Skip to Main Content
Regression Analysis by Example, 4th Edition
book

Regression Analysis by Example, 4th Edition

by Samprit Chatterjee, Ali S. Hadi
July 2006
Beginner content levelBeginner
408 pages
10h 3m
English
Wiley-Interscience
Content preview from Regression Analysis by Example, 4th Edition

CHAPTER 7

WEIGHTED LEAST SQUARES

7.1 INTRODUCTION

So far in our discussion of regression analysis it has been assumed that the underlying regression model is of the form

images

where the εi's are random errors that are independent and identically distributed (i.i.d.) with mean zero and variance σ2. Various residual plots have been used to check these assumptions (Chapter 4). If the residuals are not consistent with the assumptions, the equation form may be inadequate, additional variables may be required, or some of the observations in the data may be outliers.

There has been one exception to this line of analysis. In the example based on the Supervisor Data of Section 6.5, it is argued that the underlying model does not have residuals that are i.i.d. In particular, the residuals do not have constant variance. For these data, a transformation was applied to correct the situation so that better estimates of the original model parameters could be obtained (better than the ordinary least squares (OLS) method).

In this chapter and in Chapter 8 we investigate situations where the underlying process implies that the errors are not i.i.d. The present chapter deals with the heteroscedasticity problem, where the residuals do not have the same variance, and Chapter 8 treats the autocorrelation problem, where the residuals are not independent.

In Chapter 6 heteroscedasticity was handled by transforming ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Regression Analysis

Regression Analysis

J. Holton Wilson, Barry P. Keating, Mary Beal
Regression Analysis

Regression Analysis

J. Holton Wilson
Regression Analysis with R

Regression Analysis with R

Giuseppe Ciaburro, Pierre Paquay, Manoj Kumar, Shaikh Salamatullah
Solutions Manual to Accompany Introduction to Linear Regression Analysis, 5th Edition

Solutions Manual to Accompany Introduction to Linear Regression Analysis, 5th Edition

Ann G. Ryan, Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Anne G. Ryan

Publisher Resources

ISBN: 9780471746966Purchase book