# Chapter 9

# Regression Problems

# Introduction

Among the most common applications of statistical techniques are those involving some sort of regression analysis. Such procedures are designed to detect and interpret stochastic relationships between a dependent (response) variable and one or more independent (predictor) variables. These regression relationships can vary from that of a simple linear relationship between the dependent variable and a single independent variable to complex, nonlinear relationships involving a large number of predictor variables.

In Sections 9.1–9.4, we present nonparametric procedures designed for the simplest of regression relationships, namely, that of a single stochastic linear relationship between a dependent variable and one independent variable. (Such a relationship is commonly referred to as a *regression line*.) In Section 9.1, we present a distribution-free test of the hypothesis that the slope of the regression line is a specified value. Sections 9.2 and 9.3 provide, respectively, a point estimator and distribution-free confidence intervals and bounds for the slope parameter. In Section 9.4, we complete the analysis for a single regression line by discussing both an estimator of the intercept of the line and the use of the estimated linear relationship to provide predictions of dependent variable responses to additional values of the predictor variable. In Section 9.5, we consider the case of two or more regression lines and describe an asymptotically ...

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