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# 8. Regression Estimation

1. Steven K. Thompson

Published Online: 10 FEB 2012

DOI: 10.1002/9781118162934.ch8

## Sampling, Third Edition

#### How to Cite

Thompson, S. K. (2012) Regression Estimation, in Sampling, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118162934.ch8

#### Publication History

1. Published Online: 10 FEB 2012
2. Published Print: 23 FEB 2012

#### Book Series:

1. Wiley Series in Probability and Statistics

#### Book Series Editors:

1. Walter A. Shewhart and
2. Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780470402313

Online ISBN: 9781118162934

## SEARCH

### Keywords:

• linear regression estimator;
• multiple regression models;
• regression estimation;
• unequal probability design

### Summary

This chapter describes the linear regression estimator with one auxiliary variable, initially in the design-based or fixed-population context. It covers the regression estimation with unequal probability designs and multiple regression models. Like the ratio estimator, the regression estimator is not design-unbiased under simple random sampling. Under usual regression model assumptions, however, the estimator is unbiased. If a regression model describing a stochastic relationship between the auxiliary variables and the variable of interest is assumed, a natural objective of sampling is the “prediction” of some characteristic of the y-values of the population. The characteristic to be predicted may be the population mean or total or the y-value of a single unit not yet in the sample. The basic results of the linear prediction approach are summarized for the simple linear regression model with one auxiliary variable and then in general for multiple regression models with any number of auxiliary variables.

#### Controlled Vocabulary Terms

linear regression; Multiple regression; probability distribution