**Date:** Thu, 22 Feb 2001 12:46:05 +0100
**Reply-To:** Dr Olaf Kruse <olaf.kruse@VST-GMBH.DE>
**Sender:** "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
**From:** Dr Olaf Kruse <olaf.kruse@VST-GMBH.DE>
**Subject:** AW: Regression problem.
**In-Reply-To:** <416A07CFC6C1D311A796000083295C33072B13@VSTPC04>
**Content-Type:** text/plain; charset="iso-8859-1"
(Original message included after the signature)

Hi Joe,

Two remarks:

If you want to predict the salary of a faculty-member depending on the
classes
she/he has taught, it would be fine to include a intercept. The intercept
could
be interpreted as a base-salary (e.g. for research and administrative
duties).
That you receive huge intercept values is a sign, that salary doesn't depend
much on classes taught. (This holds true also for the german college-system
;-))

If you want to assign cost-rates for each semester credit hour (like your
funding-
matrix)resulting on the faculty-salary, it would be better not to include
intercepts.
In this case, you don't have a classical regression problem but more an
accounting-
problem that could be solved by various OR-procedures. In this case
regression wouldn't
be the best choice, because it doesn't guarantee _positive_ coefficients
(weights).

Cheers,

Olaf

+-----------------------------------------------------+
Dr. Olaf Kruse
VST -Gesellschaft fuer Versicherungsstatistik
Roscherstr. 10
30161 Hannover/FRGermany

mail: Olaf.kruse@vst-gmbh.de
phone:++49-511-339 599 21
fax: ++49-511-388 57 13
+-----------------------------------------------------+

I am trying to handle an unusual regression problem and need advice. I have
to provide a little background first: Texas has approved a funding rate of
$54.44 per semester credit hour taught at the lower level (freshman or
sophomore) in the liberal arts discipline. Higher instructional levels and
other
disciplines are weighted by using multipliers to result in higher funding
rates
per semester credit hour. The result of this funding system is a matrix
that
looks something like this, though the weights are mostly fictional:

Lower Upper Master Doctoral

Liberal Arts 1.00 1.96 3.00 12.00
Science 2.34 3.75 5.76 14.00
Fine Arts 1.05 2.06 3.55 13.25
Education 1.15 2.34 3.75 14.13
Etc.

So, following the logic described above, a lower-level liberal arts course
would receive (1.00 x $54.44 x semester credit hours) in state funding. I
am
trying to develop a similar matrix of weights to estimate how faculty
salaries
are actually spent by instructional level and discipline at Southwest Texas
State University. I know how many credit hours are taught at each
instuctional level and in each discipline, so I just need to assign faculty
salaries to each instructional level and discipline to have the information
needed to calculate salary cost per semester credit hour in each discipline
and instructional level. Once I have salary cost per semester credit hour
at
each instructional level and discipline, I can divide each cell in the above
matrix by faculty salaries expended for teaching a lower-level semester
credit
hour in liberal arts to get the weights I need.

To estimate how faculty salaries are allocated, I fit a regression model to
faculty who taught in purely one discipline. The following independent
variables were significant for the disciplines of education and business,
which are the only disciplines I have fitted regression models to thus far:

salary (dependent variable) =
lower-level credit hours taught +
upper-level credit hours taught +
masters-level credit hours taught +
doctoral credit hours taught +
zero for y-intercept.

Finally, my question: The only way that I could think to apportion the
faculty salary predictions to instructional levels and disciplines was to
develop a unique regression model for each discipline and have no
y-intercept,
which I know is not a good idea. However, if I use a y-intercept, I get a
large
intercept value that I cannot apportion to the different instructional
levels. Does
anyone know a better way to estimate how much of each faculty member's
salary goes to teaching at each instructional level for a given discipline?
Am
I greatly skewing the results by forcing the regression model through the
origin?

Thanks for any advice you can offer.

Joe Meyer
Institutional Research
Southwest Texas State University