Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Principles of Statistics
- 3 Introduction to Linear Regression
- 4 Assessing the Regression
- 5 Multiple Linear Regression
- 6 Indicators, Interactions, and Transformations
- 7 Nonparametric Statistics
- 8 Logistic Regression
- 9 Diagnostics for Logistic Regression
- 10 Poisson Regression
- 11 Survival Analysis
- 12 Proportional Hazards Regression
- 13 Review of Methods
- Appendix: Statistical Tables
- References
- Selected Solutions and Hints
- Index
3 - Introduction to Linear Regression
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Principles of Statistics
- 3 Introduction to Linear Regression
- 4 Assessing the Regression
- 5 Multiple Linear Regression
- 6 Indicators, Interactions, and Transformations
- 7 Nonparametric Statistics
- 8 Logistic Regression
- 9 Diagnostics for Logistic Regression
- 10 Poisson Regression
- 11 Survival Analysis
- 12 Proportional Hazards Regression
- 13 Review of Methods
- Appendix: Statistical Tables
- References
- Selected Solutions and Hints
- Index
Summary
In this book we develop mathematical models for explaining the variability of measurements made on an outcome of interest. The aim is to try to explain the different values of this outcome in response to other information available to us. Random variation in the values of the response makes this difficult, and at best we will only be able to make a statement about the typical or average value of the response under a given set of circumstances. Let us make this clear with an example in which we try to explain the different birth weights of a group of 100 low-birth-weight babies using only information about their length.
Low-Birth-Weight Infants
One of the health problems associated with low-birth-weight infants is just that: their low weight is associated with a myriad of health problems. A “low birth weight” is any value lower than 1,500 grams. Figure 3.1 plots the length and birth weight of 100 low-birth-weight infants born in one of two Boston-area hospitals.
In this figure we see a rough relationship between birth weight and length. In general, larger birth weight is associated with greater length. Despite a small number of notable exceptions in this plot, we can see that most of the infants follow a general pattern. The large “cloud” of observations along the right half of this figure defines the general pattern of the data. The values of length were rounded to the nearest centimeter, and this explains the vertical “stripes” that appear in Figure 3.1.
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- Applied Linear Models with SAS , pp. 58 - 74Publisher: Cambridge University PressPrint publication year: 2010