Using Regression Analysis in Departmental Budget

Allocations

Andrew L. Luna, University of North Alabama

Kelly A. Brennan, The University of Alabama

Contents of Discussion

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

alluna@una.edukbrennan@bama.ua.edu

Importance of Budget Process 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 Focused on departments within

colleges across the university (1980’s)

Faculty performance in relation to departmental productivity (1990’s)

Distribution of scarce resources acrossthe university (2000)

(Casper/Henry, 2006; Middaugh, 2001; Santos 2007)

Departmental Information

Departmental activities are personnel intensive

Instructional costs account for 40% of educational expenditures

Need to account for decentralized management system

Variables often Cited

Faculty FTE Number of Majors/Grad Students Credit Hour Production Number of Degrees Awarded Equipment Faculty Rank

Delaware Study

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

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/decision-making

Annual Budget Process

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….

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

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 PlanningThe Complete Approach

Statis

tical

Met

hodo

logy Experience

Discussion

Regression Analysis

y

x

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.

Predictive Versus Explanatory Regression Analysis

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

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.

ixxxxAllocBud 321 ,,..

Simple Regression Model

y

x

Predicted Values

Actual Values

iY

iY

ir ˆ

Residuals

Slope

Multiple Regression Model

Y

X2

X1

The First Model - Variables 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 ExplainedArea Mean

SalariesRatio Variable

Used

Dept 1 65,423 1.13

Dept 2 52,142 0.90

Dept 3 71,417 1.24

Dept 4 50,758 0.88

Dept 5 48,775 0.85

Dept 6 57,331 0.99

Dept 7 58,155 1.01

Average

57,714

Interactions

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

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

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

VariableParameter Estimate Pr > |t| Variable

Parameter Estimate Pr > |t|

INTERCEPT -526733 0.0905 MARKET 847717 0.0065

PROF 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

PR

OF

SU

M_M

AJ

MA

RK

ET

R-Square and IndependentVariable Contribution ToBudget Allocation

CH

RS

UG

_MA

J

GR

_MA

J

DEGREES

R-Square increases with each new variable

Results of Selected Model

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

VariableParameter Estimate Pr > |t|

Intercept -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

CHRS*PROF -1.48669 0.002

What do the Parameter Estimates Mean for Main Effects? 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? 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?

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

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?