Transcript New Freshman Survey Summer 2001

Using Regression Analysis in
Departmental Budget Allocations
Andrew L. Luna, University of North Alabama
Kelly A. Brennan, The University of Alabama
Contents of Discussion
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General information about budget allocations
Regression Analysis – what is it and how it is
used in this process
Methodology
Results of the analysis, how the results where
used, and recommendations
Didn’t get a paper?
For a copy of this presentation/paper
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[email protected]
Importance of Budget Process
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Offers thorough understanding of the
institutions cost structure for long range
planning
Increases awareness of strengths and
weaknesses
Effective budgeting models enables
institutions to evaluate the changing
institutional environment
Evolution of Resource Allocation
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Focused on departments within colleges
across the university (1980’s)
Faculty performance in relation to
departmental productivity (1990’s)
Distribution of scarce resources across
the university (2000)
(Casper/Henry, 2006;
Middaugh, 2001; Santos 2007)
Departmental Information
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Departmental activities are personnel
intensive
Instructional costs account for 40% of
educational expenditures
Need to account for decentralized
management system
Variables often Cited
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Faculty FTE
Number of Majors/Grad Students
Credit Hour Production
Number of Degrees Awarded
Equipment
Faculty Rank
Delaware Study
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Documents instructional and educational
expenditures at an academic discipline
level of analysis since 1992
Offers insights to how higher education
on a macro level is managing and
allocating instructional resources
Focuses on productivity of faculty based
on the cost per credit hour
Market Influence on Salary
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Strategic decisions involve the evaluation of
both internal and external environments
(Constantin & Lusch, 1994)
Incorporate discipline specific average
faculty salary
Accounts for differences in departmental
budgets & assists in planning/decisionmaking
Annual Budget Process
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In February, all Academic Departments
submit their budget request to the dean
of the college in which they reside.
In March, each dean meets with the Vice
President to discuss college allocation.
Based upon this information, the Vice
President presents his allocation to the
colleges.
The VPAA Wanted to Know….
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Is there a quantitative method to help in
this decision process?
If a method is found can it be
unbiased/equitable?
Will the people and departments affected
be able to understand the quantitative
model?
“There are lies, damned lies, and
statistics.” Mark Twain
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Statistical models can help explain
phenomena, but they are not a sliver
bullet and they are not perfect
It is important to effectively communicate
the methodology behind the models and
to educate when necessary
Statistical Planning
The Complete Approach
Discussion
Regression Analysis
Around the turn of the century, geneticist Francis
Galton discovered a phenomenon called
Regression Toward The Mean. Seeking laws of
inheritance, he found that sons’ heights tended to
regress toward the mean height of the population,
compared to their fathers’ heights. Tall fathers
tended to have somewhat shorter sons, and vice
versa.
y
x
Predictive Versus Explanatory
Regression Analysis
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Prediction – to develop a model to
predict future values of a response
variable (Y) based on its relationships
with predictor variables (X’s)
Explanatory Analysis – to develop an
understanding of the relationships
between response variable and predictor
variables
Problem Statement
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A regression model will be used to try to explain
the relationship between departmental budget
allocations and those variables that could
contribute to the variance in these allocations.
Bud . Alloc. x1 , x2 , x3  xi 
Simple Regression Model
y
Predicted Values
Residuals
r  Y  Yˆ
i
i i
Slope
Actual Values
x
Multiple Regression Model
Y
X1
X2
The First Model - Variables
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Total Departmental Budget (Dependent)
Number of full-time professors
Number of majors
Total degrees conferred
Total credit hours generated
Total credit hours generated by majors
Total lower-level credit hours generated
Total upper-level/grad. Hours generated
Delaware cost per credit hour
Market value of the discipline
Marketability Explained
Area
Dept 1
Dept 2
Mean Salaries Ratio Variable Used
65,423
1.13
52,142
0.90
Dept 3
Dept 4
Dept 5
71,417
50,758
48,775
1.24
0.88
0.85
Dept 6
Dept 7
Average
57,331
58,155
57,714
0.99
1.01
Interactions
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In addition to observing main effects from each
IV, various interactions were observed
Interaction occurs when the magnitude of the
effect of one IV (X) on DV (Y) varies as a
function of a second IV (Z)
The interaction term is simply the product of
two variables
Centering Variables
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Centering variable used in interactions increases
the interpretability and strength of the
interaction
Centering is the process of subtracting the mean
from a variable, leaving deviation scores
Results of Complete Model
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Average budget allocation for the 28
departments = $952,786. The Max =
$2,008,792 and the Min = $310,468
F Statistic = 26.59 (.0001)
R-Squared - .9708
Standard Deviation of the unexplained
budget allocation (Root MSE) = $97,690
Parameter Estimates of Complete
Model
Variable
INTERCEPT
Parameter
Estimate
Pr > |t|
Variable
Parameter
Estimate
Pr > |t|
-526733
0.0905
MARKET
847717
0.0065
44104
<.0001
DELAWARE
117005
0.1767
MAJORS
-228.63457
0.4183
PROF*MAJORS
-55.2971
0.4946
DEGREES
-1480.0107
0.6309
PROF*DEGREES
-283.4041
0.4133
MAJCHRS
17.5550
0.6959
MAJORS*DEGREES
3.4660
0.2394
CHRS
-71.6280
0.5198
CHRS*PROF
-2.2653
0.0226
LLUG
89.7550
0.4350
PROF*MAJCHRS
6.8917
0.5660
ULUG_GRD
36.7241
0.7161
CHRS*DEGREES
0.3978
0.0340
PROF
GR_MAJ
UG_MAJ
CHRS
MARKET
PROF
R-Square and Independent
Variable Contribution To
Budget Allocation
R-Square
increases
with each
new
variable
Results of Selected Model
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F Statistic = 66.04 (.0001)
Adjusted R-Squared - .9497
Standard Deviation of the unexplained
budget allocation (Root MSE) = $96,942
Parameter Estimates of Selected
Model
Variable
Intercept
Parameter
Estimate
Pr > |t|
-544842
0.0027
PROF
43586
<.0001
CHRS
9.4536
0.1474
DEGREES
-1346.6
0.2206
MARKET
842966
<.0001
CHRS*DEGREES
0.20361
0.0104
-1.48669
0.002
CHRS*PROF
What do the Parameter Estimates
Mean for Main Effects?
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Variance in 1 professor increases/decreases the
budget estimate an average of $43,586
Variance in 1/10 in the marketability ratio
increases/decreases the budget estimate an
average of $84,296
What do the Parameter Estimates
Mean for the Interactions?
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Variance in 1 credit hour increases/decreases
the budget estimate an average of 20 cents for
a department with an average number of
degrees conferred
Variance in 1 faculty member
increases/decreases the budget estimate an
average of $1.50 for a department with an
average number of credit hours
Outcome
Turn to page 15 in the Paper
So, What Happened?
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The VPAA reviewed the model along with
the departmental budget requests
He used the model to identify those
departments that were either significantly
under funded or over funded
VPAA made adjustments to budget
allocations based in part upon the model
Recommendations
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Run the model every year and compare to
previous years
Larger universities may want to include
research, distinguished faculty, or differentiate
medical, law, and dental schools from other
programs
Research other factors that may influence
budget allocation
Questions?