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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


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