 176 Multivariate Fitting Examples ............................................................................................................... 176 Chapter III-8 — Curve Fitting Example One — Remove Planar Trend Using Poly2D............................................................... 176 Example Two — User-Defined Simplified 2D Gaussian Fit ...................................................... 177 Problems with the Curve Fitting Dialog .............................................................................................. 178 Built-in Curve Fitting Functions ................................................................................................................... 179 Inputs and Outputs for Built-In Fits............................................................................................................. 184 Curve Fitting Dialog Tabs.............................................................................................................................. 185 Global Controls ........................................................................................................................................ 186 Function and Data Tab............................................................................................................................ 186 Data Options Tab..................................................................................................................................... 188 Coefficients Tab........................................................................................................................................ 188 Output Options Tab ................................................................................................................................ 188 Computing Residuals..................................................................................................................................... 189 Residuals Using Auto Trace................................................................................................................... 191 Removing the Residual Auto Trace ............................................................................................... 191 Residuals Using Auto Wave .................................................................................................................. 192 Residuals Using an Explicit Residual Wave ........................................................................................ 192 Explicit Residual Wave Using New Wave.................................................................................... 192 Calculating Residuals After the Fit ....................................................................................................... 192 Estimates of Error............................................................................................................................................ 193 Confidence Bands and Coefficient Confidence Intervals .................................................................. 193 Calculating Confidence Intervals After the Fit ............................................................................ 195 Confidence Band Waves.................................................................................................................
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