MODEL FOR ESTIMATING GENERAL AVIATION

OPERATIONS AT NON-TOWERED AIRPORTS

USING TOWERED AND

NON-TOWERED AIRPORT DATA

July 2001

Prepared for:

Statistics and Forecast Branch

Office of Aviation Policy and Plans

Federal Aviation Administration

Prepared by:

GRA, Inc.

115 West Avenue, Suite 201

Jenkintown, PA 19046
i

TABLE OF CONTENTS

 Page

List of Tables ............................................................................................................ ii

List of Figures .......................................................................................................... iii

Executive Summary................................................................................................ iv

Section

1. Introduction ................................................................................................. 1

2. Methodology and Results from Prior Study........................................... 2

3. New Variables That May Affect Aviation Activity at Small 

 Towered and Non-Towered Airports...................................................... 3

4. New Approaches to Estimating Aviation Activity Levels at Small 

Towered

 and Non-Towered Airports....................................................................... 6

4.1 Models of GA Operations..................................................................... 6

4.2 Model of GA Operations per Based Aircraft ................... 17

5. Applying the Estimated Model to Small Non-Towered GA Airports

 Nationwide .................................................................................................. 18

6. Conclusion ................................................................................................... 22

Appendix A: An Explanation of the Chow Test................................................ 24

Appendix B: Complete Data Set Used for Regression Analysis ..................... 26
ii

LIST OF TABLES

Number Page

Table 1: Selected Equations from Regression Analysis in Hoekstra (2000)... 2

Table 2: Categories of New Independent Variables Used in 

 Regression Analysis................................................................................ 6

Table 3: GA Operations Regression Equations—Data for Small Towered

 GA Airports Only ................................................................................... 8

Table 4: GA Operations Regression Equations—Data for Small Towered

 GA Airports and Non-Towered GA Airports—No Dummy

 Variable..................................................................................................... 12

Table 5: GA Operations Regression Equations—Data for Small Towered 

 GA Airports and Non-Towered GA Airports—With Dummy

 Variable..................................................................................................... 13

Table 6: GA Operations Regression Equations 

 Small Towered GA Airports and Truncated Non-Towered GA 

 Airports Data Set using Dummy Variable to Examine Fit to 

 Non-Towered Airports .......................................................................... 14

Table 7: Best Equation from Minitab Stepwise Regression for Small 

 Towered Airport Operations per Based Aircraft ............................... 17

Table 8: Summary State Data for 2,780 Non-Towered GA Airports .............. 19

Table 9: Model Goodness of Fit Measures for Towered GA Airports, 

 State-Estimated Non-Towered GA Airports, and Form 5010 

 Non-Towered GA Airports ................................................................... 22
iii

LIST OF FIGURES

Number Page

Figure 1: State Estimated and Equation Estimated Annual Operations at 

 Non-Towered Airports ........................................................................ 9

Figure 2: Fit of Out-of-Sample Estimates for 13 Non-Towered Airports 

 Excluded from Estimating Data for Equation 16 ............................. 14

Figure 3: Comparison of Tower Counts and State Estimates to Model 

 Estimates (Equation 9) for Small Towered GA Airports and 

 Non-Towered Airports—Model Without Tower 

 Dummy Variable................................................................................... 15

Figure 4: Comparison of Tower Counts and State Estimates to Model 

 Estimates (Equation 13) for Small Towered GA Airports and 

 Non-Towered Airports—Model with Tower 

 Dummy Variable .................................................................................. 16

Figure 5: Form 5010 Estimates and Model Estimates for Annual 

 GA Operations....................................................................................... 20

Figure 6: Variability of Differences between Form 5010 Annual 

 Operations Estimates and Model Estimates of Annual 

 Operations for U.S. Non-Towered GA Airports .............................. 21
iv

EXECUTIVE SUMMARY

This report develops a model for estimating general aviation (GA) 

operations at

non-towered airports. It builds on previous research done for the FAA Office of 

Policy and Plans, Statistics and Forecast Branch. In the previous research, 

statistical relationships were developed between GA operations at small towered 

airports and the characteristics of these airports. Models based on these 

relationships were used to estimate GA operations for a set of non-towered 

airports for which state estimates (derived primarily from counter and survey 

estimation procedures) were available. The model estimates of operations for the 

non-towered airports tended to exceed the state estimates.

In this report, a new model was estimated that augments the previous 

research by using additional variables for population, airport regional 

prominence, and certificated flight schools. In addition, the model uses a 

combined data set for small towered and non-towered GA airports and 

incorporates a dummy variable to distinguish the two airport types. The new 

model produced operation estimates for non-towered airports that were 

unbiased relative to the state estimates based primarily on sampling procedures. 

The new model was also applied to a large set of 2,789 non-towered GA 

airports. This data set includes all of the non-towered GA airports in the 

Terminal Area Forecast (TAF) not included in the development of the model 

estimation. For the majority of these airports, operation estimates reported on 

DOT Form 5010 are roughly developed and are not based on sampling 

procedures. For these airports, model estimates of annual GA activity were 

compared to the Form 5010 estimates. On average, the model estimates tended 

to be unbiased relative to the reported Form 5010 estimates. In the future, 

research efforts can focus on testing and refining the model for specific subsets of 

the large data set of non-towered GA airports.
1

1. INTRODUCTION

This report presents results from a GRA study aimed at refining and 

improving recent efforts by the FAA Office of Policy and Plans (APO) to model 

aviation activity at non-towered airports. This study was undertaken as part of 

Task Order 16, Task 1 under FAA contract DTFA01-98-C-00096.

In a previous report1, FAA identified several characteristics of small 

towered airports that have a statistically significant relationship to operations at 

these airports. The results quantify observations made in prior APO-funded 

research2 which noted that aviation activity at individual airports is highly 

dependent on “local factors.” It remained clear, however, that additional 

research could improve the set of possible “local factors” considered and could 

refine the equations used to model the relationships between these factors and 

airport activity.

A principal purpose of the research that is contained in this report has 

been to develop models relating “local factors” to airport activity that could be 

used to estimate operations at non-towered airports for which the only counts of 

activity available are at best cursory. Since the FAA uses data on current and 

projected airport activity to guide its airport capital investment decisions, there is 

always a pressing need to improve FAA’s ability to estimate activity at these 

airports and to assess the forecasts made by airport sponsors to support 

investment or facility upgrade requests.

The remainder of this report is organized as follows. Section 2 

summarizes the methodology and results from Hoekstra (2000) and discusses the 

avenues for improving and refining the results applied in this report. Section 3 

identifies and discusses the new data and variables that are used for the current 

analysis and suggests some refinements to the models used in Hoekstra (2000). 

Section 4 reports on the effectiveness of these model refinements, including the 

closeness of fit between the model estimates of airport activity—expressed either 

as annual operations or as average annual operations per based aircraft—and the 

observed values (which may be tower counts from small towered airports in the 

sample or estimates of airport activity based on an explicit sampling procedure). 

Section 5 applies the equations developed in Section 4 to a large set of small nontowered GA airports throughout the United States. These results are examined 

at a very broad level to assess the equation’s value for estimating airport activity. 

Section 6 summarizes the report findings and identifies possible next steps for 

 

1 Mark Hoekstra, “Model for Estimating General Aviation Operations at Non-Towered Airports” 

prepared for FAA Office of Aviation Policy and Plans, April 2000.

2 GRA, Inc. “Review of TAF Methods,” Final Report, prepared for FAA Office of Aviation Policy 

and Plans under Work Order 45, Contract No. DTFA01-93-C-00066, February 25, 1998.
2

future research. Appendix A describes a statistical procedure used in the report, 

and Appendix B contains the data for small towered and non-towered GA 

airports used in the regression analysis.

2. METHODOLOGY AND RESULTS FROM PRIOR STUDY

Hoekstra (2000) developed a sizeable set of airport characteristics from 

varied sources and used these data to estimate regression models explaining 

annual general aviation (GA) operations and annual GA operations per based 

aircraft, using a data set of 127 small towered U.S. airports. These airports had 

fewer than 100,000 GA operations in FY 1999.3 Extensive documentation on 

these airports and the variables collected for them is contained in the Hoekstra 

report. After analysis of these data using the Minitab software and its Stepwise 

Regression procedure, the “best” equations—in terms of proportion of variance 

explained (R2),—were reported. These equations are shown in Table 1 below 

(which is identical to Hoekstra’s Table 11).

Table 1

Selected Equations from Regression Analysis in Hoekstra (2000)

Hoekstra 

Equation 

Number

Equation4 R

2

H-7

H-11

OPS = 813.5 + 417 BA + 0.80 PCI –0.63 BA2 – 11,683 WST – 21,752 AAL –7,072 FAR139 + 4.0 EMP

 (0.12) (7.46) (3.74) (-4.40) (-3.75) (-2.86) (-2.11) (1.68) 

OPSBA = 581.3 – 138.5 BAE100 – 125.9 WST – 326.1 AAL + 113.1 R12

 (18.37) (-3.31) (-2.50) (-2.51) (2.10)

.7296

.2556

The variables that appear in Equations H-7 and H-11 in Table 1 include:

OPS—Annual GA Operations at an airport (FY1999)

OPSBA—Annual GA Operations per Based Aircraft (BA) at an 

airport

BA—Total Based Aircraft at an airport (FY1999)

BA2—Based Aircraft squared, which is included since airport 

operations

 tend to increase as the number of based aircraft increases, but at a 

 slower and slower rate

 

3 Hoekstra (2000) began with 138 such airports, but data considerations reduced this figure to 127 

airports susceptible to analysis. The current report uses the same set of 127 small towered GA 

airports.

4 T-statistics are given in parentheses under each coefficient.
3

PCI—Per Capita Income in the county in which the airport is 

located

 ($1999)

EMP—Non-agricultural Employment in the airport’s county (1999)

FAR139—Categorical variable, 1 if airport is certificated for 

commercial

 air carrier service, 0 otherwise

WST—Categorical variable, 1 if airport is located in FAA Western 

Region

 (excluding Alaska), 0 otherwise

AAL—Categorical variable, 1 if airport is located in Alaska, 0 

otherwise

R12 –Categorical variable, 1 if airport is located in FAA New 

England

 Region or FAA Eastern Region, 0 otherwise

BAE100—Categorical variable, 1 if airport based aircraft is 100 or 

greater,

 0 otherwise

Hoekstra used the equations in Table 1 to assess the results from sampling-based 

counting and extrapolation procedures5 used by nine states at 129 small nontowered airports. It was found that the equations tended to produce higher 

annual operations estimates than the state estimates of annual operations at these 

airports. In addition, the model of Equation H-11 produces modestly better 

estimates of activity at the non-towered airports than that of Equation H-7, even 

though H-7 has a “tighter” fit to the small towered airport data (in terms of R2) 

than does H-11. In addition, Equation H-11 is based entirely on categorical data 

about the FAA region the airport is located in and on the airport having greater 

or fewer than 100 based aircraft.

3. NEW VARIABLES THAT MAY AFFECT AVIATION ACTIVITY AT 

SMALL TOWERED AND NON-TOWERED AIRPORTS

For this analysis several additional types of data were developed for consideration 

as “local factors” affecting activity at small towered and non-towered airports. The set of 

airports used for the analysis is identical to that used in Hoekstra (2000), with the 

exception of a reduction in the set of non-towered airports considered, for reasons given 

below. In some cases these new variables are similar to demographic variables developed

in Hoekstra (2000), and in others the variables represent new types of “local factors.”

Population: County population (POP) and county employment (EMP) are 

significant demographic variables in Hoekstra (2000), but counties vary in size and airports 

vary in position within a county. An airport in a small county may serve those in nearby 

 

5 A variety of counting procedures were cited, including acoustic counters, machine counts, 

surveys, and operations logs, at these airports.
4

counties as well, and an airport located near a county boundary may provide some or most 

of its services to the residents of other counties. To capture this type of demographic 

effect, GRA calculated the 1998 population within 100 miles, 50 miles, and 25 miles from 

each airport in the Hoekstra (2000) data set that also appears in the FAA Terminal Area 

Forecast (TAF).6 It is expected that these variables will be positively correlated with airport 

annual operations. GRA also calculated the ratio of population within 25 miles of the 

airport to population within 100 miles of the airport (which will be a value between 0 and 1) 

as a proxy for relative population density around the airport. While this seems to be a 

reasonable candidate for being a “local factor” influencing airport activity, GRA had no 

prior belief on the direction of its influence.

Airport Prominence--The Proportion of Based Aircraft in Region: GRA calculated, 

for each towered and non-towered TAF airport in Hoekstra (2000), its proportion of based 

aircraft among all TAF GA airports within 50 miles and within 100 miles. This variable will 

be a number between 0 and 1. If the airport has all the based aircraft within the radius in 

question, the variable will take the value 1. GRA’s initial beliefs about this “airport 

prominence” proxy were that it would have a positive influence on airport operations, 

since if an airport were more prominent (had a greater percentage of based aircraft) in its 

region, it would be a more attractive or popular site for aviation, and therefore have more 

operations. As the regression results below indicate, however, this belief was incorrect—it 

turns out that the greater the airport’s “regional prominence” the smaller the number of 

annual operations. This result can be rationalized in the following way: If a single airport 

is “prominent” in its region—has a relatively high percentage of based aircraft—that 

airport likely has the lion’s share of the region’s operations as well, but it also indicates 

that the region itself does not support many operations overall. It seems that if the airport 

is “the only game in town” or “ the major game in town” for a region then the region itself 

is not very active. The “regionally prominent” airport seems to be the big frog in a small 

pond, but not a big frog overall.

Complexity of the Airport’s Based Aircraft: This variable is the ratio of the airport’s 

single engine piston based aircraft to all the based aircraft at the airport. The higher this 

ratio, the less complex (and less costly) are the airport’s based aircraft. It is not clear how 

this variable might be expected to influence airport operations, although the variable may 

be related to the flight school variable, since lower cost single engine piston aircraft might 

be the preferred aircraft for flight school use.

Presence of Certificated Flight School: In Hoekstra (2000) it was found that nearly 

every airport in the data set had flight instruction available, although it was unclear what 

level of complexity or comprehensiveness characterized these training facilities from 

airport to airport. Because flight instruction was virtually ubiquitous across the airports 

examined, the variable provided no meaningful information about airport activity levels. 

 

6

There were 24 non-towered airports that did not appear in the TAF, and for which the “population within 

X miles” could not be calculated. These non-towered airports are not included in the analyses and 

equations that follow, since a complete set of new variables could not be developed for them. These 

airports are: (1H3) Linn State, MO; (1N0) Ridgley Airpark, MD; (2W2) Clearview Airpark, MD; (6MO) 

Washington County, MO; (75K) Bethany Memorial, MO; (7S3) Stark’s Twin Oaks, OR; (8W2) New Market, 

VA; (AOV) Ava Bill Martin, MO; (C16) Frasca Field, IL; (CJR) Culpepper Regional, VA; (DMW) Carroll 

County, MD; (H17) Buffalo Muni, MO; (HRI) Hermiston Muni, OR; (IGQ) Lansing Muni, IL; (K52) Monroe 

City, MO; (M17) Bolivar Muni, MO; (MO3) Stockton Muni, MO; (OXB) Ocean City Muni, MD; (RPD) Rice 

Lake Regional, WI; (S49) Miller Memorial, OR; (SPB) Scappose Industrial, OR; (UAO) Aurora State, OR; and 

(VCB) Nut Tree, CA. In addition, Frederick Municipal in Maryland (FDK) has an unusually large number 

of based aircraft, and is omitted from estimations as an outlier.
5

For this update, GRA examined the FAA VITALS database, maintained by the FAA Flight 

Standards Service. This database contains information on individuals and entities that are 

certificated under various FAR Parts. FAR Part 141 covers requirements for flight school 

certification, and the VITALS data for Part 141 certification identified those certificate 

holders, including the number of employees at each certificated flight school. In addition, 

some airports have more than one certificated flight school on site. Therefore, GRA

developed data on the presence of Part 141 certificated flight schools at each of the 

Hoekstra (2000) data set airports, constructing three specific variables: the presence or 

absence of a certificated flight school at an airport, the number of these flight schools at 

each of these airports, and the number of flight school employees at each of these airport 

certificated flight schools.7

Pacific Coast States: The regional variable WSTAK used in Hoekstra (2000) 

combined states with a Pacific coast boundary (California, Oregon, Washington, and 

Alaska) with more inland western states such as Idaho, Montana, Utah, and others. These 

inland states are more sparsely populated than the coastal states (with the exception of 

Alaska). Because models estimated using the WSTAK variable often resulted in estimates 

of negative annual operations for airports in these inland states, a new categorical regional 

variable was created for those four Pacific coast states for this analysis. This new 

variable—called WACAORAK—turns out to have greater explanatory power than the 

WSTAK variable in the Minitab stepwise regression procedure. 

Table 2 shows the new independent variables used to complement and refine the 

analysis in Hoekstra (2000). Data used in the regression analysis in this report are 

contained in Appendix B. 

 

7 The number of flight school employees is of interest as a proxy for the relative size of each 

school, or for the relative size of certificated flight instruction at each airport for those airports 

with more than one certificated flight school.
6

Table 2

Categories of New Independent Variables Used In Regression Analysis

Variable Name and Definition Measurement/Units Source

Pop25 1998 Population w/i 25 miles

Pop50 Within 50 miles

Pop100 Within 100 miles

Number of people By census tract, U.S. 

Census

Pop25/100 Ratio of Pop25 to Pop100 Proportion, between 0 and 1 By census tract, U.S. 

Census

Se BA/BA Single engine based

 Aircraft/All based aircraft 

Proportion, between 0 and 1 Terminal Area Forecast 

(TAF)

TOWDUM

%in50mi Percentage of based aircraft 

among based aircraft at GA airports 

within 50 miles

%in100mi Percentage of based 

aircraft among based aircraft at GA 

airports within 100 miles

VITFS Presence or absence of 

FAR141 certificated pilot school

VITFSnum Number of FAR141 

certificated pilot schools on airport

VITFSemp Employees of FAR141 

certificated pilot schools at airport

WACAORAK

1 if towered airport, 0 

otherwise

Proportion, between 0 and 1

Proportion, between 0 and 1

1 if FAR141 certificated pilot 

school present, 0 otherwise

Number of FAR141 

certificated pilot schools on 

airport

Number of employees

1 if state is CA, OR, WA, or 

AK, 0 otherwise

TAF

TAF and Mapinfo 

software

TAF and Mapinfo 

software

FAA Flight Standards 

VITALS database

FAA Flight Standards 

VITALS database

FAA Flight Standards 

VITALS database

Categorical/geographical

 4. NEW APPROACHES TO ESTIMATING AVIATION ACTIVITY LEVELS 

AT SMALL TOWERED AND NON-TOWERED AIRPORTS

4.1 Models of GA Operations

The approach taken by GRA for enhancing the Hoekstra (2000) report was to use 

the final models specified in that report as the starting point for our investigations. 
7

Therefore, the new variables developed as potential inputs for modeling smaller airport 

activity were added to the list of variables included in the final Hoekstra (2000) equations, 

and stepwise regression was used to identify those variables that most strongly 

contributed to explaining airport activity, expressed as either annual operations or annual 

operations per based aircraft. These new variables were identified in Section 3 above. 

Table 3 contains the results of this stepwise regression. Note that many of the variables 

developed by Hoekstra remain in the final regression equation, and that some of the newly 

defined variables do not contribute enough to explanatory power to enter the equations in 

Table 3 (or into subsequent sets of equations). 

Since the number of based aircraft remains a highly significant and positive 

regressor, it is important to note that the inverse relationship between annual operations 

and the square of based aircraft also continues from the earlier results in Hoekstra (2000). 

Other things equal, it seems that the number of operations grows as the number of based 

aircraft increases, but at an increasingly slower rate. This “slowdown” is governed by the 

negative coefficient on the square of based aircraft.8

As Equation 9 of Table 3 indicates, towered airport operations are positively related 

to the number of based aircraft, to the population within 100 miles of the airport, and to the 

ratio of the population within 25 miles of the airport to the population within 100 miles of 

the airport. This last result seems to imply that the denser the population is nearby the 

airport (relative to the total population within 100 miles), the greater number of operations 

that occur. Equation 9 also indicates that other things equal, airport activity is negatively 

related to an airport’s presence in the Pacific Coast states of Washington, California, 

Oregon or Alaska, to the square of the number of based aircraft, to the airport’s proportion 

of based aircraft among all based aircraft for GA airports within 100 miles9and to FAR 139 

carrier certification at the airport. 

 

8

It may be worth noting that the coefficients on BA and BA2 in Equation 9 imply that other things 

equal, the number of operations at an airport begins to decrease once the number of based aircraft 

exceeds 653 (which is what 421 divided by 0.64 approximately equals).

9 The negative parameter estimate for the airport’s percentage of based aircraft among all based 

aircraft at airports within 100 miles is somewhat counterintuitive. It might be thought that an 

airport with more of an area’s based aircraft would have more operations, other things equal, but 

this seems to be true only relatively. What seems to be more important is that if a single airport is 

dominant (in terms of based aircraft) within the surrounding 100 miles, then the area itself has 

relatively low levels of GA activity, even if that dominant airport has the bulk of it.
8

Table 3

GA Operations Regression Equations—Data for Small Towered GA Airports Only

Equation 

Number

Equation10 R

2

1

2

3

4

5

6

7

8

9

OPS = 21,555 + 242 BA

 (8.11) (12.52)

OPS = 18,606 + 211 BA + 0.002 Pop100

 (7.55) (11.46) (5.37)

OPS = 18,718 + 229 BA + 0.001 Pop100 –10,059 WACAORAK

 (7.85) (12.2) (5.46) (-3.11)

OPS = 7,495 + 425 BA + 0.001 Pop100 – 12,501 WACAORAK – 0.56 BA2

 (2.04) (7.95) (5.26) (-4.00) (-3.88)

OPS = 12,598 + 453 BA + 0.001 Pop100 – 12,956 WACAORAK - 0.62 BA2 –19,958 %in50mi

 (3.19) (8.60) (2.80) (-4.39) (-4.39) (-2.96) 

OPS = 10,422 + 462 BA + 0.001 Pop100 – 13,754 WACAORAK - 0.68 BA2 – 23,481 %in50mi 

 (2.61) (8.60) (3.07) (-4.58) (-4.84) (-3.46) 

 + 18,587 Pop25/100

 (2.33)

OPS = 9,142 + 449 BA + 0.001 Pop100 – 13,292 WACAORAK - 0.67 BA2 – 8,448 %in50mi 

 (2.29) (8.69) (3.23) (-4.47) (-4.81) (-0.83) 

 

 + 32,823 Pop25/100 - 44,094 %in100mi

 (3.07) (-1.97)

OPS =7,954 + 440 BA + 0.001 Pop100 – 13,024 WACAORAK - 0.65 BA2 

 (2.13) (8.73) (3.87) (-4.41) (-4.74) 

 

 + 36,362 Pop25/100 - 58,055 %in100mi

 (3.71) (-3.93)

OPS =14,449 + 421 BA + 0.001 Pop100 – 12,452 WACAORAK - 0.64 BA2 

 (2.73) (8.25) (3.69) (-4.22) (-4.66) 

 

 + 31,361 Pop25/100 – 52,130 %in100mi - 5,528 FAR139

 (3.09) (-3.47) (-1.72)

.5564

.6402

.6664

.7031

.7231

.7351

.7435

.7420

.7482

One of the principal objectives of this research study is to develop equations by 

which airport “local conditions” can be used to estimate annual operations at other 

airports, in particular non-towered airports for which activity data may be of low or 

uncertain quality. In Hoekstra (2000) a set of non-towered airports from selected states for 

which “reasonable” state estimates of GA operations activity were available was used to 

assess the accuracy of models developed from activity and “local conditions” data at 

small towered airports for estimating non-towered airport activity. A similar assessment 

was used for this report, for a smaller set of non-towered airports as explained above. For 

this purpose, the model represented by Equation 9 in Table 3 was applied to data for 105 

non-towered airports.

Figure 1 shows the comparison between the annual operations estimates at the 

non-towered airports, as extrapolated from the state counter and survey programs used at 

the airports, and the annual operations estimated at each non-towered airport, based on 

 

10 T-statistics are given in parentheses under each coefficient.
9

Equation 9 in Table 3. For 94 airports, or 90 percent of the 105 non-towered airports, the 

operations estimates produced by the equations exceed the state estimates, and for 57 

airports, or 54 percent, the number of annual operations estimated using Equation 9 is 

more than double the state estimates.

Figure 1

State Estimated and Equation Estimated Annual Operations 

at Non-Towered Airports

Thus, as in Hoekstra (2000), a model of GA annual activity developed 

from local conditions at small towered airports explains GA activity at the 

towered airports quite well (in terms of R2), but tends to produce higher 

estimates than the state estimation procedures for a set of non-towered airports. 

This suggests that fundamental distinctions may exist between the determinants 

of activity at these two types of airports (or that there are systematic 

underestimations of activity occurring in the count programs at these nontowered airports). 

It is possible to “bridge” this apparent divergence between the 

characteristics of data from small towered GA airports and data from nontowered GA airports, and to confirm statistically that it exists. The tendency of 

the Equation 9 model to produce higher estimated operations than the state 

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

105 Non-Towered GA Airports

Annual Estimated GA Operations

State Estimates Model Estimates
10

estimates at non-towered GA airports is certainly apparent in Figure 1. This 

tendency may be an expression of the value that a tower adds to an airport’s 

effectiveness and attractiveness to users. Alternately, the tendency may simply 

reflect the effectiveness of FAA establishment criteria for towers, since the 

tendency seems to imply that towers have been placed at airports that, other 

things equal, have more activity than comparable non-towered airports. Finally, 

the tendency of the model may in fact imply that the state estimate programs 

tend to underestimate annual activity levels. 

Regardless of the reason for their differences, bridging the divergence 

between the two data sets can be done by combining them into a single data set 

outright or by combining them in a way that continues to treat the two groups of 

airports somewhat differently. Grouping them together outright overlooks the 

fact that significant differences may exist between the two groups of airports, 

and linking them together in a more discriminating way provides a compromise 

that recognizes that the two groups are in some ways dissimilar even though 

both groups provide information that may be useful for modeling and estimating 

activity at less well documented non-towered airports.

To test the hypothesis that there is a statistically significant difference 

between the estimating equations for small towered and non-towered GA 

airports, a common test procedure, known as the Chow test, was used. The 

Chow test “is the most popular way of testing whether the parameter values 

associated with one data set (say, Period 1 [or with the set of small towered GA 

airports]) are the same as those associated with another data set (say, Period 2 [or 

with the set of GA non-towered airports]).”11 Additional information on the 

Chow test is contained in Appendix A. In both approaches to estimating joint 

equations that include data from both small towered airports and non-towered 

airports (or equations with no dummy variable for “towered” airports and one 

with that dummy variable), the stepwise regression procedure was used to 

choose the best fitting set of variables. 

To perform this test, the stepwise procedure was used to find the best 

estimating equation for the entire data set of towered airports and non-towered 

airports. Because this estimate “forces” the model coefficients to be the same for 

small towered GA airports and non-towered airports, it represents a “restricted” 

regression. The unrestricted regressions occur when the same variables are used 

to estimate separate equations for the small towered GA airport set and the nontowered airport set. The difference in the regression sums of squares for these 

two scenarios (“restricted” and “unrestricted”) can be examined using an F 

distribution, and a significant test result indicates that the two data sets are 

 

11 Peter Kennedy, A Guide to Econometrics, Cambridge, MA: The MIT Press, 1979, p. 87.
11

sufficiently different as to give rise to different model parameters—they cannot 

be combined into a statistically homogeneous single data set.

A second functional form was also estimated in an attempt to relate 

operations at small towered airports and those at non-towered airports. An 

equation that included a dummy variable for “towered airports” was used—a 

variable—denoted TOWDUM—that took the value 1 if the airport was one of the 

127 small towered airports and took the value 0 otherwise. Using an equation of 

this form to estimate a joint model that included both small towered and nontowered airports has the effect of letting each group have its own intercept term, 

while restricting all other coefficients to be equal on other parameters. The 

validity of this method can also be assessed using the Chow test mentioned 

above. 

Tables 4 and 5 show the equations that resulted from these stepwise 

regressions, for the “no dummy variable” and the “with dummy variable” cases 

respectively. (In Table 4, POP is the estimated 1999 population of the county in 

which the airport is located.) In each table, the calculated F-statistic is shown, 

along with the critical F-statistic at the 0.01 level of significance. In both cases, 

we must reject the hypothesis that the small towered airport data set and the 

non-towered airport data set are from similar distributions. (This is so even 

though a comparison of the two tables shows that the strategy of using a dummy 

variable for distinguishing between towered and non-towered airports in the 

joint data set provides a modestly improved R2.)
12

Table 4

GA Operations Regression Equations—Data for Small Towered GA Airports and 

Non-Towered GA Airports—No Dummy Variable

Equation 

Number

Equation12

(No Dummy Variable Used for “Towered Airports”)

R

2

10

All 232 

Airports

11

127 Towered 

Airports

12

105

Non-towered

Airports

OPS = 9,309 + 391 BA – 0.47 BA2 + 3.1 POP + 7,095 FAR139 + 0.001 Pop100 + 5,190 VITFSnum 

 (1.49) (9.19) (-3.69) (2.62) (3.22) (3.32) (2.45) 

 

 - 11,091 WACAORAK – 11,220 seBA/BA Regression SS: 1.15679E+11

 (-4.39) (-1.57)

OPS = 13,256 + 386 BA – 0.55 BA2 + 0.33 POP – 7,711 FAR139 + 0.001 Pop100 + 3,764 VITFSnum 

 (1.92) (7.20) (-3.96) (0.28) (-2.28) (4.37) (1.67) 

 

 - 12,272 WACAORAK + 4,997 seBA/BA Regression SS: 5.23207E+10

 (-3.81) (0.64)

OPS = 21,905 + 216 BA – 0.07 BA2 + 27.3 POP + 20,641 FAR139 + 0.001 Pop100 + 3,701 VITFSnum 

 (1.66) (2.62) (-0.27) (2.95) (3.40) (1.08) (0.91) 

 

 - 5,697 WACAORAK – 21,853 seBA/BA Regression SS: 3.11064E+10

 (-1.50) (-1.44)

Chow Test result: F-statistic calculated from data: 9.19, distributed as F(232,9), with critical 

value 4.33 at 1% significance level: Reject hypothesis that the Towered and Non-Towered data 

come from similar distributions as represented by Equation 10.

.7170

.7270

.6480

While the Chow test results indicate that there are basic differences 

between the towered and non-towered airport data sets, it may remain practical 

to use the joint models, with the dummy variable TOWDUM to distinguish 

between towered and non-towered characteristics. This is especially true 

because activity levels for the non-towered airports in the data set are themselves 

based on state estimates, rather than actual counts as with the small towered 

airports. To see how effectively the dummy variable approach might be used for 

estimating activity at non-towered airports outside the sample set, GRA made 

two comparisons. 

 

12 T-statistics are given in parentheses under each coefficient.
13

Table 5

GA Operations Regression Equations 

Data for Small Towered GA Airports and Non-Towered GA Airports—With Dummy Variable

Equation 

Number

Equation13

( Dummy Variable for “Towered” Used)

R

2

13

All 232 

Airports,

Dummy

Variable for 

Towered

14

127 Towered 

Airports

15

105 NonTowered

Airports

OPS = -571 + 355 BA – 0.46 BA2 – 40,510 %in100mi + 3,795 VITFSnum + 0.001 Pop100 

 (-0.25) (8.41) (-3.83) (-2.79) (1.87) (3.48) 

 

 - 8,587 WACAORAK + 24,102 Pop25/100 + 13,674 TOWDUM Regression SS: 

 (-3.61) (2.67) (6.44) 1.19818E+11

OPS = 7,731 + 428 BA – 0.65 BA2 – 54,681 %in100mi + 3,485 VITFSnum + 0.001 Pop100 

 (2.08) (8.47) (-4.77) (-3.69) (1.63) (4.07) 

 

 - 12,856 WACAORAK + 34,958 Pop25/100 Regression SS: 5.3772E+10

 (-4.38) (3.58) 

OPS = 775 + 241 BA – 0.14 BA2 + 31,478 %in100mi + 5,577 VITFSnum + 0.001 Pop100 

 (0.22) (2.52) (-0.46) (0.85) (1.23) (1.80) 

 

 - 3,736 WACAORAK + 12,121 Pop25/100 Regression SS: 2.7327E+10

 (-0.89) (0.65) 

Chow Test result: F-statistic calculated from data: 11.5, distributed as F(232,9), with critical 

value 4.33 at 1% significance level: Reject hypothesis that the Towered and Non-Towered data 

come from similar distributions as represented by Equation 13.

.7430

.7480

.5690

In the first, one-seventh of the non-towered airports were randomly 

excluded from the joint data set.14 Using this combined but “truncated” data set 

of 127 towered airports and 90 non-towered airports, GRA re-estimated the 

model (using the dummy variable approach). Then, using this re-estimated 

equation, the expected operations at the omitted non-towered airports were 

calculated. Table 6 shows the equation that resulted from this estimation for the 

truncated data set (note that the equation has the same functional form as 

Equation 13 in Table 5 above). Figure 2 shows the state estimates and equation 

estimates for this “out of sample” estimation of annual GA operations for the 15 

non-towered airports randomly excluded from the data set. In Figure 2, the 

airports are listed, left to right, in ascending order of state estimated annual GA 

operations, for ease of viewing. The data shown in Figure 2 depict a closer fit of 

model estimates to state estimates than does Figure 1 above. For Figure 2, only 

six, or 40 percent of the model estimates exceed the state estimates (compared to 

90 percent in Figure 1), and only one, or seven percent of the model estimates are 

more than double the state estimates (compared to 54 percent in Figure 1).

 

13 T-statistics are given in parentheses under each coefficient.

14 Airports were randomly excluded from the list of 105 non-towered GA airports by ordering the 105 

airports alphabetically by LOCID and then excluding every seventh airport from this list. The LOCIDS of 

the 15 excluded airports are (in order of state estimated annual GA operations, as along the horizontal axis 

of Figure 2) RIF, BUM, AJG, GLY, M58, FWC, OKV, O61, RBG, GGW, 7S5, CBE, 0W3, JYO, and 

ESN. 
14
15

Table 6

GA Operations Regression Equations

Small Towered GA Airports and Truncated Non-Towered GA Airports Data Set 

using Dummy Variable to Examine Fit to Non-Towered Airports

Equation 

Number

Equation15

( Dummy Variable for “Towered” Used)

R

2

16

All Airports

Dummy

Variable for 

Towered, 15 

Non-Towered 

Airports 

Excluded

OPS = -1,215 + 370 BA – 0.49 BA2 – 48,631 %in100mi + 3,663 VITFSnum + 0.001 Pop100 

 (-0.50) (8.45) (-4.01) (-3.21) (1.75) (3.04) 

 

 7,793 WACAORAK + 26,801 Pop25/100 + 13,791 TOWDUM 

 (-3.21) (2.92) (6.17) 

.7450

Figure 2

Fit of Out-of-Sample Estimates for 15 Non-Towered Airports Excluded from 

Estimating Data for Equation 16

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

Non-Towered GA Airports, Ranked by State Estimated Annual GA Operations

State and Model Estimated Annual GA Operations

State Ops Estimate Model Ops Estimate

Visual examples can be seen in Figures 3 and 4. Both figures show the 

annual operations tower counts (on the left) and annual operations state 

 

15 T-statistics are given in parentheses under each coefficient.
16

estimates (on the right), each ranked from least to greatest. Thus, on the 

horizontal axis of both Figure 3 and Figure 4 is a sequence of the 232 airport data 

set, first the 127 small towered GA airports, ranked from fewest annual 

operations to greatest, and then the 105 non-towered GA airports, ranked from 

fewest state estimated operations to greatest.

In Figure 3, model estimates for both the towered airports and the nontowered ones are shown using Equation 9 from Table 3, the best fitting equation 

based on the towered airport data alone. On the left side of the Figure, the 

equation estimates are evenly distributed around the towered airport data set, 

but on the right side one can clearly see the tendency of this equation to produce 

higher estimates relative to the state estimates of activity at the non-towered 

airports. (Note: The right side of Figure 3 shows the same comparison of model 

estimates and state operations estimates as Figure 1.)

Figure 3

 Comparison of Tower Counts and State Estimates to Model Estimates 

 (Equation 9) for Small Towered GA Airports and Non-Towered Airports—Model

 Without Tower Dummy Variable

In Figure 4, however, the model estimates are based on Equation 13, the 

best-fitting equation for the joint set of 232 towered and non-towered GA 

airports (using the TOWDUM dummy variable to separate some of the towered 

and non-towered effects). In this figure, the model estimates are evenly 

distributed around both the towered airport tower count data and the non0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

Towered GA Airports, Ranked by --- Non-Towered GA Airports, Ranked by 

Annual GA Ops (Left) State Estimated Annual GA Ops (Right)

Annual GA Operations

Tower Counts/State Estimates Model Estimates
17

towered airport state estimates. This equation can be regarded as utilizing 

information about small towered GA airports to model small non-towered GA 

airports, while maintaining some unique factors of these non-towered facilities 

(in a way that Equation 9, based solely on towered airport data does not).

Figure 4

 Comparison of Tower Counts and State Estimates to Model 

 Estimates (Equation 13) for Small Towered GA Airports and Non-Towered 

Airports—Model with Tower Dummy Variable

The out of sample procedure and the value of information from the 

towered airport data for modeling estimates of annual operations in the nontowered airport set suggest a productive next step for this modeling and research 

analysis. One use of the model equations shown above, in particular, Equation 

13, is to estimate operations for a large data set of U.S. non-towered airports 

contained in the Terminal Area Forecast (TAF). For the majority of these 

airports, operation estimates reported on DOT Form 5010 are roughly developed 

and are not based on sampling procedures. This step would allow a rough 

assessment to be made of the plausibility of these 5010 data, and would 

potentially provide APO staff with a means of assessing claims about airport 

operations at these types of poorly documented non-towered airports.

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

Towered GA Airports, Ranked by --- Non-Towered GA Airports, Ranked by 

Annual GA Ops (Left) State Estimated Annual GA Ops (Right)

Annual GA Operations

Tower Counts/State Estimates Model Estimates
18

4.2 Model of GA Operations per Based Aircraft

Hoekstra (2000) also estimated models of operations per based aircraft at 

the small towered GA airports in the data set; these models generally had poorer 

explanatory power than the models of GA operations per se. Also worth noting 

is the fact that the model of GA operations per based aircraft that was most 

effective—shown as Equation H-11 in Table 1 above—actually included no 

airport “local factors” other than the range of based aircraft and some dummy 

variables for the airport’s FAA region. For this study, GRA used the Minitab 

Stepwise Regression procedure to modestly improve the model of Equation H-11 

by including the four categorical variables included in H-11 and the new 

variables developed for this report. The results of this procedure are reported in 

Table 7. In Equation 17, operations per based aircraft are reduced (i.e., have 

negative coefficients) for airports with greater than 100 based aircraft, for those 

in the Western or Alaska regions, for those that are “regionally prominent” in the 

sense that they have a large proportion of all based aircraft at nearby airports, 

and for those with relatively higher populations within 50 miles. Operations per 

based aircraft are modestly increased (i.e., have positive coefficients) for those 

airports with relatively higher populations within 100 miles.

Table 7

Best Equation from Minitab Stepwise Regression for Small Towered Airport Operations per 

Based Aircraft

Equation 

Number Equation16 R

2

17 OPSBA = 595.2 – 164 BAE100 – 325 %BA100 - 107 WST – 244 AAL 

 (15.2) (-3.84) (-1.56) (-2.17) (-1.85)

 + 0.00002 Pop100 – 0.00002 Pop50

(2.51) (-1.79)

.3072

The modeling approach represented by Equation 17, which estimates 

annual GA operations per based aircraft, has not been pursued further in this 

report for three reasons. First, the goodness of fit to the data, based on the model 

R2, is significantly lower than that in the models that estimate annual GA 

operations alone. Second, the explanatory variables that are significant for the 

regression equation are mainly categorical or regional variables, and thus say 

little about sources of variability from airport to airport (which may include the 

number of based aircraft at an airport, a factor that is only included in the 

categorical variable BAE100 in equation 17). Finally, for many of the nontowered airports that are the focus of this report, based aircraft may be a more 

 

16 T-statistics are given in parentheses under each coefficient.
19

reliable estimate than annual operations. This circumstance makes a model that 

treats an airport's number of based aircraft as an important factor in explaining 

annual GA operations somewhat more compelling.

5. APPLYING THE ESTIMATED MODEL TO SMALL NON-TOWERED GA 

AIRPORTS NATIONWIDE

The estimating equation shown as Equation 13 of Table 5 was used to 

develop model estimates for 2,789 non-towered GA airports across the country 

and its territories. This data set includes all of the non-towered GA airports in 

the TAF not included in the development of the model estimation. For the 

majority of these airports the operation estimates reported on DOT Form 5010 

are not based on sampling procedures. The demographic and other “local 

factors” data were gathered, and the model equation applied. This section 

discusses some broad initial results from this effort.

Table 8 summarizes data for 2,780 of the non-towered GA airports that are 

located in U.S. states (the remainder are located in U.S. territories such as the 

Virgin Islands). For each state, the data include the number of non-towered TAF 

airports in the state (excluding those non-towered airports that were part of the 

modeling process in Hoekstra (2000) and the prior sections of this report), the 

maximum number of annual GA operations per airport reported in the state and 

the minimum number reported. Some airports (13, or 0.5%) report 0 annual GA 

operations on their 5010 report, and 225, or eight percent, report fewer than 1,000 

annual GA operations. Also shown in the table are average absolute percentage 

deviations between model estimates (based on Equation 13) and the airport 5010 

estimate.17

The state-by-state data shown in Table 8 indicates a wide range of 

reported annual operations by non-towered GA airports in most states. Since 

these data are based on airport-specific Form 5010 estimates, it is not clear how 

much of this range should be attributed to variability in airport usage and how 

much to variability in Form 5010 reporting and estimation procedures. The table 

also suggests that a closer look, on a state-by-state basis, at relationships between 

airport operations and the other demographic or “local factor” data could add to 

APO’s understanding of the determinants of airport activity by GA users of the 

National Airspace System.

 

17 No percentage absolute deviation is reported for Alaska because several Alaska airports report 0 annual 

operations, which (even if changed to 1 operation) make the absolute deviation from the model estimate 

quite large in percentage terms. For other states, those airports reporting 0 or very small numbers of annual 

operations are omitted from the average absolute percentage deviation.
20

 Table 8

 Summary State Data for 2,780 Non-Towered GA Airports

Maximum Minimum Average

NonTowered Annual GA Annual GA Absolute

State GA Airports Ops (5010) Ops (5010) Deviation (%)

AK 226 61,000 0 ----

AL 62 90,000 672 49%

AR 74 90,000 200 67%

AZ 33 64,000 700 68%

CA 145 100,000 100 88%

CO 47 95,990 259 59%

CT 10 58,656 1,345 128%

DE 3 42,000 35,000 45%

FL 54 97,085 0 72%

GA 85 73,000 1,000 55%

HI 9 73,950 100 580%

IA 73 47,408 1,000 38%

ID 32 85,710 5,787 46%

IL 75 90,980 950 62%

IN 62 63,622 2,483 40%

KS 80 87,473 1,300 39%

KY 44 49,909 800 31%

LA 41 63,772 500 49%

MA 22 97,105 6,922 45%

MD 17 91,100 1,295 64%

ME 22 60,500 1,400 62%

MI 92 86,534 1 59%

MN 75 68,400 2,420 44%

MO 57 33,128 1,091 41%

MS 66 60,000 400 59%

MT 68 62,300 1 54%

NC 61 65,624 2,300 45%

ND 40 63,681 100 56%

NE 63 65,000 225 35%

NH 11 93,381 5,730 34%

NJ 29 90,000 2,635 46%

NM 41 67,483 10 164%

NV 25 77,000 50 115%

NY 73 90,000 0 73%

OH 83 81,915 2,100 56%

OK 69 93,504 50 56%

OR 48 74,267 1,572 52%

PA 62 80,310 3,000 43%

RI 4 34,390 9,008 80%

SC 52 92,266 1,000 56%

SD 44 52,806 300 54%

TN 61 67,704 576 37%

TX 175 97,000 600 38%

UT 34 94,583 607 68%

VA 42 93,882 1,000 52%

VT 10 33,800 400 66%

WA 44 96,215 2,700 51%

WI 82 84,391 2,000 45%

WV 21 48,356 110 124%

WY 32 29,927 650 43%
21

Figure 5 depicts the Form 5010 report of annual GA operations estimates 

for the entire set of 2,789 non-towered GA airports. For ease of viewing, the 

airports are ranked, from left to right on the horizontal axis of the figure, from 

fewest 5010 operations to greatest. Thus, the horizontal axis of the figure is made 

up of 2,789 individual airport data filings, which are shown increasing in a 

somewhat exponential curve from least to greatest. For each of these airports, 

the model estimate of annual GA operations is also shown. These estimates vary 

in their accuracy, and appear as dots around the increasing line depicting the 

ranked 5010 operations reports. The model produces higher estimates of annual 

GA operations, relative to the Form 5010 estimate, for 973 airports (or about 35 

percent), and produces lower estimates for 1,816 airports (about 65 percent). For 

84 airports (or about three percent) the model produces estimates of negative 

annual operations. This occurs predominantly in Alaska and other sparsely 

populated northwestern states, in which an airport may be quite prominent 

within the surrounding 100 miles, leading its model estimate to be strongly 

affected by the large negative coefficient on local prominence.

Figure 5

Form 5010 Estimates and Model Estimates for Annual GA Operations 

at 2,789 Non-Towered GA Airports

-60000.0

-40000.0

-20000.0

0.0

20000.0

40000.0

60000.0

80000.0

100000.0

120000.0

2,789 Nontowered GA Airports Ranked by 5010 Ops Estimates

Estimated Annual Ops

Model Estimate Airport 5010 Estimate
22

Figure 6 illustrates the pattern of variability that exists between Form 5010 

and model-based operations estimates. In Figure 6, the horizontal axis again 

contains the 2,789 non-towered GA airports ranked, from left to right, by Form 

5010 GA operations estimates. For each of these airports, the chart displays the 

absolute percentage deviation of the model estimate from the airport’s 5010 

estimate of annual operations. Also shown in the chart is a trend line, which is 

constructed by averaging the 25 average percentage deviation calculations to the 

right and left of each airport. Such a trending procedure, called a “moving 

average,” smoothes the airport-to-airport variability out of the absolute 

percentage deviation data to make general patterns more visible. This figure 

shows that for most of the 2,789 airports (and in particular after Form 5010 

estimated GA annual operations exceed 3,000) absolute percentage deviation 

remains fairly stable at between 40 and 55 percent. Note, however, that Figure 5 

indicates in addition that with growing estimates of annual operations (that is, 

moving from left to right in the figure), model estimates tend to be less than 

those reported in Form 5010 estimates.

Figure 6

Variability of Differences between Form 5010 Annual Operations Estimates and Model 

Estimates of Annual Operations for U.S. Non-Towered GA Airports

0%

50%

100%

150%

200%

250%

300%

Nontowered GA Airports Ranked by 5010 Ops Estimates

Absolute Percentage Deviation, Form 5010 Operations Estimates and 

Model Estimates

% Absolute Deviation Moving Average Trend 
23

 The "flattening out" of the moving average trend in Figure 6 provides 

evidence that the model developed in this paper provides a consistent approach 

to estimating non-towered GA airport operations using demographic and "local 

factor" data. Table 9 reports the average absolute deviations and the average 

absolute percentage deviations for the small towered GA airports (Equations 9 

and 13), for the non-towered GA airports with state operation estimates based 

primarily on sampling procedures (Equations 9 and 13), and for the large set of 

non-towered GA airports (Equation 13 only, for all 2, 789 airports, for those 2,628 

airports reporting more than 500 annual GA operations, and for those 2,469 

airports reporting more than 2,000 annual GA operations). These values indicate 

that the joint Equation 13, which links the towered and non-towered GA airport 

data, provides a model with improved estimating consistency for the 105 nontowered airports with state estimates based primarily on sampling procedures. 

Table 9

Model Goodness of Fit Measures for Towered GA Airports, State-Estimated Non-Towered 

GA Airports, and Form 5010 Non-Towered GA Airports

Set of Airports Equation Average 

Absolute 

Deviation

Standard 

Deviation of 

Absolute 

Deviation

Average 

Absolute 

Percentage 

Deviation

Standard 

Deviation of 

Absolute 

Percentage 

Deviation

127 Small 

Towered GA 

Airports

Equation 9 (no dummy) 9,537.0 7,213.8 25.2 % 30.82 %

Equation 13 (w/ dummy) 10,121.2 6987.8 28.4 % 39.7 %

105 NonTowered GA 

Airports

Equation 9 (no dummy) 20,029.8 11,648.3 236.5 % 427.8 %

Equation 13 (w/ dummy) 10,011.7 10,640.4 80.0 % 190.1 %

2,789 NonTowered GA 

Airports

Eq. 13, all 2,789 airports 8,634 11,063 2,114 % 38,180 %

Eq. 13, Est. Ops > 500 8,949 11,235 60 % 103 %

Eq. 13, Est. Ops > 2,000 9,540 11,482 50 % 62 %

6. CONCLUSION

The work described in this report has refined the modeling technique 

developed in Hoekstra (2000) by adding new explanatory variables that are 

related to the “local factors” that influence aviation activity at small airports and 

by developing new functional approaches that allow joint equations to link the 

small towered airport data set and the non-towered airport data set. This linkage

addresses and remedies to some extent the tendency of models based solely on 

towered airport data to exceed state-estimated activity (with estimates based on 
24

other non-econometric methods) at non-towered airports. The modeling has also 

quantified important differences between small towered GA airports and nontowered ones, giving an improved view of the impact a tower might have on 

aviation activity. Statistical testing indicates that there are fundamental 

differences between the characteristics of activity at small towered airports and 

activity at their non-towered counterparts. In spite of these differences, the 

report has also shown that a joint model of towered GA airports and nontowered ones can provide more unbiased estimates for activity at these nontowered airports, compared to a model based on towered airport activity alone.

These improvements suggest that the joint models may be used, in 

combination with “local factors” and demographic data for a broader set of nontowered airports, to begin a rough assessment of activity at these non-towered 

airports. This report has provided a preliminary estimate of this data for 2,789 

small non-towered GA airports. A more detailed examination of these airports 

and of the relationship between the activity levels estimated for them in 5010 

data and their demographic and other characteristics may provide new tools for 

characterizing and categorizing these airports. Such an assessment tool for small 

GA airports could provide APO analysts with an improved ability to assess the 

reliability of master plans and activity forecasts at these smaller airports. 
25

APPENDIX A

THE CHOW TEST FOR CHANGING PARAMETER VALUES

The Chow test (named after the noted econometrician Gregory Chow) is a 

commonly used test for determining whether a single regression equation can be 

applied to a data set. The test compares results from a regression run over the 

entire data set of interest—the “restricted” or “constrained” regression, since the 

parameters are “restricted” or “constrained” to be equal for the entire data set—

with results from an “unrestricted” or “unconstrained” regression which allows 

the data set to be broken into two pieces for which there is some plausible 

rationale. Examples of such rationales might be breaking a time series of 

economic data into a pre-World War II set and a post-World War II set, or 

breaking a set of small airport data into two subsets, one for small towered 

airports and one for small non-towered airports. For the defined subsets, the 

regression equation identical to that used for the “restricted” regression (in some 

or all parameters) is used for each of the subgroups of data. 

The test statistic, which is distributed as an F-distribution, is based on the 

regression sums of squares from the “restricted” and “unrestricted” estimations. 

Test statistic parameters are the number of data points in the total data set—N—

(that used for the “restricted” estimation), the number of parameters being 

“restricted” to being held constant in the restricted estimation—R, and the 

number of regressor variables in the “unrestricted” estimation—K. The test 

statistic is calculated as 

 

 ( )/( )

( ( ) ( ) /

SSE unrestricted N K

SSE restricted SSE unrestricted R





and is distributed as an F-statistic with R and (N-K) degrees of freedom. If the 

test statistic exceeds the critical F(R,N-K) value of choice, we conclude that the 

two sub-data sets should not be regarded as coming from the same population.
APPENDIX B

COMPLETE DATA SET USED FOR REGRESSION ANALYSIS