Database Reference
In-Depth Information
6.4
where:
is the outcome variable
are the input variables, for j = 1, 2,…, p - 1
is the value of
when each
equals zero
is the change in
based on a unit change in
, for j = 1, 2,…, p - 1
and the
are independent of each other
This additional assumption yields the following result about the expected value of
y, E(y) for given
:
Because
are constants, the E(y) is the value of the linear regression
model for the given
. Furthermore, the variance of y, V(y), for given
is this:
Thus, for a given , y is normally distributed with mean
and variance . For a regression model with
just one input variable,
Figure 6.3
illustrates the normality assumption on the error
terms and the effect on the outcome variable, , for a given value of .
