Announcement
**Introduction to Regression Models
**

Gerard E. Dallal, Ph.D.

[Notation: Upper case Roman letters represent random variables. Lower case
Roman letters represent realizations of random variables. For example,
if X is WEIGHT, then x is 159 lbs. E(Y) is the population mean value of
the random variable Y. E(Y|X) is the population mean value of Y when X is
known. E(Y|X=x) is the population mean value of Y when X=x.]
The least squares regression equation

= b_{0} +
b_{1} x
is an estimate of the population regression equation
E(Y|X=x) = _{0} +
_{1} x
The response variable, Y, is described by the model

Y_{i} = _{0} +
_{1} X_{i} + _{i},
where _{i} is a random error.
The usual tests produced by most statisical program packages assume the
errors
- are independent and
- follow a normal distribution with mean 0 and
- constant variance. This means that the variability of responses for
small X values is the same as the variability of responses for large X
values.

This is usually written ~N(0,^{2})--that is, normally distributed with
mean 0 and variance ^{2}--where is a fixed but unknown constant. (The standard
error of the estimate estimates .)

Copyright © 2000 Gerard E. Dallal