2012
Hanover College
Clarence Cledanor
[INSIDE THE NFL: HOW DO
MINORITY HEAD COACHES
MEASURE UP AGAINST THE
MAJORITY?]
In 1921, the NFL hired its first minority head coach, Fritz Pollard. Another minority would not be hired
as a head coach until the 1979 season when the Oakland Raiders hired Tom Flores. This project will
attempt to examine the labor discrimination that existed, and still may exist, in the NFL. Using data prior
to the beginning of the 2012 season, this assessment will primarily look to analyze the salaries of NFL
head coaches and see if they differ amongst whites and minorities as evidence reveals that, on average,
minorities are paid significantly less.
Inside the NFL |2
Table of Contents
Introduction
Page 3
Literature Review
Page 4
Model
Page 8
Data
Page 11
Empirical Results
Page 11
Conclusion
Page 15
Appendix
Page 17
Bibliography
Page 26
Inside the NFL |3
Introduction
This econometric model will look to delve into the prosperous realm of professional
sports and attempt to provide substantial knowledge regarding the state of the minority head
coach in professional sports with the main focus being that of the National Football League.
Wage and labor discrimination will be the primary issues investigated by this model. More
precisely, this model will look to answer the following three questions; 1.) On average, is there a
significant gap in salary between those coaches who are of the minority and those who are not?
2.) On average, who are more successful (based on winning percentage), minority head coaches
or the majority? 3.) Has the "Rooney Rule", established in 2003, been successful for minority
head coaching candidates? Furthermore, in addition to answering the previous questions, by use
of empirical research and statistical evidence, this model, in the overall scheme of the project,
will also look to explain the behaviors of employers. For example, this assessment will look to
provide information on why employers may, or may not, delegate minorities to managing, or
leadership, roles. The essential purpose of this equation will be to provide inferences on NFL
head coaches' salaries as well as see what variables, if any, have the more significant impact on
them.
Cross-sectional data prior to the beginning of the 2012 season is used for each head coach
and, therefore, all thirty-two NFL teams. The dependent variable in this model is the salary of
each head coach. The independent variables include head coaching experience, winning
percentage, ethnicity, playing experience, and the number of championships won. Intuition, as
well as previous literature, indicates that these factors significantly affect the salaries of NFL
head coaches.
The data gathered for this project comes by way of several sources such as ESPN, official
team websites, and the websites of teams' local newspaper. The data concerning the salary of
Inside the NFL |4
each head coach was, for the most part, obtained from teams' official websites. The data for all of
the independent variables was obtained from different credible league sources such as the ones
already alluded to.
Literature Review
The history of minority coaches in professional sports does not possess a long lineage, as,
quite frankly, they have not been given as many opportunities in contrast to their counterparts.
One would think that for sports where minorities, mainly Hispanics and African-Americans, are
practically the playing majority, there would be more minorities in leadership and managing
roles. However, such is not the case. Over the eighty-plus year history of the NFL, there have
been only twenty-two minority head coaches, with six of the twenty-two only being able to hold
the “interim” head coach title. In 1921, the NFL had its first African-American head coach, Fritz
Pollard. Another minority would not be hired as a head coach until the 1979 season when the
Oakland Raiders hired Tom Flores. Could there be any particular reasons for this? How does the
evaluation process for coaching proceed? Does the labor force in professional sports reflect that
of the real world labor force? Is there anything being done to counteract this practice? Does it
even matter? What follows is a review of literature aimed at analyzing why minority coaches
have remained "locked out" for such a long period of time.
A review of the literature shows that researchers have observed a common process for the
hiring of coaches. For the most part, coaches are hired based upon their experience as well as
past successes. However, the basis upon whether or not a coach is hired depends on the
preferences of the owner along with social changes in the economy. Goff and Tollison (2008)
examined data from the NFL from 1987 through 2007 and revealed that integration was more
commonplace in larger populated cities. They also reveal that the hiring process of management
Inside the NFL |5
is totally different from the hiring process for players (p. 127). Furthermore, examinations of the
regular season win records and of making the playoffs for NFL teams coached by both AfricanAmericans and Caucasians between 1990 and 2002 show that African-American coaches were
more successful (Madden, 2010, p.16). Madden gives evidence that supports that teams who hire
African-American coaches are more successful than those who do not. However, AfricanAmerican coaches have not been as successful in the playoffs as only three have won the Super
Bowl (p.16). Perhaps this may be a particular reason as to why minorities, for the most part, have
not been able to get their foot in the door. Another reason could be that most owners are
Caucasians over the age of 60. This insinuates that most of the people whom are in charge come
from a time where things were socially different due to social schisms, segregation, civil rights
movements, etc. Therefore, they may be unconsciously engaging in labor discrimination against
hiring minorities, especially African-Americans.
One of the more famous minority NFL coaches, Tony Dungy, went through a series of
secondary and assistant coaching jobs before he became a head coach. Dungy was often
delegated as a head coaching candidate by his peers when Dungy was an assistant under Chuck
Noll in the 1980s with the Steelers, but he would not become a head coach until 1996 when he
began his own legacy coaching the Tampa Bay Buccaneers (Bouchette). For some reason, in
most cases, minorities must go through numerous assistant coaching positions before even being
considered as head coaching candidates. In essence, it is as if minority coaches are
disadvantageously evaluated compared to their counterparts. Despite being equally qualified and
seemingly more successful, minority coaches, for the most part, just do not get the opportunity.
Nevertheless, as Madden (2009) states, “…the results are consistent with African American
coaches being held to higher standards to get their jobs in the NFL (p. 1).”
Inside the NFL |6
One of the more notable movements to bringing awareness to labor discrimination in
professional sports is the NFL’s “Rooney Rule.” The Rooney Rule is somewhat the NFL’s
version of affirmative action. The Rooney Rule requires NFL teams to interview a specified
number of minority candidates for head coaching and senior football operation opportunities
whenever there is a vacancy. Prior to its establishment in 2003, there were seven minority head
coaches in the history of the NFL, with only two actively coaching during the rules
implementation. Madden and Ruther (2010) raise the idea of whether the performance advantage
of minority head coaches had been eliminated in the time since the establishment of the Rooney
Rule is analyzed. First, just four years after the Rooney Rule implementation there were seven
active minority head coaches in the NFL. Evidently, the Rooney Rule is effective (p. 2).
However, in accordance with Madden and Ruther, the advantage that minority head coaches had,
in terms of being more successful, was now eliminated, as they state, “Since the Rooney Rule
was put into place, there are no racial differences in performance among head coaches in the
NFL.” There are currently six minority head coaches in the NFL.
The sports industry and its related components (managing, coaching, media, marketing,
etc.) are a reflection of society. Muster (2001) analyzes the individual industries of Major League
Baseball, the National Basketball Association, and the National Football League and compares
them to the overall labor force to determine how professional sports fare in creating jobs for
minority groups. With the overall labor force becoming more diverse by the moment, the
significance of this research was to observe and analyze to what degree these two factions
correlate. Muster recognizes that professional athletes have traditionally been male and, mainly,
African-American or Caucasian. However, with the emergence of new professional sports
organizations for women, opportunities for female athletes have increased. As Muster questions,
Inside the NFL |7
“But who is working off-field for these organizations? How have sports teams and leagues
staffed their organizations? Are they in line with the national labor hiring practices? Or, are they
in stark contrast with the real world?” An unfriendly hiring process for minorities could have
negative impacts on marketing, participation, popularity, and support for each league.
The reason why professional sports industries and society reflect each other, as Muster
concludes, is that professional sports are a business first. Therefore, as a business, team officials
and league officials must concern themselves with social issues. Minorities in the National
Basketball Association, National Football League, and Major League Baseball make up a big
percentage of the players. However, of course, the question of whether labor discrimination is
practiced has not to do with the players, but rather those in the “front-office.” Muster states, “As
far as head coaching positions are concerned, one must remember that these are very exclusive
and competitive jobs." Only thirty-two positions are available in the NFL. The six AfricanAmericans who currently hold head coaching positions (18%) clearly mirror the overall U.S.
population of this minority group. Muster also expresses, "Are there more qualified AfricanAmerican candidates to assume these roles? Most certainly. Should the number of AfricanAmerican head coaches be raised simply to reflect the over-representation of African-American
athletes participating in the games? Absolutely not!”
It could be the possibility that owners are not hiring minorities purposely, but rather
unconsciously. Madden and Ruther (2009) chimes in by stating, "We believe the facts to be
consistent with implicit racial discrimination in hiring. [6] NFL teams are not consciously
rejecting African American coaches, but are unconsciously or implicitly discounting them in the
presence of uncertainty and ambiguity as to who will be a successful coach for the initial hire as
an NFL head coach." Muster refutes such notion as he expresses, “If owners are putting the best
Inside the NFL |8
available talent on the field, and are color-blind enough to bolster their rosters with AfricanAmericans, then it is just as conceivable that they are staffing their front offices with the best
talent that they know.” Unfortunately, such notion cannot be accurately determined. As a result,
the subject can be endlessly debated.
Model
As previously mentioned, the essential purpose of this equation will be to provide
inferences on NFL head coaches' salaries as well as see what variables, if any, have the more
significant impact on them. The equation for the model is as follows:
*SALi = β0 + β1Expi + β2Winsi + β3Racei + β4Playi + β5SBi + εi
Where:
SAL = Salary of head coach
Exp = Coaching experience; total number of years as head coach in NFL
Wins = Winning percentage of coach throughout career
Race = Dummy variable indicating whether or not a coach is a minority; 1 = minority, 0 =
majority
Play = Dummy variable indicating whether or not a coach has played in the NFL; 1 = yes, 0 =
no
SB = Total number of Super Bowl wins in coaching career
ε = measurement error due to omitted variables, season
i = 2012-2013 NFL Season
The main hypothesis being tested by this model is that minority coaches are paid differently than
white coaches. The null and alternative hypotheses are as follows:
Inside the NFL |9
H0: β1 ≤ 0; β2 ≤ 0; β3 ≥ 0; β4 ≤ 0; β5 ≤ 0
Ha: β1 > 0; β2 > 0; β3 < 0; β4 > 0; β5 > 0
The dependent variable (SAL) in the equation is the salary for an NFL head coach during
the 2012-2013. This variable will be measured in millions (of dollars). The independent variables
represented in the equation are an individual's years of coaching experience, number of wins in
their career, ethnicity, playing experience, and number of Super Bowl wins.
The first independent variable represented in the equation is coaching experience. More
precisely, this variable represents the total years an individual has been coaching in the NFL.
This variable is expressed as Exp in the formulated equation. It is expected that the higher an
individual's total years of experience or as an individual's coaching experience increases, then the
higher his salary. It is apparent that those who have been coaching longer are those with the
highest salaries. This notion is perfectly logical as it can be assumed that those coaches who have
plenty of experience coaching in the NFL have been able to do so, because they have been
successful and are therefore rewarded with higher salaries. Since this notion is presumably
verified, then the sign of the coefficient for Exp should be positive.
The second independent variable represented in the equation is an individual's winning
percentage throughout his head coaching career in the NFL. This variable is expressed as Wins
in the formulated equation. It is expected that the higher an individual's winning percentage then
the higher his salary. Literature, as well as media, suggests this notion as it can be explained
intuitively that those who are more prone to winning are, or should be, rewarded with more
lucrative contracts. Assuming this interpretation is correct, the sign of the coefficient for Wins
should be positive.
I n s i d e t h e N F L | 10
The third independent variable represented in the equation is ethnicity. This variable is a
dummy variable that indicates if an individual is not Caucasian. This variable is expressed as
Race in the formulated equation. It is expected that if a coach is a minority (Race = 1) then there
will be an inexplicable decrease in the coach's salary compared to if the coach were Caucasian
(Race = 0). It can be assumed that due to the low number of minority head coaches in the NFL,
minorities, on average, have lower salaries. As a result, the sign of the coefficient for Race
should be negative.
The fourth independent variable represented in the equation relates to familiarity. This
variable is a dummy variable that indicates if a coach had ever played in the NFL. This variable
is expressed as Play in the formulated equation. It is expected that if a coach has played in the
NFL (Play = 1) then there will be an increase in the coach's salary compared to if the coach did
not (Play = 0). Although research has yet to be acquired on this subject, it can be assumed that
those coaches who have played in the NFL are more familiar with players which can lead to
great camaraderie amongst players and coaches. It can also be assumed that some coaches get
their jobs, and salaries, as a result of how successful they were during their playing careers rather
than what they have done as a coach. As a result, the sign of the coefficient for Play should be
positive.
The final independent variable represented in the equation, Super Bowl wins, is probably
the most important, in regards to salary.. More precisely, this variable represents the total number
of NFL championships a coach has won throughout his career. This variable is expressed as SB
in the formulated equation. It is expected that the more championships a coach has won (as a
coach's Super Bowl wins increases) then the higher their salary (there will be an increase in the
salary of that head coach). This notion is defended by the data and makes sense as it can be
I n s i d e t h e N F L | 11
expressed that those coaches who complete the ultimate goal deserve to be rewarded. Therefore,
the sign of the coefficient for SB should be positive.
Data
The data presented in the model is cross-sectional from each of the thirty-two head
coaches currently in the NFL. The descriptive statistics can be seen in Table 0. Only in one of the
variables, WINS, was percentages used to eliminate large variances between head coaches
because of differences in the years of experience. Doing this helped limit, and possibly eliminate,
the issue of heteroskedasticity. All data was collected from numerous National Football League
sources with the most useful being that of ESPN from which the majority of the data for all
variables were attained. Fortunately, in regards to data collection, problems such as
mismeasurement or missing observations were not encountered during the process.
Empirical Results
The ordinary least squares method was used several times in the analysis of this model.
The initial regression equation of the model was:
SALi = 2347925 + 140821.3Expi + 1437283Winsi – 134045.5Racei + 465766.2Playi +
779294SBi
In accordance to the signs of the coefficients, it is apparent that the prior expected judgments
were correct. More precisely, as a head coach’s years of coaching experience increases by an
additional year then there will be a $140,821 increase in that coach’s salary. Also, a one
percentage point increase in a head coach’s winning percentage will result in a $1,437,283 boost
in the coach’s salary. In addition, as expected, being a minority head coach has its disadvantages
as the model expresses that if a head coach is a minority then there will be a $134,045 decrease
I n s i d e t h e N F L | 12
in the coach’s salary. In the same sense, it is apparent that if a head coach has had any playing
experience in the NFL then they will see a $465,766 boost in their salary. Furthermore, the
model expresses that for every Super Bowl won there will be a $779,294 increase in the coach’s
salary. Of course, all of these are assumed ceteris paribus.
As can be seen in Table 1, the R-squared in this regression equation was 0.57 and the
adjusted R-squared was 0.4884. The goodness of fit of the variance in the model can be
interpreted as being decent enough since there is not a significant difference between the values
of R-squared and the adjusted R-squared. In other words, the model is a good fit and the various
variables explain approximately forty-nine percent of the variance in head coach salaries.
Other notable inferences that can be made about the model and this particular regression
is that the probability for the F-statistic is practically zero which means a conclusion can be made
that the model is significant due to the rejecting of the null hypothesis (Ho: β1 = β2 = β3 = β4= β5
0) at the ninety-nine percent confidence level.
After conducting a Ramsey Rest Test (Table 3), it is revealed that the regression lacks no
omitted variables or specification errors due to the inability to reject the null (at the five percent
level of significance) with the calculated F-statistic, 2.195, being lesser than the critical Fstatistic, 3.03. Multicollinearity is not much of an issue as well in this model. As can be seen in
Table 2, there are no major correlations between any two variables other than that of EXP and
SB which logically makes sense as it can be assumed that the longer one has been coaching then
the more likely it is that the head coach has won, or has a better chance, of winning a
championship. Serial correlation is not of much issue in this model either due primarily to the
fact that this model deals with cross-sectional data rather than time-series. However, the DurbinWatson test statistic of 1.735, being that is close to 2, ensures us that the model lacks any
I n s i d e t h e N F L | 13
autocorrelation.
Heteroskedasticity, due to this model being a cross-sectional study, should be the primary
econometric issue present. After running a White test (Table 4) to see if the model has
heteroskedasticity, it is apparent that at the ninety-five percent confidence level the null
hypothesis cannot be rejected due to the calculated NR2, 10.66, being lesser than the critical NR2,
28.9. As a result, it can be concluded that this model does not have the econometric issue of
heteroskedasticity.
A series of hypothesis tests were conducted to see which of the independent variables
were more significant in relations to salary. The null and alternative hypotheses are as follows:
H0: β1 ≤ 0; β2 ≤ 0; β3 ≥ 0; β4 = 0; β5 ≤ 0
Ha: β1 > 0; β2 > 0; β3 < 0; β4 ≠ 0; β5 > 0
For all tests, the ninety-five percent confidence level was used to determine if the null would be
rejected. With p-values of 0.0114 and 0.0256, EXP and SB, respectively, are able to reject the
null and it can be concluded that these two variables are significant. The others, however, do not
even come close to being significant at a ninety percent level of confidence (Table 1). Therefore,
in an attempt to provide a better model, a second regression equation was formulated with the
omission of the PLAY variable due to the insignificance of the coefficient. The equation is as
follows:
SAL = 2406181 + 130736Exp + 1784881Wins – 140134.1Race + 729680.5SB
The omission did not change much. First, the expected signs of the coefficients remained the
same. Secondly, there is an apparent increase in the coefficients of all variables other than SB
which has an apparent decrease in the magnitude of its coefficient. This reveals that omitting
PLAY could be causing some bias in the analysis of the independent variables. Furthermore, this
I n s i d e t h e N F L | 14
new regression reveals a minor increase in R-squared and adjusted R-Squared (Table 4).
Essentially, the goodness of fit of this second regression equation is slightly better than the first
regression. Lastly, at the ninety percent level of confidence, it can be concluded that Wins is
now statistically significant with a p-value of approximately 0.07 (Table 5).
In an attempt to build on the previous regression, a final regression equation was formed
with the addition of an interaction term, WINS*RACE. This slope dummy variable accounts for
the slopes of the salary variable and the winning percentage variable to be different depending on
whether or not a head coach is a minority. It is of high importance, because it allows for an inmodel analysis to take place whenever the RACE variable impacts SAL depending on whether or
not the coach is a minority or not. The final regression equation is as follows:
SAL =
2573911 + 133132.1Exp + 1425597Wins – 2427478Race + 685979.4SB +
4951807Wins*Race
There is no significant change in the estimated output in comparison to the first two equations
(Table 8). However, this last regression equation does provide a revealing fact. A salary equation
with both an intercept dummy variable and a slope dummy variable can take on different shapes
when graphed with wins on the horizontal axis. By use of algebra, the system of two equations is
able to be solved and the following conclusion can be made: if two coaches, one white and the
other non-white, begin their head coaching careers at the same time (along with everything else
equal) then it is apparent that the white head coach will be paid more due to the intercept
dummy. However, there is a point at which the minority head coach can exceed the white coach
in salary (due to the magnitude of the slope dummy coefficient) and that is when he surpasses a
I n s i d e t h e N F L | 15
particular winning percentage.
If a head coach is white, the change in salary over the change in winning percentage is
equal to $1,425,597. However, if the head coach is a minority, this same change is equal to
$6,377,404. This represents the additional returns of winning for a minority head coach. The
intercept dummy, however, tells us that initially, when all variables are constant, a minority head
coach sees a negative $2,427,478 change in salary (the change in salary over the change in the
race variable is 4,951,807 - 2,427,478 = $2,524,329). The point at which the minority head coach
would exceed the white head coach in salary is when he achieves a winning percentage of
approximately forty-nine percent.
A more detailed and comprehensive assessment might look to include the number of
years it may take a minority coach to exceed the Caucasian coach as well as the details of
contractual agreements (amongst other things) to accurately explain this notion.
Conclusion
It is more than likely that this model does not include all the possible factors that could
affect the salaries of NFL head coaches. Some other factors that could have been helpful to this
model are; 1.) The inclusion of all head coaches since 1990 as a way of being able to compare
and contrast statistics amongst white and minority head coaches along a wider period and 2.) To
go along with the previous idea, the inclusion of a dummy variable that measured the impact the
Rooney Rule has had on the NFL since 2003. The variable simply would have measured
minority head coaches amongst each other by distinguishing if a minority coach was hired prior
to 2003 or after. With these two inclusions, the success of minority head coaches in comparison
to that of whites could have been analyzed. The difference in salary as well as the number of
I n s i d e t h e N F L | 16
minority hires since, and prior to, 2003 could have been analyzed, too. However, due to the
inability to acquire such information, this model was unable to include such factors. The reason
for wanting to include such factors comes by way of the assertion, "The evidence on fire and
rehire, when combined with the other evidence of greater successes for African American
coaches presented in Madden (2004), is consistent with implicit racial discrimination in the NFL
during the 1990-2002 period (Madden & Ruther 2009)."
In the end, this assessment serves as a decent model that, for the most part, explains the
overall factors that determine the salaries of head coaches in the NFL. The R-squared and
adjusted R-squared in all presented regressions are rather favorable. The F-statistics in all
presented regressions also reveal that this model is significant. Fortunately, econometric issues
such as functional form, omitted variables, multicollinearity, serial correlation, and
heteroskedasticity are not a problem in this model. However, the insignificance of the coefficient
for RACE in all presented regressions is puzzling. Reasons for such results could include the
exclusion of some other variable that relates to ethnicity and/or the sample size, or it could very
well be the case that ethnicity does not play a role in the salaries given to NFL head coaches. If
all information were able to be acquired, it would be interesting to see the affect the
aforementioned inclusions would have had on this model.
I n s i d e t h e N F L | 17
Appendix.
Table 1.
Regression results
Dependent Variable: SAL
Method: Least Squares
Date: 11/14/12 Time: 23:45
Sample: 1 32
Included observations: 32
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
WINS
RACE
PLAY
SB
2347925.
140821.3
1437283.
-134045.5
465766.2
779294.0
556282.8
58206.22
1250355.
571540.0
514493.3
381456.1
4.220740
2.419352
1.149501
-0.234534
0.905291
2.042945
0.0003
0.0228
0.2608
0.8164
0.3736
0.0513
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.570960
0.488452
1254612.
4.09E+13
-491.4386
6.920076
0.000315
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
4174063.
1754148.
31.08991
31.36474
31.18101
1.734561
Table 2.
Correlation Table
SAL
EXP01
WINS
RACE
PLAY
SB
SAL
1.000000
0.670735
0.496089
-0.092485
0.015986
0.605656
EXP01
0.670735
1.000000
0.463853
-0.077102
-0.178340
0.582798
WINS
0.496089
0.463853
1.000000
-0.005791
0.175591
0.318260
RACE
-0.092485
-0.077102
-0.005791
1.000000
0.021592
-0.096471
PLAY
0.015986
-0.178340
0.175591
0.021592
1.000000
-0.197288
SB
0.605656
0.582798
0.318260
-0.096471
-0.197288
1.000000
I n s i d e t h e N F L | 18
Table 3.
Ramsey RESET
Test:
F-statistic
Log likelihood ratio
Prob.
2.195031 F(3,23)
Prob. Chi8.056844 Square(3)
0.1160
0.0449
Test Equation:
Dependent Variable:
SAL
Method: Least Squares
Date: 12/07/12 Time:
03:20
Sample: 1 32
Included observations:
32
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
WINS
RACE
PLAY
SB
FITTED^2
FITTED^3
FITTED^4
-36756869
-4795873.
-43950092
5200551.
-15680926
-27118930
9.54E-06
-1.10E-12
4.65E-20
27580073
3028452.
30380229
3085214.
9960919.
16920601
7.10E-06
1.01E-12
5.16E-20
-1.332733
-1.583606
-1.446668
1.685637
-1.574245
-1.602717
1.343319
-1.096658
0.901830
0.1957
0.1269
0.1615
0.1054
0.1291
0.1226
0.1923
0.2841
0.3765
R-squared
0.666456
Adjusted R-squared
0.550441
S.E. of regression
1176142.
Sum squared resid
3.18E+13
Log likelihood
-487.4102
F-statistic
Prob(F-statistic)
5.744557
0.000448
Mean
dependent
var
S.D.
dependent
var
Akaike info
criterion
Schwarz
criterion
HannanQuinn criter.
DurbinWatson stat
4174063.
1754148.
31.02564
31.43787
31.16228
1.909705
I n s i d e t h e N F L | 19
Table 4.
Heteroskedasticity Test: White
F-statistic
0.360677
Obs*R-squared
Scaled explained SS
Prob. F(18,13)
Prob. Chi10.65811 Square(18)
Prob. Chi6.736504 Square(18)
0.9767
0.9083
0.9922
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 11/19/12 Time: 14:23
Sample: 1 32
Included observations: 32
Collinear test regressors dropped from
specification
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
EXP01^2
EXP01*WINS
EXP01*RACE
EXP01*PLAY
EXP01*SB
WINS
WINS^2
WINS*RACE
WINS*PLAY
WINS*SB
RACE
RACE*PLAY
RACE*SB
PLAY
PLAY*SB
SB
SB^2
4.86E+11
1.75E+12
-3.68E+10
-1.96E+12
-3.48E+11
-2.06E+10
2.12E+11
-5.80E+12
6.50E+12
2.06E+13
3.47E+12
2.49E+13
-8.44E+12
1.87E+12
-5.42E+12
-1.25E+12
-3.74E+11
-1.50E+13
-1.23E+12
1.12E+12
1.40E+12
4.61E+10
3.00E+12
8.52E+11
2.95E+11
4.25E+11
1.41E+13
2.39E+13
2.47E+13
1.84E+13
2.46E+13
9.11E+12
5.59E+12
7.99E+12
9.91E+12
4.43E+12
1.54E+13
1.74E+12
0.433138
1.246065
-0.797894
-0.653484
-0.408243
-0.069845
0.498192
-0.410248
0.271382
0.836849
0.188248
1.012344
-0.926507
0.334437
-0.678306
-0.125714
-0.084488
-0.971465
-0.706063
0.6720
0.2347
0.4393
0.5248
0.6897
0.9454
0.6267
0.6883
0.7904
0.4178
0.8536
0.3298
0.3711
0.7434
0.5095
0.9019
0.9340
0.3490
0.4926
0.333066
-0.590381
2.27E+12
6.68E+25
-941.3845
0.360677
0.976659
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
1.28E+12
1.80E+12
60.02403
60.89431
60.31250
1.697726
I n s i d e t h e N F L | 20
Table 5.
Dependent Variable:
SAL
Method: Least Squares
Date: 11/19/12 Time:
14:27
Sample: 1 32
Included observations:
32
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
WINS
RACE
SB
2406181.
130736.0
1784881.
-140134.1
729680.5
550698.8
56938.93
1185958.
569587.5
376235.2
4.369322
2.296074
1.505012
-0.246027
1.939427
0.0002
0.0297
0.1439
0.8075
0.0630
R-squared
0.557436
Adjusted R-squared
0.491871
S.E. of regression
1250413.
Sum squared resid
4.22E+13
Log likelihood
-491.9351
F-statistic
Prob(F-statistic)
Table 6.
8.502028
0.000142
Mean
dependent
var
S.D.
dependent
var
Akaike info
criterion
Schwarz
criterion
HannanQuinn criter.
DurbinWatson stat
4174063.
1754148.
31.05845
31.28747
31.13436
1.637109
I n s i d e t h e N F L | 21
Ramsey RESET
Test:
F-statistic
Log likelihood ratio
Prob.
1.407064 F(3,24)
Prob. Chi5.184619 Square(3)
0.2650
0.1588
Test Equation:
Dependent Variable:
SAL
Method: Least Squares
Date: 12/07/12 Time:
05:20
Sample: 1 32
Included observations:
32
White
HeteroskedasticityConsistent Standard
Errors & Covariance
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
WINS
RACE
SB
FITTED^2
FITTED^3
FITTED^4
-39895430
-4484171.
-57367864
5101531.
-25440417
1.00E-05
-1.21E-12
5.33E-20
16233434
1601206.
21605131
1962204.
8816476.
3.99E-06
5.75E-13
2.97E-20
-2.457609
-2.800495
-2.655289
2.599899
-2.885554
2.505833
-2.106103
1.794397
0.0216
0.0099
0.0139
0.0157
0.0081
0.0194
0.0458
0.0854
R-squared
0.623633
Adjusted R-squared
0.513859
S.E. of regression
1223059.
Sum squared resid
3.59E+13
Log likelihood
-489.3428
F-statistic
Prob(F-statistic)
Table 7.
5.681067
0.000586
Mean
dependent
var
S.D.
dependent
var
Akaike info
criterion
Schwarz
criterion
HannanQuinn criter.
DurbinWatson stat
4174063.
1754148.
31.08393
31.45036
31.20539
1.736279
I n s i d e t h e N F L | 22
Heteroskedasticity Test: White
F-statistic
1.058159
Obs*R-squared
Scaled explained SS
Prob. F(13,18)
Prob. Chi13.86173 Square(13)
Prob. Chi8.351858 Square(13)
0.4459
0.3837
0.8199
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 11/19/12 Time: 14:29
Sample: 1 32
Included observations: 32
Collinear test regressors dropped
from specification
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
EXP01^2
EXP01*WINS
EXP01*RACE
EXP01*SB
WINS
WINS^2
WINS*RACE
WINS*SB
RACE
RACE*SB
SB
SB^2
4.31E+11
2.03E+12
-2.15E+10
-2.90E+12
-5.14E+11
9.16E+10
-7.20E+12
1.17E+13
1.94E+13
2.96E+13
-6.61E+12
-7.50E+12
-1.60E+13
-1.27E+12
8.51E+11
8.53E+11
2.18E+10
1.45E+12
5.19E+11
2.60E+11
7.71E+12
1.04E+13
1.60E+13
1.81E+13
4.95E+12
4.98E+12
1.16E+13
1.12E+12
0.506349
2.380113
-0.986258
-2.000617
-0.991770
0.351546
-0.934163
1.120339
1.212838
1.636121
-1.334768
-1.505829
-1.382595
-1.129284
0.6188
0.0286
0.3371
0.0607
0.3345
0.7293
0.3626
0.2773
0.2409
0.1192
0.1986
0.1495
0.1837
0.2736
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Table 8.
Mean dependent
0.433179 var
0.023809
S.D. dependent var
1.72E+12
Akaike info criterion
5.34E+25
Schwarz criterion
Hannan-Quinn
-937.8016 criter.
1.058159
Durbin-Watson stat
0.445860
1.32E+12
1.74E+12
59.48760
60.12886
59.70016
1.591157
I n s i d e t h e N F L | 23
Dependent Variable:
SAL
Method: Least Squares
Date: 11/19/12 Time:
14:52
Sample: 1 32
Included observations:
32
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
WINS
RACE
SB
WINS*RACE
2573911.
133132.1
1425597.
-2427478.
685979.4
4951807.
560498.8
56343.65
1206703.
1891511.
373687.7
3909071.
4.592180
2.362859
1.181398
-1.283354
1.835702
1.266748
0.0001
0.0259
0.2481
0.2107
0.0779
0.2165
R-squared
0.583162
Adjusted R-squared
0.503001
S.E. of regression
1236642.
Sum squared resid
3.98E+13
Log likelihood
-490.9769
F-statistic
Prob(F-statistic)
Table 9.
7.274871
0.000223
Mean
dependent
var
S.D.
dependent
var
Akaike info
criterion
Schwarz
criterion
HannanQuinn criter.
DurbinWatson stat
4174063.
1754148.
31.06106
31.33588
31.15216
1.426366
I n s i d e t h e N F L | 24
Ramsey RESET
Test:
F-statistic
Log likelihood ratio
Prob.
0.754934 F(3,23)
Prob. Chi3.005377 Square(3)
0.5308
0.3908
Test Equation:
Dependent Variable:
SAL
Method: Least Squares
Date: 12/07/12 Time:
05:29
Sample: 1 32
Included observations:
32
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
WINS
RACE
SB
WINS*RACE
FITTED^2
FITTED^3
FITTED^4
-26133995
-2697899.
-27069403
47230359
-14279716
-97184838
6.03E-06
-7.33E-13
3.27E-20
37392659
3274242.
34999464
58725244
16872864
1.20E+08
8.34E-06
1.21E-12
6.31E-20
-0.698907
-0.823977
-0.773423
0.804260
-0.846313
-0.809870
0.723113
-0.606274
0.518004
0.4916
0.4184
0.4471
0.4295
0.4061
0.4263
0.4769
0.5503
0.6094
R-squared
0.620528
Adjusted R-squared
0.488538
S.E. of regression
1254506.
Sum squared resid
3.62E+13
Log likelihood
-489.4742
F-statistic
Prob(F-statistic)
Table 10.
4.701326
0.001637
Mean
dependent
var
S.D.
dependent
var
Akaike info
criterion
Schwarz
criterion
HannanQuinn criter.
DurbinWatson stat
4174063.
1754148.
31.15464
31.56688
31.29129
1.460589
I n s i d e t h e N F L | 25
Heteroskedasticity Test: White
F-statistic
0.939150
Obs*R-squared
Scaled explained SS
Prob. F(15,16)
Prob. Chi14.98282 Square(15)
Prob. Chi9.649036 Square(15)
0.5462
0.4527
0.8412
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 12/07/12 Time: 05:28
Sample: 1 32
Included observations: 32
Collinear test regressors dropped
from specification
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EXP01
EXP01^2
EXP01*WINS
EXP01*RACE
EXP01*SB
EXP01*(WINS*RACE)
WINS
WINS^2
WINS*RACE
WINS*SB
WINS*(WINS*RACE)
RACE
RACE*SB
SB
SB^2
2.47E+11
2.22E+12
-1.92E+10
-3.33E+12
-2.82E+12
8.35E+10
5.54E+12
-7.19E+12
1.27E+13
1.46E+13
3.08E+13
-3.28E+13
-4.03E+11
-3.38E+12
-1.65E+13
-1.26E+12
8.84E+11
9.05E+11
2.29E+10
1.54E+12
6.33E+12
2.72E+11
1.47E+13
8.07E+12
1.09E+13
1.44E+14
1.88E+13
2.51E+14
1.90E+13
2.06E+13
1.21E+13
1.17E+12
0.279432
2.453047
-0.836390
-2.160099
-0.445494
0.307434
0.375889
-0.890227
1.161511
0.101899
1.632205
-0.130546
-0.021207
-0.164407
-1.369789
-1.077103
0.7835
0.0260
0.4153
0.0463
0.6619
0.7625
0.7119
0.3865
0.2625
0.9201
0.1222
0.8978
0.9833
0.8715
0.1897
0.2974
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Mean dependent
0.468213 var
-0.030337
S.D. dependent var
1.79E+12
Akaike info criterion
5.13E+25
Schwarz criterion
Hannan-Quinn
-937.1377 criter.
0.939150
Durbin-Watson stat
0.546165
1.24E+12
1.76E+12
59.57111
60.30398
59.81403
1.536135
I n s i d e t h e N F L | 26
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