Regression Analysis 4e Montgomery, Peck & Vining

Slides:

Advertisements

Similar presentations

11-1 Empirical Models Many problems in engineering and science involve exploring the relationships between two or more variables. Regression analysis.

Advertisements

Probability & Statistical Inference Lecture 9

11 Simple Linear Regression and Correlation CHAPTER OUTLINE

Nonlinear Regression Ecole Nationale Vétérinaire de Toulouse Didier Concordet ECVPT Workshop April 2011 Can be downloaded at

A Short Introduction to Curve Fitting and Regression by Brad Morantz

Classification and Prediction: Regression Via Gradient Descent Optimization Bamshad Mobasher DePaul University.

Some useful linear algebra. Linearly independent vectors span(V): span of vector space V is all linear combinations of vectors v i, i.e.

Curve Fitting and Interpolation: Lecture (IV)

Statistics 350 Lecture 16. Today Last Day: Introduction to Multiple Linear Regression Model Today: More Chapter 6.

/k 2DS00 Statistics 1 for Chemical Engineering lecture 5.

Statistics 350 Lecture 23. Today Today: Exam next day Good Chapter 7 questions: 7.1, 7.2, 7.3, 7.28, 7.29.

NOTES ON MULTIPLE REGRESSION USING MATRICES  Multiple Regression Tony E. Smith ESE 502: Spatial Data Analysis  Matrix Formulation of Regression  Applications.

Chapter 9 Multicollinearity

Linear Regression Analysis 5E Montgomery, Peck & Vining Hidden Extrapolation in Multiple Regression In prediction, exercise care about potentially.

11-1 Empirical Models Many problems in engineering and science involve exploring the relationships between two or more variables. Regression analysis.

Section 8.3 – Systems of Linear Equations - Determinants Using Determinants to Solve Systems of Equations A determinant is a value that is obtained from.

Chapter 6 Feature-based alignment Advanced Computer Vision.

9 - 1 Intrinsically Linear Regression Chapter Introduction In Chapter 7 we discussed some deviations from the assumptions of the regression model.

Geo479/579: Geostatistics Ch17. Cokriging

Chapter 15 Modeling of Data. Statistics of Data Mean (or average): Variance: Median: a value x j such that half of the data are bigger than it, and half.

Non-Linear Models. Non-Linear Growth models many models cannot be transformed into a linear model The Mechanistic Growth Model Equation: or (ignoring.

Last Lecture (optical center) origin principal point P (X,Y,Z) p (x,y) x y.

Regression analysis Control of built engineering objects, comparing to the plan Surveying observations – position of points Linear regression Regression.

Non-Linear Models. Non-Linear Growth models many models cannot be transformed into a linear model The Mechanistic Growth Model Equation: or (ignoring.

1 Chapter 3 Multiple Linear Regression Multiple Regression Models Suppose that the yield in pounds of conversion in a chemical process depends.

Multiple Regression I KNNL – Chapter 6. Models with Multiple Predictors Most Practical Problems have more than one potential predictor variable Goal is.

Thomas Knotts. Engineers often: Regress data  Analysis  Fit to theory  Data reduction Use the regression of others  Antoine Equation  DIPPR.

1 11 Simple Linear Regression and Correlation 11-1 Empirical Models 11-2 Simple Linear Regression 11-3 Properties of the Least Squares Estimators 11-4.

Simple Linear Regression. The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x.

Linear Regression Analysis 5E Montgomery, Peck & Vining 1 Chapter 8 Indicator Variables.

Linear Regression Analysis 5E Montgomery, Peck & Vining

Linear Regression Analysis Using MS Excel Tutorial for Assignment 2 Civ E 342.

Introduction to Matrices and Matrix Approach to Simple Linear Regression.

Ch14: Linear Least Squares 14.1: INTRO: Fitting a pth-order polynomial will require finding (p+1) coefficients from the data. Thus, a straight line (p=1)

Non-Linear Models. Non-Linear Growth models many models cannot be transformed into a linear model The Mechanistic Growth Model Equation: or (ignoring.

Lecture 18 Today: More Chapter 9 Next day: Finish Chapter 9.

Copyright ©2012, Joanna Szyda Nonlinear regression BIOSTATISTICS.

Chapter 14 Introduction to Regression Analysis. Objectives Regression Analysis Uses of Regression Analysis Method of Least Squares Difference between.

Computacion Inteligente Least-Square Methods for System Identification.

Statistics 350 Lecture 2. Today Last Day: Section Today: Section 1.6 Homework #1: Chapter 1 Problems (page 33-38): 2, 5, 6, 7, 22, 26, 33, 34,

Statistics 350 Review. Today Today: Review Simple Linear Regression Simple linear regression model: Y i =  for i=1,2,…,n Distribution of errors.

GEOMETRIC CAMERA CALIBRATION The Calibration Problem Least-Squares Techniques Linear Calibration from Points Reading: Chapter 3.

MathematicalMarketing Slide 3c.1 Mathematical Tools Chapter 3: Part c – Parameter Estimation We will be discussing  Nonlinear Parameter Estimation  Maximum.

Regression and Correlation of Data Summary

11-1 Empirical Models Many problems in engineering and science involve exploring the relationships between two or more variables. Regression analysis.

Regression Analysis Part D Model Building

CH 5: Multivariate Methods

Validation of Regression Models

Precisions of Adjusted Quantities

Nonlinear Regression KNNL – Chapter 13.

Matrices Definition: A matrix is a rectangular array of numbers or symbolic elements In many applications, the rows of a matrix will represent individuals.

Chapter 12 Curve Fitting : Fitting a Straight Line Gab-Byung Chae

Solving Nonlinear Equation

Non-linear Least-Squares

Some useful linear algebra

The regression model in matrix form

Chapter 3 Multiple Linear Regression

Chapter 1: Introduction

Linear regression Fitting a straight line to observations.

Chapter 1 Linear Functions

Nonlinear regression.

Simple Linear Regression

Nonlinear Fitting.

Example 3.3 Delivery Time Data

Topic 11: Matrix Approach to Linear Regression

Solving a System of Linear Equations

Model Adequacy Checking

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Regression and Correlation of Data

Lecture 20 Two Stage Least Squares

Presentation transcript:

Regression Analysis 4e Montgomery, Peck & Vining Chapter 12 Introduction to Nonlinear Regression Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining 12.1.2. Nonlinear Regression Models Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining If the derivatives of the expectation function for a regression model still contains the parameters, then the function is nonlinear. For example, Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Text also contains a famous example of a nonlinear model, the Clausius-Clapeyron Equation Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining 12.2 Nonlinear Least Squares Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining 12.2 Nonlinear Least Squares Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Example 12.1 Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining 12.2 Nonlinear Least Squares Geometry of Linear and Nonlinear Least Squares Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining 12.3 Transformation to a Linear Model Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining 12.3 Transformation to a Linear Model If a transformation can be applied to the function, and the result is a linear function, we say the original function is “intrinsically linear”. Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Example 12.2 The Puromycin Data Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Example 12.2 The Puromycin Data Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Example 12.2 The Puromycin Data Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Example 12.2 The Puromycin Data Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Linearizing the model expectation function to produce a linear regression model did not produce a satisfactory result Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Estimation of the variance and the covariance matrix: Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining How linearization works: Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Problems May converge very slowly S may actually increase or fail to converge Dependence on the starting values of 0 Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining Alternative Methods of Estimation Method of Steepest Descent Fractional Increments Marquardt’s Compromise Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining

Regression Analysis 4e Montgomery, Peck & Vining