1 / 10

Fitting Parameters in Data Analysis: Minimizing Chi-Square for Optimal Results

This document outlines a procedure for fitting parameters in data to minimize the chi-square function. The goal is to adjust fit parameters to accurately model data points with associated errors, specifically in the context of basketball projectile motion analysis. Steps include importing data into IGOR, creating necessary waves for Y-position and Y-velocity, and performing polynomial fits. The process also involves defining error waves, using built-in functions for curve fitting, and visualizing results with graphical representation, including error bars for accurate assessment of fits.

morwen
Télécharger la présentation

Fitting Parameters in Data Analysis: Minimizing Chi-Square for Optimal Results

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction Fitting program - goal is to vary the fit parameters to minimize the chi-square defined as: function Fit parameters data points errors f{g,x) = 2πsqrt(length/g)

  2. Basketball Movie Go to the notes for Week 3 find data Excel file Y-pos Y-vel time

  3. Import to IGOR Make waves - called:tt, ypos and yvel Make table - Under Windows - new tableThen cut from the Excel file and pasteinto IGOR table

  4. Graph Position Data

  5. Fit Data to a Polynomial This dialog box - from choosing Curve Fitting under Analysis in themain menu Specify waves for the fit Built - infunctions areavailable 3 terms or quadratic

  6. Results of Fit

  7. Fit in a Range of Data With a graph selected - underthe Graph menu select Show Info - then move cursors overthe data points that define therange to be fitted

  8. Procedure Define error wave and inverse error wave. In this example: err and errinv= 1/err. In the graph of period vs length, use markers for data and show error bars. Define the user-function in the Procedure window. In this example pend Make fitting coefficients wave and set to reasonable starting values. In this example coef.

  9. Evaluating Fit

  10. Terminal Velocity

More Related