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
= b0 +
b1 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
Yi = 0 +
1 Xi + 
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