Chapter 8 Nonlinear Regression Functions. 2 Nonlinear Regression Functions (SW Chapter 8)

Slides:

Advertisements

Similar presentations

Nonlinear models Hill et al Chapter 10. Types of nonlinear models Linear in the parameters. –Includes models that can be made linear by transformation:

Advertisements

Prediction, Goodness-of-Fit, and Modeling Issues ECON 6002 Econometrics Memorial University of Newfoundland Adapted from Vera Tabakova’s notes.

Qualitative Variables and

1 Nonlinear Regression Functions (SW Chapter 8). 2 The TestScore – STR relation looks linear (maybe)…

Excel Part III Curve-Fitting, Regression Section 8 Fall 2013 EGR 105 Foundations of Engineering I.

1 Interactions Between Independent Variables (SW Section 8.3)

Regression with a Binary Dependent Variable

Statistics for Managers Using Microsoft® Excel 5th Edition

Linear vs. exponential growth Linear vs. exponential growth: t = 0 A = 1x(1+1) 0 = 1 A = 1x0 + 1 = 1.

Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression.

Linear Regression with One Regression

Introduction to Econometrics The Statistical Analysis of Economic (and related) Data.

Introduction to Econometrics The Statistical Analysis of Economic (and related) Data.

Statistical Analysis SC504/HS927 Spring Term 2008 Session 7: Week 23: 7 th March 2008 Complex independent variables and regression diagnostics.

Standard Trend Models. Trend Curves Purposes of a Trend Curve: 1. Forecasting the long run 2. Estimating the growth rate.

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 15-1 Chapter 15 Multiple Regression Model Building Basic Business Statistics 11 th Edition.

Introduction to Linear and Logistic Regression. Basic Ideas Linear Transformation Finding the Regression Line Minimize sum of the quadratic residuals.

1 Lecture 25 (Dec.4) In the last lecture, we covered 1. Log-log specification 2. Interaction term This lecture introduces you to 1. Interaction term.

Copyright ©2011 Pearson Education 15-1 Chapter 15 Multiple Regression Model Building Statistics for Managers using Microsoft Excel 6 th Global Edition.

Hypothesis Tests and Confidence Intervals in Multiple Regressors

Transforming to Achieve Linearity

Copyright © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Functional Forms of Regression Models chapter nine.

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

Nonlinear Regression Functions

Chapter 8 Nonlinear Regression Functions.

Chapter 14 Introduction to Multiple Regression Sections 1, 2, 3, 4, 6.

© 2003 Prentice-Hall, Inc.Chap 11-1 Business Statistics: A First Course (3 rd Edition) Chapter 11 Multiple Regression.

Lesson Transforming to Achieve Linearity. Knowledge Objectives Explain what is meant by transforming (re- expressing) data. Tell where y = log(x)

© 2004 Prentice-Hall, Inc.Chap 15-1 Basic Business Statistics (9 th Edition) Chapter 15 Multiple Regression Model Building.

Chapter 14 – Correlation and Simple Regression Math 22 Introductory Statistics.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Calculating the shape of a polynomial from regression coefficients Jane E. Miller,

4.1 Modeling Nonlinear Data.  Create scatter plots of non linear data  Transform nonlinear data to use for prediction.

Bivariate Data When two variables are measured on a single experimental unit, the resulting data are called bivariate data. You can describe each variable.

Transformations. Transformations to Linearity Many non-linear curves can be put into a linear form by appropriate transformations of the either – the.

BASIC DATA ANALYSIS AND STATISTICS R. SHAPIRO American University in Cairo June 3-6, 2012 Motivation, Intuition, and Numerology (AUCShapiroPresent1.ppt)

Chapter 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals.

1 Hypothesis Tests & Confidence Intervals (SW Ch. 7) 1.For a single coefficient 2.For multiple coefficients 3.Other types of hypotheses involving multiple.

Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.

EXAMPLES Linear models The log-linear model Semilog models

Prediction, Goodness-of-Fit, and Modeling Issues Prepared by Vera Tabakova, East Carolina University.

Exam Review Day 6 Chapters 2 and 3 Statistics of One Variable and Statistics of Two Variable.

Nonlinear Models. Agenda Omitted Variables Dummy Variables Nonlinear Models Nonlinear in variables Polynomial Regressions Log Transformed Regressions.

Solving Exponential Equations. We can solve exponential equations using logarithms. By converting to a logarithm, we can move the variable from the exponent.

Chapter 6 Introduction to Multiple Regression. 2 Outline 1. Omitted variable bias 2. Causality and regression analysis 3. Multiple regression and OLS.

Transformations.

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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 14-1 Chapter 14 Multiple Regression Model Building Statistics for Managers.

Unit 3 Test Review – Identifying Parent Functions October 30, 2014.

Chapter Nonlinear models. Objectives O Classify scatterplots O Use scatterplots and a graphing utility to find models for data and choose the model.

The Probit Model Alexander Spermann University of Freiburg SS 2008.

Correlations: Linear Relationships Data What kind of measures are used? interval, ratio nominal Correlation Analysis: Pearson’s r (ordinal scales use Spearman’s.

Chapter 13 Nonlinear and Multiple Regression. Polynomial Regression For k th-degree model: Y=  0 +  1 x +  2 x 2 +…+  k x k +  Where  is N(0, 

Yandell – Econ 216 Chap 15-1 Chapter 15 Multiple Regression Model Building.

Instrumental Variables Regression

Chapter 15 Multiple Regression Model Building

Chapter 8 Linear Regression.

Nonlinear Regression Functions

Curvilinear Relationships

Chapter 4 Basic Estimation Techniques

Linear Regression with One Regression

Lecturer: Ing. Martina Hanová, PhD.

Chapter 13 Nonlinear and Multiple Regression

1) A residual: a) is the amount of variation explained by the LSRL of y on x b) is how much an observed y-value differs from a predicted y-value c) predicts.

Introduction to Econometrics

Chapter 12 Review Inference for Regression

Lecturer: Ing. Martina Hanová, PhD.

Nonlinear Fitting.

Ch 4.1 & 4.2 Two dimensions concept

Integrated Math 3 – Mod 3 Test Review

Regression and Correlation of Data

Presentation transcript:

Chapter 8 Nonlinear Regression Functions

2 Nonlinear Regression Functions (SW Chapter 8)

3 The TestScore – STR relation looks linear (maybe)…

4 But the TestScore – Income relation looks nonlinear...

5 Nonlinear Regression Population Regression Functions – General Ideas (SW Section 8.1)

6 The general nonlinear population regression function

7

8 Nonlinear Functions of a Single Independent Variable (SW Section 8.2)

9 1. Polynomials in X

10 Example: the TestScore – Income relation

11 Estimation of the quadratic specification in STATA

12 Interpreting the estimated regression function:

13 Interpreting the estimated regression function, ctd:

14

15 Estimation of a cubic specification in STATA

16

17 Summary: polynomial regression functions

18 2. Logarithmic functions of Y and/or X

19 The three log regression specifications:

20 I. Linear-log population regression function

21 Linear-log case, continued

22 Example: TestScore vs. ln(Income)

23 The linear-log and cubic regression functions

24 II. Log-linear population regression function

25 Log-linear case, continued

26 III. Log-log population regression function

27 Log-log case, continued

28 Example: ln( TestScore) vs. ln( Income)

29 Example: ln( TestScore) vs. ln( Income), ctd.

30 The log-linear and log-log specifications:

31 Summary: Logarithmic transformations

32 Other nonlinear functions (and nonlinear least squares) (SW App. 8.1)

33 Negative exponential growth

34 Nonlinear Least Squares

35

36

37 Interactions Between Independent Variables (SW Section 8.3)

38 (a) Interactions between two binary variables

39 Interpreting the coefficients

40 Example: TestScore, STR, English learners

41 (b) Interactions between continuous and binary variables

42 Binary-continuous interactions: the two regression lines

43 Binary-continuous interactions, ctd.

44 Interpreting the coefficients

45 Example: TestScore, STR, HiEL (=1 if PctEL  10)

46 Example, ctd: Testing hypotheses

47 (c) Interactions between two continuous variables

48 Interpreting the coefficients:

49 Example: TestScore, STR, PctEL

50 Example, ctd: hypothesis tests

51 Application: Nonlinear Effects on Test Scores of the Student-Teacher Ratio (SW Section 8.4)

52 Strategy for Question #1 (different effects for different STR?)

53 Strategy for Question #2 (interactions between PctEL and STR?)

54 What is a good “base” specification?

55

56 Tests of joint hypotheses:

57 Interpreting the regression functions via plots:

58 Next, compare the regressions with interactions:

59 Summary: Nonlinear Regression Functions