Mathematica fits vs. Root

Slides:

Advertisements

Similar presentations

Modeling of Data. Basic Bayes theorem Bayes theorem relates the conditional probabilities of two events A, and B: A might be a hypothesis and B might.

Advertisements

The Maximum Likelihood Method

Excel Notes Phys244/246 © 2007, B.J. Lieb. Calculating Velocity The velocity is calculated by entering the following: =(B3-B2) / (A3-A2). Then drag the.

Previous Work. Gauss fit with pion, proton, electron.

4.5 Supplemental Notes - Factoring Special Products - Solutions

Geology 5670/6670 Inverse Theory 26 Jan 2015 © A.R. Lowry 2015 Read for Wed 28 Jan: Menke Ch 4 (69-88) Last time: Ordinary Least Squares (   Statistics)

Stats for Engineers Lecture 9. Summary From Last Time Confidence Intervals for the mean t-tables Q Student t-distribution.

Holt Algebra Order of Operations Warm Up 8/12/09.

2.13 Use Square Roots to Solve Quadratics Example 1 Solve quadratic equations Solution Write original equation. 5 Solve the equation. Add __ to each side.

Sec 1.5 Scatter Plots and Least Squares Lines Come in & plot your height (x-axis) and shoe size (y-axis) on the graph. Add your coordinate point to the.

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data.

Chapter 6 (cont.) Difference Estimation. Recall the Regression Estimation Procedure 2.

Powers and roots. Square each number a) 7 b) 12 c) 20 d) 9 e) 40 a) 49 b) 144 c) 400 d) 81 e) 1600.

Calculator Tricks Magic Buttons for the TI-30Xa. Squares Squared 5 2 A = s 2 (area of a square) Find the following: 1.12 squared 2.Area of a square with.

Material and thickness for pi0 Y.Sudo Univ. of Tsukuba 2008/07/18.

Objectives The student will be able to:

Standard Deviation A Measure of Variation in a set of Data.

Math 8 - Unit 1 Square Roots and the Pythagorean Theorem A square number or perfect square is any number that is a product that forms when we multiply.

Factoring trinomials ax² + bx +c a = any number besides 1 and 0.

How to detect the change of model for fitting. 2 dimensional polynomial 3 dimensional polynomial Prepare for simple model (for example, 2D polynomial.

Announcements Starting Unit 7 (Non-Calculator Part) Unit 6 Make-up Test (Pick one of these) –Wednesday: 3:50-5:00pm –Thursday: 7:15-8:30am Unit 6 Reassessment.

Chi Square Test for Goodness of Fit Determining if our sample fits the way it should be.

R. Kass/W03 P416 Lecture 5 l Suppose we are trying to measure the true value of some quantity (x T ). u We make repeated measurements of this quantity.

Criterion C- Further Mathematical Processes. HOW TO DIFFERENTIATE WHAT IS NEEDED TO ACHIEVE 5 POINTS: C. Mathematical processes By: Nisleidys Gonzalez.

Indicate the length up to one estimated value…. A. B. C.

Chapter 11 Linear Regression and Correlation. Explanatory and Response Variables are Numeric Relationship between the mean of the response variable and.

The reading is 7.38 mm. The reading is 7.72 mm.

14.0 Math Review 14.1 Using a Calculator Calculator

Assignment 1: due 1/19/16 Estimate all of the zero of x3-x2-2x+1 graphically. Write a MatLab code for Newton’s method. Use your code to refine the graphical.

Fitting Equations to Data Chapter 7. Problems Classwork: 7.1, 7.8, 7.13, 7.22 Homework: 7.2, 7.9, 7.16, 7.23, 7.28.

Chapter 7 Review.

Fitting Equations to Data

Data manipulation II: Least Squares Fitting

Confidence Intervals and Hypothesis Tests for Variances for One Sample

25 Math Review Part 1 Using a Calculator

Lesson 12.2 AIM: Simplifying Rational Expressions

Day 20: Completing the Square! Oh, baby!

Square Roots Practice © T Madas.

Sizes and parking locations of aircraft

Physics 114: Exam 2 Review Material from Weeks 7-11

Goodness of Fit Tests The goal of goodness of fit tests is to test if the data comes from a certain distribution. There are various situations to which.

Rate vs. Thickness Jan 18, 2017.

Plus Endcap Transfer Lines

Data fitting programming Math 570

Data fitting programming Math 371 Hao Wang University of Alberta

Summary of Ao extrapolation

Multiplying by 10, 100 & 1000 Maths Term 1.

Count the number of dots and write down your answer

Fitting different functional forms

Figure 1. Histograms of pull-off force values for three different amino acids and silicon at a loading rate of 5.5 nN/s (pH 6.8). The most probable force.

Statistical Process Control

Graphing Techniques.

!'!!. = pt >pt > \ ___,..___,..

A study of education followed a large group of fourth-grade children to see how many years of school they eventually completed. Let x be the highest year.

Nonlinear Fitting.

Industrial Engineering Majors Authors: Autar Kaw, Luke Snyder

Pade order investigation Re-run of functional forms

CALCULATING EQUATION OF LEAST SQUARES REGRESSION LINE

Warmup A study was done comparing the number of registered automatic weapons (in thousands) along with the murder rate (in murders per 100,000) for 8.

Looking at the 500 nm data point

3.8 Sum & Differences of Areas

Small group Mott meeting

JMP Example 5 Use the previous yield data from different dissolution temperatures. Make a model that describes the effect of temperature on the yield.

Opener Notes Name__________________________________________________

6.6 Factoring Polynomials

Adding variables. There is a difference between assessing the statistical significance of a variable acting alone and a variable being added to a model.

Warm-Up 5 minutes Multiply. 1) (x – 3)(x – 2) 2) (6x + 5)(2x + 1)

Completing the Square pages 544–546 Exercises , – , –2

MATH 2311 Section 8.6.

Presentation transcript:

Mathematica fits vs. Root 17Jan 2017

Asym vs. T, Run 1

Asym vs. T, Run 1

Asym vs. T, Run 2

Root vs. Mathematica A vs. T ao Δao a1 a2 b1 Chi sq Pade (2,0) 44.0557 .1090 -13.76 3.4 1.36 Root Pade(1,1) 44.095 .124 2.8 0.39 1.27 Pade (0,1) 44.05 0.095 0.31 1.15 44.1216 .1222 -13.99 3.74 1.29 Rt run2 44.175 .1393 4.8 0.45 1.16 44.09 0.1006 -11.36 0.3136 1.14 A vs. T ao Δao a1 a2 b1 Chi sq Pade (2,0) 44.0492 0.129 -0.0137 3.45e-6 1.37 MM run 1 Pade(1,1) 44.0928 0.139 0.00336 0.0002747 1.27 Pade (0,1) 44.0395 0.1012 0.0003122 1.62 44.1172 0.1413 -0.014 3.85e-6 1.29 MM run 2 44.1759 0.152 0.00564 0.000469 1.18 44.0809 0.1131 0.000312

Asym vs. Rate run 1

A vs. R run 1

Asym. vs rate run 2

A vs. R run 2

A vs. R Ao dAo Chi squared Run Pade (2,0) 43.96 0.08 1.65 Root, 1 Pade (1,1) 44.08 0.09 1.12 Pade (0,2) 44.05 1.19 43.99 0.093 3.00 Root, 2 44.18 0.11 1.71 44.11 0.100 2.00 A vs. R Ao dAo Chi squared Run Pade (2,0) 43.913 0.125 2.68 MM, 1 Pade (1,1) 44.0829 0.105 1.38 Pade (0,2) 44.0279 1.63 43.959 0.187 4.28 MM, 2 44.1744 0.170 2.54 44.0948 0.167 2.95

Summary Extrapolated Ao in agreement with two methods (mathematica and root analysis of same data set) Some differences in the Chi squared values may come from slightly different methods for calculation, x-error bar handling Pick one, pick thickness units, proceed.

Math in mathematica Get y(x+dx), y(x-dx) for fitting function, add this dy due to x error bar in quadrature Use weighting function: w=(1/dy)^2 at each pt Use the mathematica “NonlinearModelFit” function – least squares, using weighted data points, standard error on Ao term Define χ2 (sum over all data pts) SUM{[(data pt – fit(xi))/Δyi]^2} Reduced χ2 : χ2 /(# data points - fit parameters)