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 .)