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

Slides:

Advertisements

Similar presentations

Chap 12-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 12 Simple Regression Statistics for Business and Economics 6.

Advertisements

13- 1 Chapter Thirteen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

1 Multiple Regression Response, Y (numerical) Explanatory variables, X 1, X 2, …X k (numerical) New explanatory variables can be created from existing.

Some Terms Y =  o +  1 X Regression of Y on X Regress Y on X X called independent variable or predictor variable or covariate or factor Which factors.

Chapter 13 Multiple Regression

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 4-1 © 2006 by Prentice Hall, Inc., Upper Saddle River, NJ Chapter 4 RegressionModels.

Chapter 14 Introduction to Multiple Regression

Chapter 12 Simple Regression

Chapter 12 Multiple Regression

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

Linear Regression and Correlation

© 2003 Prentice-Hall, Inc.Chap 14-1 Basic Business Statistics (9 th Edition) Chapter 14 Introduction to Multiple Regression.

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 14-1 Chapter 14 Introduction to Multiple Regression Basic Business Statistics 11 th Edition.

Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 2000 LIND MASON MARCHAL 1-1 Chapter Twelve Multiple Regression and Correlation Analysis GOALS When.

Ch. 14: The Multiple Regression Model building

Correlation and Regression Analysis

Simple Linear Regression Analysis

Review for Final Exam Some important themes from Chapters 9-11 Final exam covers these chapters, but implicitly tests the entire course, because we use.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 13-1 Chapter 13 Introduction to Multiple Regression Statistics for Managers.

Introduction to Linear Regression and Correlation Analysis

Chapter 13: Inference in Regression

Chapter 11 Simple Regression

Regression Method.

Lecture 14 Multiple Regression Model

OPIM 303-Lecture #8 Jose M. Cruz Assistant Professor.

Linear Trend Lines = b 0 + b 1 X t Where is the dependent variable being forecasted X t is the independent variable being used to explain Y. In Linear.

Statistics for Business and Economics 7 th Edition Chapter 11 Simple Regression Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch.

Chapter 14 Introduction to Multiple Regression

EQT 373 Chapter 3 Simple Linear Regression. EQT 373 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value.

Applied Quantitative Analysis and Practices LECTURE#23 By Dr. Osman Sadiq Paracha.

Multiple Linear Regression. Purpose To analyze the relationship between a single dependent variable and several independent variables.

Regression. Population Covariance and Correlation.

Multiple Regression and Model Building Chapter 15 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

Chap 14-1 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 14-1 Chapter 14 Introduction to Multiple Regression Basic Business Statistics.

Chapter 5: Regression Analysis Part 1: Simple Linear Regression.

Lesson Multiple Regression Models. Objectives Obtain the correlation matrix Use technology to find a multiple regression equation Interpret the.

Section 9-1: Inference for Slope and Correlation Section 9-3: Confidence and Prediction Intervals Visit the Maths Study Centre.

Multiple Regression BPS chapter 28 © 2006 W.H. Freeman and Company.

14- 1 Chapter Fourteen McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.

CORRELATION: Correlation analysis Correlation analysis is used to measure the strength of association (linear relationship) between two quantitative variables.

Regression Analysis Relationship with one independent variable.

Lecture 4 Introduction to Multiple Regression

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 13-1 Introduction to Regression Analysis Regression analysis is used.

1 Quadratic Model In order to account for curvature in the relationship between an explanatory and a response variable, one often adds the square of the.

Multiple Regression. Simple Regression in detail Y i = β o + β 1 x i + ε i Where Y => Dependent variable X => Independent variable β o => Model parameter.

Basic Managerial Accounting Concepts Cost Behavior: Fixed Costs Fixed vs. Variable Relevant range: normal production levels Behavior of fixed costs as.

28. Multiple regression The Practice of Statistics in the Life Sciences Second Edition.

Copyright ©2011 Pearson Education, Inc. publishing as Prentice Hall 14-1 Chapter 14 Introduction to Multiple Regression Statistics for Managers using Microsoft.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 14-1 Chapter 14 Introduction to Multiple Regression Basic Business Statistics 10 th Edition.

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Simple Linear Regression Analysis Chapter 13.

Introduction to Multiple Regression Lecture 11. The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & 2 or more.

Multiple Regression Learning Objectives n Explain the Linear Multiple Regression Model n Interpret Linear Multiple Regression Computer Output n Test.

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 14-1 Statistics for Managers Using Microsoft® Excel 5th Edition Chapter.

© 2000 Prentice-Hall, Inc. Chap Chapter 10 Multiple Regression Models Business Statistics A First Course (2nd Edition)

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Multiple Regression Chapter 14.

© 2001 Prentice-Hall, Inc.Chap 13-1 BA 201 Lecture 19 Measure of Variation in the Simple Linear Regression Model (Data)Data.

Chapter 14 Introduction to Multiple Regression

CHAPTER 3 Describing Relationships

Chapter 11 Simple Regression

Relationship with one independent variable

Chapter 13 Multiple Regression

CHAPTER 29: Multiple Regression*

Prepared by Lee Revere and John Large

Relationship with one independent variable

Regression and Categorical Predictors

Chapter Thirteen McGraw-Hill/Irwin

Presentation transcript:

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

14.1: Developing the Multiple Regression Model Often, a better-fitting model of the dependent variable results from using multiple independent variables. Multiple independent variables means multiple regression. The “omni-power” example models sales as a function of price and promotion.

Software Output Be able to construct the model from the output. The technique is still “least squares” because we are assuming a linear relationship between each independent variable and the dependent variable.

Notes on Mechanics We refer to “k” explanatory or independent variables. A slope coefficient is interpreted as the change in the mean of Y for every change in X 1, taking into account the effect of other X (sometimes said “holding all other X constant”). In multiple regression, this “slope” called a “net regression coefficient.”

14.2: r 2, adjusted r 2, and the overall F test R-squared, R 2, the proportion of variation in Y explained by the set of explanatory variables in the data set. R 2 will increase every time a new independent variable is added to the regression model, EVEN if the new independent variable is NOT useful. Use adjusted R 2 to compare models.

Overall F test Is there a significant relationship between the dependent variable and the set of explanatory variables? H 0 : β 1 = β 2 = … = β k = 0. H 1 : at least one of the β s ≠ 0. F calc = MSR/MSE (formula 14.6) Table 14.2 defines the test constituents. Use p.

14.3: Residual Analysis for the Multiple Regression Model Page 580 lists the useful plots. Note that they are the same plots used in Chapter 13. What are the assumptions?

14.4: Inferences Concerning the Population Regression Coefficients The hypothesis test for a single slope is the same “t test” used in Chapter 13. H 0 : β i = 0 and H 1 : β i ≠ 0. 1 tailed tests are possible. Recommend using the observed significance, i.e. the “p-value.” Important note on page 583.

14.6: Using Dummy Variables and Interaction Terms in Regression Models Dummy: Use categorical independent variables. Interaction: Use products of independent variables.