develops and presents a regression model for estimating general aviation
(GA) operations at non-towered airports. Independent variables used in
the model include airport characteristics, demographics, and geographic
features. The model was derived using a combined data set for small
towered and non-towered GA airports and incorporates a dummy variable to
distinguish the two airport types. In addition, the report applies the
model to estimate activity at 2,789 non-towered GA airports contained in
the Terminal Area Forecast.

Publication Date: July 2001

APO Contact: J. Peter LeBoff

E-mail: Peter.LeBoff@faa.gov

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

TABLE OF CONTENTS

[Page]{.underline}

List of Tables ii

List of Figures iii

Executive Summary iv

[Section]{.underline}

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

**LIST OF TABLES**

[Number]{.underline} [Page]{.underline}

## 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

**LIST OF FIGURES**

[Number]{.underline} [Page]{.underline}

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

**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. 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 report[^1], 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 research[^2] 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 non-towered 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 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 (R^2^),---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)**

+-------+--------------------------------------------------------+----+
| **Hoe | **Equation**[^4]                                       | ** |
| kstra |                                                        | R^ |
| Equ   |                                                        | 2^ |
| ation |                                                        | ** |
| Num   |                                                        |    |
| ber** |                                                        |    |
+-------+--------------------------------------------------------+----+
| H-7   | OPS = 813.5 + 417 BA + 0.80 PCI --0.63 BA2 -- 11,683   | .  |
|       | WST -- 21,752 AAL --7,072 FAR139 + 4.0 EMP             | 72 |
| H-11  |                                                        | 96 |
|       | (0.12) (7.46) (3.74) (-4.40) (-3.75) (-2.86) (-2.11)   |    |
|       | (1.68)                                                 | .  |
|       |                                                        | 25 |
|       | OPSBA = 581.3 -- 138.5 BAE100 -- 125.9 WST -- 326.1    | 56 |
|       | AAL + 113.1 R12                                        |    |
|       |                                                        |    |
|       | (18.37) (-3.31) (-2.50) (-2.51) (2.10)                 |    |
+-------+--------------------------------------------------------+----+

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
>
> 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 procedures[^5] used by nine
states at 129 small non-towered 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 R^2^)
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 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. 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.

# Table 2

**Categories of New Independent Variables Used In Regression Analysis**

+----------------------------+---------------------+------------------+
| **Variable Name** **and    | ######              | ####### Source   |
| Definition**               | # Measurement/Units |                  |
+----------------------------+---------------------+------------------+
| **Pop25** 1998 Population  | Number of people    | By census tract, |
| w/i 25 miles               |                     | U.S. Census      |
|                            |                     |                  |
| **Pop50** Within 50 miles  |                     |                  |
|                            |                     |                  |
| **Pop100** Within 100      |                     |                  |
| miles                      |                     |                  |
+----------------------------+---------------------+------------------+
| **Pop25/100** Ratio of     | Proportion, between | By census tract, |
| Pop25 to Pop100            | 0 and 1             | U.S. Census      |
+----------------------------+---------------------+------------------+
| **Se BA/BA** Single engine | Proportion, between | Terminal Area    |
| based                      | 0 and 1             | Forecast (TAF)   |
|                            |                     |                  |
| Aircraft/All based         |                     |                  |
| aircraft                   |                     |                  |
+----------------------------+---------------------+------------------+
| ### TOWDUM                 | 1 if towered        | TAF              |
|                            | airport, 0          |                  |
| **%in50mi** Percentage of  | otherwise           | TAF and Mapinfo  |
| based aircraft among based |                     | software         |
| aircraft at GA airports    | Proportion, between |                  |
| within 50 miles            | 0 and 1             | TAF and Mapinfo  |
|                            |                     | software         |
| **%in100mi** Percentage of | Proportion, between |                  |
| based aircraft among based | 0 and 1             | FAA Flight       |
| aircraft at GA airports    |                     | Standards VITALS |
| within 100 miles           | 1 if FAR141         | database         |
|                            | certificated pilot  |                  |
| **VITFS** Presence or      | school present, 0   | FAA Flight       |
| absence of FAR141          | otherwise           | Standards VITALS |
| certificated pilot school  |                     | database         |
|                            | Number of FAR141    |                  |
| **VITFSnum** Number of     | certificated pilot  | FAA Flight       |
| FAR141 certificated pilot  | schools on airport  | Standards VITALS |
| schools on airport         |                     | database         |
|                            | Number of employees |                  |
| **VITFSemp** Employees of  |                     | Categori         |
| FAR141 certificated pilot  | 1 if state is CA,   | cal/geographical |
| schools at airport         | OR, WA, or AK, 0    |                  |
|                            | otherwise           |                  |
| ### WACAORAK               |                     |                  |
+----------------------------+---------------------+------------------+

**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. 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 miles[^9] and to FAR 139
carrier certification at the airport.

## Table 3

######### GA Operations Regression Equations---Data for Small Towered GA Airports Only

+-------+--------------------------------------------------------+----+
| **Equ | **Equation**[^10]                                      | ** |
| ation |                                                        | R^ |
| Num   |                                                        | 2^ |
| ber** |                                                        | ** |
+-------+--------------------------------------------------------+----+
| 1     | OPS = 21,555 + 242 BA                                  | .  |
|       |                                                        | 55 |
| 2     | (8.11) (12.52)                                         | 64 |
|       |                                                        |    |
| 3     | OPS = 18,606 + 211 BA + 0.002 Pop100                   | .  |
|       |                                                        | 64 |
| 4     | (7.55) (11.46) (5.37)                                  | 02 |
|       |                                                        |    |
| 5     | OPS = 18,718 + 229 BA + 0.001 Pop100 --10,059 WACAORAK | .  |
|       |                                                        | 66 |
| 6     | (7.85) (12.2) (5.46) (-3.11)                           | 64 |
|       |                                                        |    |
| 7     | OPS = 7,495 + 425 BA + 0.001 Pop100 -- 12,501 WACAORAK | .  |
|       | -- 0.56 BA2                                            | 70 |
| 8     |                                                        | 31 |
|       | (2.04) (7.95) (5.26) (-4.00) (-3.88)                   |    |
| 9     |                                                        | .  |
|       | OPS = 12,598 + 453 BA + 0.001 Pop100 -- 12,956         | 72 |
|       | WACAORAK - 0.62 BA2 --19,958 %in50mi                   | 31 |
|       |                                                        |    |
|       | (3.19) (8.60) (2.80) (-4.39) (-4.39) (-2.96)           | .  |
|       |                                                        | 73 |
|       | OPS = 10,422 + 462 BA + 0.001 Pop100 -- 13,754         | 51 |
|       | WACAORAK - 0.68 BA2 -- 23,481 %in50mi                  |    |
|       |                                                        | .  |
|       | (2.61) (8.60) (3.07) (-4.58) (-4.84) (-3.46)           | 74 |
|       |                                                        | 35 |
|       | \+ 18,587 Pop25/100                                    |    |
|       |                                                        | .  |
|       | (2.33)                                                 | 74 |
|       |                                                        | 20 |
|       | OPS = 9,142 + 449 BA + 0.001 Pop100 -- 13,292          |    |
|       | WACAORAK - 0.67 BA2 -- 8,448 %in50mi                   | .  |
|       |                                                        | 74 |
|       | (2.29) (8.69) (3.23) (-4.47) (-4.81) (-0.83)           | 82 |
|       |                                                        |    |
|       | \+ 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)                                 |    |
+-------+--------------------------------------------------------+----+

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 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

![](media/image1.wmf){width="5.976388888888889in"
height="4.086111111111111in"}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 R^2^), 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 non-towered airports).

It is possible to "bridge" this apparent divergence between the
characteristics of data from small towered GA airports and data from
non-towered GA airports, and to confirm statistically that it exists.
The tendency of the Equation 9 model to produce higher estimated
operations than the state 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
non-towered 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 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 non-towered 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 R^2^.)

## Table 4

**GA Operations Regression Equations---Data for Small Towered GA
Airports and**

**Non-Towered GA Airports---No Dummy Variable**

+-------+--------------------------------------------------------+----+
| **Equ | **Equation**[^12]                                      | ** |
| ation |                                                        | R^ |
| Num   | **(No Dummy Variable Used for "Towered Airports")**    | 2^ |
| ber** |                                                        | ** |
+-------+--------------------------------------------------------+----+
| 10    | OPS = 9,309 + 391 BA -- 0.47 BA2 + 3.1 POP + 7,095     | .  |
|       | FAR139 + 0.001 Pop100 + 5,190 VITFSnum                 | 71 |
| All   |                                                        | 70 |
| 232   | (1.49) (9.19) (-3.69) (2.62) (3.22) (3.32) (2.45)      |    |
| Air   |                                                        | .  |
| ports | \- 11,091 WACAORAK -- 11,220 seBA/BA Regression SS:    | 72 |
|       | 1.15679E+11                                            | 70 |
| 11    |                                                        |    |
|       | (-4.39) (-1.57)                                        | .  |
| 127   |                                                        | 64 |
| To    | OPS = 13,256 + 386 BA -- 0.55 BA2 + 0.33 POP -- 7,711  | 80 |
| wered | FAR139 + 0.001 Pop100 + 3,764 VITFSnum                 |    |
| Air   |                                                        |    |
| ports | (1.92) (7.20) (-3.96) (0.28) (-2.28) (4.37) (1.67)     |    |
|       |                                                        |    |
| 12    | \- 12,272 WACAORAK + 4,997 seBA/BA Regression SS:      |    |
|       | 5.23207E+10                                            |    |
| 105   |                                                        |    |
|       | (-3.81) (0.64)                                         |    |
| N     |                                                        |    |
| on-to | OPS = 21,905 + 216 BA -- 0.07 BA2 + 27.3 POP + 20,641  |    |
| wered | FAR139 + 0.001 Pop100 + 3,701 VITFSnum                 |    |
|       |                                                        |    |
| Air   | (1.66) (2.62) (-0.27) (2.95) (3.40) (1.08) (0.91)      |    |
| ports |                                                        |    |
|       | \- 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.   |    |
+-------+--------------------------------------------------------+----+

## 

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.

## Table 5

**GA Operations Regression Equations**

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

+-------+--------------------------------------------------------+----+
| **Equ | **Equation**[^13]                                      | ** |
| ation |                                                        | R^ |
| Num   | **( Dummy Variable for "Towered" Used)**               | 2^ |
| ber** |                                                        | ** |
+-------+--------------------------------------------------------+----+
| 13    | OPS = -571 + 355 BA -- 0.46 BA2 -- 40,510 %in100mi +   | .  |
|       | 3,795 VITFSnum + 0.001 Pop100                          | 74 |
| All   |                                                        | 30 |
| 232   | (-0.25) (8.41) (-3.83) (-2.79) (1.87) (3.48)           |    |
| Airp  |                                                        | .  |
| orts, | \- 8,587 WACAORAK + 24,102 Pop25/100 + 13,674 TOWDUM   | 74 |
|       | Regression SS:                                         | 80 |
| Dummy |                                                        |    |
| Var   | (-3.61) (2.67) (6.44) 1.19818E+11                      | .  |
| iable |                                                        | 56 |
| for   | OPS = 7,731 + 428 BA -- 0.65 BA2 -- 54,681 %in100mi +  | 90 |
| To    | 3,485 VITFSnum + 0.001 Pop100                          |    |
| wered |                                                        |    |
|       | (2.08) (8.47) (-4.77) (-3.69) (1.63) (4.07)            |    |
| 14    |                                                        |    |
|       | \- 12,856 WACAORAK + 34,958 Pop25/100 Regression SS:   |    |
| 127   | 5.3772E+10                                             |    |
| To    |                                                        |    |
| wered | (-4.38) (3.58)                                         |    |
| Air   |                                                        |    |
| ports | OPS = 775 + 241 BA -- 0.14 BA2 + 31,478 %in100mi +     |    |
|       | 5,577 VITFSnum + 0.001 Pop100                          |    |
| 15    |                                                        |    |
|       | (0.22) (2.52) (-0.46) (0.85) (1.23) (1.80)             |    |
| 105   |                                                        |    |
| N     | \- 3,736 WACAORAK + 12,121 Pop25/100 Regression SS:    |    |
| on-To | 2.7327E+10                                             |    |
| wered |                                                        |    |
|       | (-0.89) (0.65)                                         |    |
| Air   |                                                        |    |
| ports | **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.   |    |
+-------+--------------------------------------------------------+----+

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).

## 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**

+-------+--------------------------------------------------------+----+
| **Equ | **Equation**[^15]                                      | ** |
| ation |                                                        | R^ |
| Num   | **( Dummy Variable for "Towered" Used)**               | 2^ |
| ber** |                                                        | ** |
+-------+--------------------------------------------------------+----+
| 16    | OPS = -1,215 + 370 BA -- 0.49 BA2 -- 48,631 %in100mi + | .  |
|       | 3,663 VITFSnum + 0.001 Pop100                          | 74 |
| All   |                                                        | 50 |
| Air   | (-0.50) (8.45) (-4.01) (-3.21) (1.75) (3.04)           |    |
| ports |                                                        |    |
|       | > 7,793 WACAORAK + 26,801 Pop25/100 + 13,791 TOWDUM    |    |
| Dummy |                                                        |    |
| Var   | (-3.21) (2.92) (6.17)                                  |    |
| iable |                                                        |    |
| for   |                                                        |    |
| Tow   |                                                        |    |
| ered, |                                                        |    |
| 15    |                                                        |    |
| N     |                                                        |    |
| on-To |                                                        |    |
| wered |                                                        |    |
| Air   |                                                        |    |
| ports |                                                        |    |
| Exc   |                                                        |    |
| luded |                                                        |    |
+-------+--------------------------------------------------------+----+

######## 

######## Figure 2

> **Fit of Out-of-Sample Estimates for 15 Non-Towered Airports Excluded
> from Estimating Data for Equation 16**

![](media/image2.wmf){width="5.976388888888889in"
height="4.086111111111111in"}

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
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
non-towered 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**

![](media/image3.wmf){width="5.95in" height="3.307638888888889in"}

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 non-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

![](media/image4.wmf){width="5.976388888888889in"
height="4.086111111111111in"}

The out of sample procedure and the value of information from the
towered airport data for modeling estimates of annual operations in the
non-towered 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.

> **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

+-------+--------------------------------------------------------+----+
| **Equ | **Equation**[^16]                                      | ** |
| ation |                                                        | R^ |
| Num   |                                                        | 2^ |
| ber** |                                                        | ** |
+-------+--------------------------------------------------------+----+
| 17    | OPSBA = 595.2 -- 164 BAE100 -- 325 %BA100 - 107 WST -- | .  |
|       | 244 AAL                                                | 30 |
|       |                                                        | 72 |
|       | (15.2) (-3.84) (-1.56) (-2.17) (-1.85)                 |    |
|       |                                                        |    |
|       | \+ 0.00002 Pop100 -- 0.00002 Pop50                     |    |
|       |                                                        |    |
|       | 51. (-1.79)                                            |    |
+-------+--------------------------------------------------------+----+

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 R^2^, 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 non-towered
airports that are the focus of this report, based aircraft may be a more
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.

####  Table 8

#### ![](media/image5.wmf){width="4.259027777777778in" height="8.453472222222222in"} Summary State Data for 2,780 Non-Towered GA Airports

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**

![](media/image6.wmf){width="5.976388888888889in"
height="4.086111111111111in"}**at 2,789 Non-Towered GA Airports**

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

![](media/image7.wmf){width="5.976388888888889in"
height="4.086111111111111in"}**Variability of Differences between Form
5010 Annual Operations Estimates and Model Estimates of Annual
Operations for U.S. Non-Towered GA Airports**

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 non-towered 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      **Equation**      **Average     **Standard    **Average     **Standard
  Airports**                      Absolute      Deviation of  Absolute      Deviation of
                                  Deviation**   Absolute      Percentage    Absolute
                                                Deviation**   Deviation**   Percentage
                                                                            Deviation**

  127 Small     Equation 9 (no    9,537.0       7,213.8       25.2 %        30.82 %
  Towered GA    dummy)                                                      
  Airports                                                                  

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

  105           Equation 9 (no    20,029.8      11,648.3      236.5 %       427.8 %
  Non-Towered   dummy)                                                      
  GA Airports                                                               

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

  2,789         Eq. 13, all 2,789 8,634         11,063        2,114 %       38,180 %
  Non-Towered   airports                                                    
  GA Airports                                                               

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

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

**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 other
non-econometric methods) at non-towered airports. The modeling has also
quantified important differences between small towered GA airports and
non-towered 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 non-towered ones can provide more unbiased
estimates for activity at these non-towered 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 non-towered 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.

**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

$$\frac{\frac{\left\lbrack (\text{SSE}(\text{restricted})\  - \ \text{SSE}(\text{unrestricted}) \right\rbrack}{R}}{\frac{\left\lbrack \text{SSE}(\text{unrestricted}) \right\rbrack}{(}N - K)}$$

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](http://www.faa.gov/data_statistics/aviation_data_statistics/general_aviation/media/AppendixB.xls)

[^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.

[^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.

[^5]: A variety of counting procedures were cited, including acoustic
    counters, machine counts, surveys, and operations logs, at these
    airports.

[^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.

[^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.

[^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.

[^10]: T-statistics are given in parentheses under each coefficient.

[^11]: Peter Kennedy, [A Guide to Econometrics]{.underline}, Cambridge,
    MA: The MIT Press, 1979, p. 87.

[^12]: T-statistics are given in parentheses under each coefficient.

[^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.

[^15]: T-statistics are given in parentheses under each coefficient.

[^16]: T-statistics are given in parentheses under each coefficient.

[^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.