Quantitative Methods in Population Health
Extensions of Ordinary Regression
Chapter One
Review of Ordinary Linear
Regression and Its Assumptions
1.1 THE ORDINARY LINEAR REGRESSION EQUATION
AND ITS ASSUMPTIONS
A linear regression equation can be alternatively specified as
(1.1)
[y.sub.i] = [ß.sub.0] + [ß.sub.1][x.sub.i] + [[element of].sub.i] or
[µ.sub.y|x] = [ß.sub.0] + [ß.sub.1]x or
E(y|x) = [ß.sub.0] + [ß.sub.1]x
to describe the quantitative relationship between a single predictor x and an outcome
y. In the population health research projects described in the Introduction,
y may be a measured GHb or the score of a very-low-birth-weight (VLBW) child
on a test, or the systolic blood pressure (SBP) at a visit to the sleep clinic. In the
first equation [[element of].sub.i] is a random regression error describing the deviation of a given
value [y.sub.i] from its mean. It can ... read full excerpt from Quantitative Methods in Population Health: Extensions of Ordinary Regression ebook
