Engineering Biostatistics

Chapter 14 Regression

The experiments showed further that the mean filial regression towards mediocrity was directly proportional to the parental deviation from it.

– Francis Galton (1886)

WHAT IS COVERED IN THIS CHAPTER

• Ordinary Linear Regression
• Confidence Intervals and Hypothesis Tests for Parameters and Responses in Linear Regression
• Multiple Regression, Matrix Formulation
• Model Selection and Assessment in Multiple Regression
• Power Analysis in Regression
• Regression Nonlinear in Predictors, Errors-in-Variables Regression
• Analysis of Covariance (ANCOVA)

14.1 Introduction

The rather curious name regression was given to a statistical methodology by British scientist Sir Francis Galton, who analyzed the heights of sons and the average heights of their parents. From his observations, Galton concluded that sons of very tall (or short) parents were generally taller (or shorter) than average, but not as tall (or short) as their parents. The results were published in 1886 under the title Regression Towards Mediocrity in Hereditary Stature. In due course of time the word regression became synonymous with the statistical study of the functional relationship between two or more variables. The data set illustrating Galton's finding and used by Pearson is given in pearson.dat ...