On Sun, 13 Feb 2000 [EMAIL PROTECTED] wrote:
> If I want to find the least squares estimator of the slope of a simple
> linear regression model where my intercept is known, will this
> estimator will be the same as if I did not know my intercept(=Sxy/sxx)?
In general, no; unless the known intercept happens to equal the value
that would be estimated if it were treated as unknown. This would be the
case, for one example, if the sample mean of the predictor were zero.
> How about the variance and the confidence interval of my estimator?
> will they be bigger or smaller than the estimator for the case where
> both my intercept and slope unknown?
Unlikely to be the same. Whether larger or smaller will depend on the
data. If the Y-axis is far from the cloud of empirical points, smaller;
if it lies near or within the cloud, and the intercept is far enough from
the OLS regression line, could be larger.
The situation is essentially the same as calculating a regression line
with zero intercept (keyword NOCONSTANT in some packages):
you postulate
Y = a + bX + e [1]
where
a is alleged to be known and b is to be estimated; this is
equivalent to
(Y-a) = bX + e [2]
which is a regression with zero intercept and dependent variable (Y-a).
I'm curious: what example(s) do you have in mind, that the intercept
would be known but the slope would not?
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
===========================================================================
This list is open to everyone. Occasionally, people lacking respect
for other members of the list send messages that are inappropriate
or unrelated to the list's discussion topics. Please just delete the
offensive email.
For information concerning the list, please see the following web page:
http://jse.stat.ncsu.edu/
===========================================================================
