ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 25 Regression Analysis-Chapter 17.

Slides:

Advertisements

Similar presentations

Kin 304 Regression Linear Regression Least Sum of Squares

Advertisements

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Curve Fitting ~ Least Squares Regression Chapter.

Regression Analysis Module 3. Regression Regression is the attempt to explain the variation in a dependent variable using the variation in independent.

Regression, Correlation. Research Theoretical empirical Usually combination of the two.

Simple Regression. Major Questions Given an economic model involving a relationship between two economic variables, how do we go about specifying the.

Read Chapter 17 of the textbook

Engineering experiments involve the measuring of the dependent variable as the independent one has been altered, so as to determine the relationship between.

Function Approximation

Least Square Regression

Curve-Fitting Regression

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 26 Regression Analysis-Chapter 17.

Least Square Regression

EGR 105 Foundations of Engineering I Fall 2007 – week 7 Excel part 3 - regression.

The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 17 Least Square Regression.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 22 CURVE FITTING Chapter 18 Function Interpolation and Approximation.

ECIV 301 Programming & Graphics Numerical Methods for Engineers REVIEW III.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 23 CURVE FITTING Chapter 18 Function Interpolation and Approximation.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 24 Regression Analysis-Chapter 17.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 171 CURVE.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 21 CURVE FITTING Chapter 18 Function Interpolation and Approximation.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 171 Least.

Least-Squares Regression

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Curve Fitting ~ Least Squares Regression Chapter.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Part 4 Curve Fitting.

MECN 3500 Inter - Bayamon Lecture 9 Numerical Methods for Engineering MECN 3500 Professor: Dr. Omar E. Meza Castillo

Chapter 8 Curve Fitting.

MANAGERIAL ECONOMICS 11 th Edition By Mark Hirschey.

Curve-Fitting Regression

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

EE3561_Unit 4(c)AL-DHAIFALLAH14351 EE 3561 : Computational Methods Unit 4 : Least Squares Curve Fitting Dr. Mujahed Al-Dhaifallah (Term 342) Reading Assignment.

Lecture 16 - Approximation Methods CVEN 302 July 15, 2002.

Residuals Recall that the vertical distances from the points to the least-squares regression line are as small as possible.  Because those vertical distances.

Linear Prediction Correlation can be used to make predictions – Values on X can be used to predict values on Y – Stronger relationships between X and Y.

Curve Fitting Pertemuan 10 Matakuliah: S0262-Analisis Numerik Tahun: 2010.

Stats of Engineers, Lecture 8. 1.If the sample mean was larger 2.If you increased your confidence level 3.If you increased your sample size 4.If the population.

Curve Fitting Introduction Least-Squares Regression Linear Regression Polynomial Regression Multiple Linear Regression Today’s class Numerical Methods.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Curve Fitting ~ Least Squares Regression.

1 Simple Linear Regression and Correlation Least Squares Method The Model Estimating the Coefficients EXAMPLE 1: USED CAR SALES.

2/12/ Linear Regression Electrical Engineering Majors Authors: Autar Kaw, Luke Snyder

Method 3: Least squares regression. Another method for finding the equation of a straight line which is fitted to data is known as the method of least-squares.

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.

Regression and Correlation of Data Correlation: Correlation is a measure of the association between random variables, say X and Y. No assumption that one.

Regression and Correlation of Data Summary

Least Squares Regression Line.

Part 5 - Chapter

Part 5 - Chapter 17.

ENME 392 Regression Theory

Kin 304 Regression Linear Regression Least Sum of Squares

Chapter 3.2 LSRL.

BPK 304W Regression Linear Regression Least Sum of Squares

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

Part 5 - Chapter 17.

LESSON 21: REGRESSION ANALYSIS

Linear Regression.

Least Squares Regression Line LSRL Chapter 7-continued

Linear regression Fitting a straight line to observations.

Major: All Engineering Majors Authors: Autar Kaw, Luke Snyder

Major: All Engineering Majors Authors: Autar Kaw, Luke Snyder

Chapter 5 LSRL.

Discrete Least Squares Approximation

Industrial Engineering Majors Authors: Autar Kaw, Luke Snyder

Least Square Regression

Mechanical Engineering Majors Authors: Autar Kaw, Luke Snyder

SKTN 2393 Numerical Methods for Nuclear Engineers

A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. Find the correlation coefficient & interpret.

Regression and Correlation of Data

Regression and Correlation of Data

Regression and Correlation of Data

Chemical Engineering Majors Authors: Autar Kaw, Luke Snyder

Presentation transcript:

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 25 Regression Analysis-Chapter 17

Curve Fitting Often we are faced with the problem… what value of y corresponds to x=0.935?

Curve Fitting Question 2 : Is it possible to find a simple and convenient formula that represents data approximately ? e.g. Best Fit ? Approximation

Experimental Measurements Strain Stress

Experimental Measurements Strain Stress

BEST FIT CRITERIA Strain y Stress Error at each Point Total Error

Best Fit => Minimize Error Not a Good Choice Not a Unique Best Fit

Best Fit => Minimize Error Try Absolute Not a Good Choice Not a Unique Best Fit

Best Fit => Minimize Error Best Strategy

Best Fit => Minimize Error Objective: What are the values of a o and a 1 that minimize ?

Least Square Approximation What x minimizes f(x)? Remember:

Least Square Approximation In our case Since x i and y i are known from given data

Least Square Approximation

2 Eqtns 2 Unknowns

Least Square Approximation

Example xyxyx2x a1= a0=

Example

Quantification of Error Average

Quantification of Error Average

Quantification of Error Average

Quantification of Error Standard Deviation Shows Spread Around mean Value

Quantification of Error

“Standard Deviation” for Linear Regression

Quantification of Error Better Representation Less Spread

Quantification of Error Coefficient of Determination Correlation Coefficient

Linearized Regression

Homework