mlb baseball attendance

8/12/2019 MLB Baseball Attendance

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Streips, Suen, Sullivan, Zerweck 45-752 Project (Trick) April 30, 2014

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INTRODUCTION

Several factors such as starting pitcher, temperature/weather, team record, traffic, andmore play a role in attendance. However, these factors are unpredictable and cannot be used forplanning ahead. As consultants to Major League Baseball (MLB), our group has the primary goalof increasing attendance through statistical analysis. Using data from over 12,000 games overfour years, we make recommendations to the MLB on changes they can make to the schedule toincrease attendance.

THE SPECIFICATION (MODEL)

The choice of estimation procedure builds upon a prior study of MLB baseball attendanceby Lemke et al. of the 2007 season. Both game attendance and log attendance are used as thedependent variables in ordinary least squares (OLS) and censored regression (CR) models. Rightcensored regression is used to model the effects of capacity on sell-out games. All models arefixed-effect (FE) models in which each home team receives its own fixed-effect to account forlocal market conditions and intercity variations. We assume that unobservable factors that mightsimultaneously affect the LHS and RHS of the regression are time-invariant. Explanatoryvariables include: time factors (day of week, time of day, year, month); factors that influenceattendance (interleague and opening day games and games on holidays); and, whether two

games are played in a city at once (New York City, San Francisco Bay Area, Chicago,Washington, DC, and Los Angeles). The OLS models are AR(1) to account for correlation oferrors in the time-series data. The Newey-West estimator is used to correct for autocorrelationand heteroskedasticity in the error terms of the OLS models, serving to weaken the assumptionsof the model. Nine dummy variables control for the day of the week and the time of the game.There is a separate dummy variable for each day, Monday through Friday, plus a variable forplaying a day game during the week. Saturday and Sunday games are each further separated bytime of day. Additionally, there are are five dummy variables to control for the month and fourmore variables to control for the year.

THE DATA

The data includes the date, time of day, and attendance records of all MLB games played

over the 2008-2012 seasons (inclusive) for a total of 12,100 observations. Mean attendance atMLB games was 30,860 people for the period in questions, with a range of 8,269 (TOR vs. TMBon April 22, 2008) and 57,099 (SFN v. LAN on April 13, 2009) (see full detail of descriptive

statistics at #$%&' (, Appendix). The observations also include whether or not each game was at

capacity, was played on opening day or a holiday, involved interleague play, or was held on thesame day as another game in the same metropolitan area (as indicator variables).

REGRESSION RESULTS

When using attendance or log attendance as the dependent variables, estimatedcoefficients are interpreted as changes in attendance or percentage changes in attendance(respectively). For example, under the OLS model, a Thursday night game averages 3,288 fewer

attendees than a Sunday afternoon game (see OLS regression at #$%&' ), Appendix). Using log

attendance, the same data would be interpreted as 14.41 percent fewer in attendance. Thebaseline is attendance at a Sunday afternoon game held in FLO in April 2008 that is not onopening day, and not on a holiday or an interleague game (21,007 people).

Based on the CR models, the semi-log functional form is judged to be the better modelbased on Akaike info criterion (0.427297 vs. 16.6486). Only OAK and the simultaneous gamecities (except NY2) are not statistically significant factors in both CR models, which confirm theconclusions that may drawn from the OLS models.


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The proportion of the variance in attendance and log attendance that is explained by theOLS models are 0.6919 and 0.6752, respectively, with the adjusted R-squared values beingslightly lower (0.6904 and 0.6752). All OLS model coefficients are statistically significant (within0.05 significance) with the exception of the simultaneous game variables, Sunday night games,home team game attendance at OAK, and (for the log attendance model) Friday night games

(see #$%&' *, Appendix). The simultaneous game coefficients were left in the model to support

the findings and recommendations of this report. Removing these variables from the model didnot have a significant impact the ability of the model to explain variability in attendance. The signsand magnitudes of the coefficients are in alignment with expectations relative to the baseline(FLO having the lowest league attendance) and with the descriptive statistics of the data set (see

#$%&' (, Appendix). Leverage plots were performed on each coefficient without suggesting

nonlinearities. The model was rejected by the Ramsey test, but given the large time series dataset, we hold the Ramsey test to be uninformative. Choosing the functional form to beuntransformed or semi-log is supported by the academic literature.

From the model we make a few general observations: Monday through Thursday gamesdraw significantly fewer fans than Saturday or Sunday afternoon games. Day games in generaloffer slightly higher attendance than night games. Attendance is expected to be less inSeptember compared to July and August, and is expected to be more on major holidays.

FINDINGS AND RECOMMENDATIONS

Monday vs. Thursday Off Days

The most commonly scheduled off days in the league are Monday and Thursday, when

teams often travel home or away for a new series. Viewing our OLS regression results (#$%&' ),

Appendix), we see that Monday and Thursday both imply a statistically significant negativeattendance effect when compared with the baseline of Sunday daytime games. At first glimpse, itseems that Monday indicates a larger negative effect on attendance than Thursday, but to be

certain, we can conduct a Wald Test (#$%&' +, Appendix).

For this Wald test, we made Monday + Daytime = Thursday + Daytime our nullhypothesis. This resulted in a p-value of 0.1865, which means that we do not have enough

evidence to reject the hypothesis at a 0.05 level that Monday and Thursday games are the same.From a statistical standpoint, there is no difference between Monday and Thursday games, butfrom a managerial perspective, it might be interesting to know that there will occasionally bedifferences. It may be prudent to slightly favor Monday off days when scheduling because theMonday coefficient has a larger negative effect on attendance.

Annual Attendance

Using numbers from the OLS regression (#$%&' ), Appendix), we put together an annual

attendance graph (,-./0' ", Appendix) as implied by the annual indicator variables (2008 - 2012).

This information will give us the means to analyze some very general attendance trends for MajorLeague Baseball.

We notice that our baseline year of 2008 indicates peak annual attendance, followed bystrong declines through 2010. The trend then turns upward with some weak growth in 2011 and2012. We conclude that the trend in attendance is directly related to the Great Recession, whichofficially lasted from December 2007 to June 2009 in the U.S (source:http://www.nber.org/cycles.html).

Looking at a chart of Real GDP (source: http://www.multpl.com/us-gdp-inflation-

adjusted/table, ,-./0' (, Appendix), we can see that baseball attendance seems to follow these

trends, lagging by about 1 year. One very important concern is that baseball attendance has not


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recovered as quickly as the rest of the American economy. While the leagues growth trend ispositive, it should try and identify other factors that may be causing slower recovery. It shouldalso use this data to anticipate attendance in the event of a future economic downturn. If MLB canuse GDP as an indicator, it can better prepare and anticipate for losses caused by poorattendance.

Should the MLB be concerned with multiple intra-city games on the same day?

While none of our OLS model two game variables (NY2, BAY2, CHI2, DC2, and LA2)were statistically significant at the 0.05 percent level, we believe there is still a usefulinterpretation to some of the coefficients. Eighty-seven percent (1-0.1264) of the time, when bothNY teams in NY play, there will be an increase of 1,564 in attendance. Eighty-five percent of thetime, when both Bay Area teams play in the Bay Area, there will be a 1,102 drop in attendance.Additionally, 80% of the time, Chicago will see a 656 person increase in attendance. NY2 isstatistically significant under our CR model analysis, further highlighting the managerialsignificance of simultaneous games in the New York metropolitan area.

These numbers are what we call managerially significant. While not enough to makemore certain statistical predictions, we recommend using this data to make educated decisions,with the realization that they will occasionally be incorrect. The NY and Chicago positive effects

could possibly be explained by the rivalry between the intra-city teams. Advising NY and Chicagoteams to work together to schedule same day home games would be a good idea, but it shouldbe emphasized that this should not be a priority. Considering that the sample size for having twoNY games is less than 25 per season, we felt that there could have been other factors (e.g.Special City-wide events) affecting attendance on those specific days that are not accounted forin the data.

The Bay Area is unique because of the negative overall effect implied. One possibleexplanation is that the Giants are much more popular than the As, as evidenced by the HTeamcoefficients of 15,789 for the Giants and 198 for the As (HTeam=OAK is far from statisticallysignificant, suggesting no effect on attendance). This data suggests that when the Giants and Asplay on the same day in the Bay Area, the Giants overpower the As and there is an overallnegative effect. It also could be explained by the fact that these two teams do not have a rivalry

with high levels of animosity, unlike NY and Chicago.

Should the MLB care about day versus night games?

Sunday afternoon games are the baseline in the regression, Saturday, and Sunday nightgames are all better than a weekend Day Game. Saturday and Sunday night games experiencean overall increase of 4,209 and 958, respectively. The main explanation for this is that peoplegenerally have more free time on weekends. Furthermore, weekday (including Friday) day gameson average have 757 more in attendance than weekday night games. Our intuitive explanation forthis is that weekday night games do not end until later in the night and many people have to workthe following morning. Additionally, many people take advantage of the businessperson specialgames and promotion/giveaway games that are in the day time.

Should the MLB move the schedule to start later in April and end in October?

Attendance increases as the season continues, peaking in July and August and dipping

in September, though remaining higher than April (,-./0' ), Appendix). While the end of the

season still has better attendance than the beginning, there is more uncertainty in cold weathercities, the start of the football season, and how the playoffs will affect attendance. However, the

combined effect of summer weekend games is even more powerful (#$%&' "). For this reason, we

would recommend eliminating as many April and September games as possible and replacingthem with day/night weekend doubleheaders in July and August.


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Saturday Day Saturday Night Sunday Night

July + 6390 + 7943 + 4692

August + 5547 + 7100 + 3849

!"#$% '( )*%++,-,%./0 *+ 1"/234"50 ".4 12.4"50 423,.6 7%"8 9*./:0

Because this recommendation would likely be resisted by the players union, we wouldalso recommend starting and ending the season later. Overall, the data suggests that doing sowould increase attendance; however, we remain cautious as autocorrelation could affect theprediction.

CONCLUSION

In conclusion, our study of attendance at MLB games for the 2008-2012 seasons yieldthe following observations:

The league should not be concerned with Monday versus Thursday off days as the variableswere not statistically different from each other. While baseball attendance had not reached 2008levels by the end of 2012, overall attendance seems to be correlated with the Great Recessionand disposable income. New York, Chicago, and Bay area teams should all be concerned withhaving multiple intra-city games on the same day. However, this should not be a major concernas there is a 0.15-0.20 probability this effect will not happen. Day games have higher attendancethan night games on weekdays, but this effect is reversed and magnified for Saturday andSunday. If possible, the league should cut games from the beginning of the season in April andmake them up in the form of double headers on weekends in July and August. If this is notrealistic, the league should cautiously begin to start and end the season later in the year, butbeware of playoff and temperature effects.


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Appendix

ATTENDANCE

Mean 30859.70

Median 31369.00

Maximum 57099.00

Minimum 8269.000

Std. Dev. 10653.21Skewness -0.091275

Kurtosis 2.047843

Jarque-Bera 473.8801

Probability 0.000000

Sum 3.73E+08

Sum Sq. Dev. 1.37E+12

Observations 12100

!"#$% ;( % 1/"/,0/,-0

Dependent Variable: ATTENDANCE

Method: Least Squares

Date: 04/30/14 Time: 08:49

Sample (adjusted): 2 12100

Included observations: 12099 after adjustments

Convergence achieved after 14 iterations

HAC standard errors & covariance (Bartlett kernel, Newey-West fixed

bandwidth = 12.0000)

Variable Coefficient Std. Error t-Statistic Prob.

C 21007.21 543.0514 38.68365 0.0000INTER 2743.328 295.9214 9.270461 0.0000

HOLIDAY 3131.878 1084.646 2.887465 0.0039

OPENING 11302.18 943.4765 11.97929 0.0000

NY2 1564.513 1023.403 1.528736 0.1264

BAY2 -1102.537 760.4260 -1.449894 0.1471

CHI2 656.8483 510.1526 1.287552 0.1979

DC2 145.8249 724.8650 0.201175 0.8406

LA2 356.4238 841.1608 0.423728 0.6718

YEAR=2009 -2233.452 237.4131 -9.407449 0.0000

YEAR=2010 -2406.716 231.7313 -10.38580 0.0000

YEAR=2011 -2152.011 233.0650 -9.233522 0.0000

YEAR=2012 -1875.283 242.1100 -7.745582 0.0000

DAY="Fri" 909.4155 457.9592 1.985800 0.0471

DAY="Mon" -3932.290 551.3640 -7.131931 0.0000DAY="Thu" -3288.636 449.7220 -7.312597 0.0000

DAY="Tue" -3613.521 484.3133 -7.461124 0.0000

DAY="Wed" -3642.751 440.6470 -8.266825 0.0000

NIGHT="D" 757.0112 202.3443 3.741203 0.0002

(DAY="Sat")*(NIGHT="D") 1899.323 452.9396 4.193325 0.0000

(DAY="Sat")*(NIGHT="N") 4209.857 500.4346 8.412401 0.0000

(DAY="Sun")*(NIGHT="N") 958.4386 535.3731 1.790225 0.0734

MONTH=5 817.3996 295.7628 2.763700 0.0057

MONTH=6 1875.373 325.7221 5.757585 0.0000


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MONTH=7 3734.020 289.5645 12.89530 0.0000

MONTH=8 2891.422 278.0575 10.39865 0.0000

MONTH=9 1582.842 292.6239 5.409133 0.0000

HTEAM="ANA" 16462.58 416.7005 39.50698 0.0000

HTEAM="ARI" 7488.247 425.5691 17.59584 0.0000

HTEAM="ATL" 9828.479 448.8976 21.89470 0.0000

HTEAM="BAL" 4413.848 480.2770 9.190213 0.0000

HTEAM="BOS" 14994.90 405.6611 36.96412 0.0000

HTEAM="CHA" 7209.076 402.4978 17.91085 0.0000

HTEAM="CHN" 15296.95 417.3289 36.65442 0.0000

HTEAM="CIN" 6352.246 430.1179 14.76862 0.0000

HTEAM="CLE" 2985.583 457.5983 6.524462 0.0000

HTEAM="COL" 12434.99 442.0033 28.13324 0.0000

HTEAM="DET" 12567.91 423.3006 29.69028 0.0000

HTEAM="HOU" 7707.297 427.4164 18.03229 0.0000

HTEAM="KCA" 2497.262 422.2319 5.914432 0.0000

HTEAM="LAN" 20763.37 530.5516 39.13544 0.0000

HTEAM="MIA" 7541.038 536.7056 14.05061 0.0000

HTEAM="MIL" 14165.73 410.0024 34.55035 0.0000

HTEAM="MIN" 12622.57 426.1675 29.61880 0.0000

HTEAM="NYA" 25278.84 428.1216 59.04593 0.0000HTEAM="NYN" 14576.52 581.4019 25.07133 0.0000

HTEAM="OAK" 198.1210 455.8608 0.434609 0.6639

HTEAM="PHI" 21873.50 429.6720 50.90744 0.0000

HTEAM="PIT" 2914.489 449.6637 6.481487 0.0000

HTEAM="SDN" 7023.768 408.3717 17.19945 0.0000

HTEAM="SEA" 5782.940 440.9146 13.11578 0.0000

HTEAM="SFN" 15789.08 424.2521 37.21628 0.0000

HTEAM="SLN" 17599.24 396.9307 44.33832 0.0000

HTEAM="TBA" 2392.621 438.5424 5.455850 0.0000

HTEAM="TEX" 11944.49 543.7304 21.96767 0.0000

HTEAM="TOR" 4943.496 457.9189 10.79557 0.0000

HTEAM="WAS" 6118.790 446.5431 13.70258 0.0000

AR(1) 0.359360 0.009121 39.40027 0.0000

R-squared 0.691876 Mean dependent var 30858.57

Adjusted R-squared 0.690417 S.D. dependent var 10652.91

S.E. of regression 5927.298 Akaike info criterion 20.21731

Sum squared resid 4.23E+11 Schwarz criterion 20.25279

Log likelihood -122246.6 Hannan-Quinn criter. 20.22920

F-statistic 474.3400 Durbin-Watson stat 2.041023

Prob(F-statistic) 0.000000 Wald F-statistic 212.6663

Prob(Wald F-statistic) 0.000000

Inverted AR Roots .36

!"#$% ?( @34,."35 A%"0/ 1B2"3%0 C@A1D

EVIEWS command for OLS model in #$%&' ):

ls attendance c @expand(year, @dropfirst)

@expand(day, @drop("Sun"), @drop("Sat"))

@expand(night, @drop("N"))


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@expand(day, @drop("Mon"), @drop("Tue"), @drop("Wed"), @drop("Thu"), @drop("Fri"),

@drop("Sun"))*@expand(night, @drop("N"))

@expand(day, @drop("Mon"), @drop("Tue"), @drop("Wed"), @drop("Thu"), @drop("Fri"),@drop("Sun"))*@expand(night, @drop("D"))


@drop("Sat"))*@expand(night, @drop("D"))

@expand(month, @drop(4))

@expand(hteam, @drop("FLO")) inter holiday opening ny2 bay2 chi2 dc2 la2 ar(1)

And we corrected for covariance with Newey-West.

Dependent Variable: LOG(ATTENDANCE)

Method: Least Squares

Date: 04/30/14 Time: 20:50

Sample (adjusted): 2 12100Included observations: 12099 after adjustments


HAC standard errors & covariance (Bartlett kernel, Newey-West fixed

bandwidth = 12.0000)

Variable Coefficient Std. Error t-Statistic Prob.

C 9.876957 0.022509 438.8063 0.0000

INTER 0.096517 0.010977 8.792401 0.0000

HOLIDAY 0.116159 0.040788 2.847869 0.0044

OPENING 0.364025 0.032482 11.20712 0.0000

NY2 0.047621 0.031119 1.530298 0.1260

BAY2 -0.055850 0.032508 -1.718036 0.0858

CHI2 0.027433 0.018534 1.480105 0.1389

DC2 0.002935 0.028721 0.102184 0.9186

LA2 -0.004848 0.026065 -0.185991 0.8525

YEAR=2009 -0.075371 0.009326 -8.081495 0.0000

YEAR=2010 -0.083857 0.009172 -9.143060 0.0000

YEAR=2011 -0.067519 0.009180 -7.355108 0.0000

YEAR=2012 -0.054640 0.009388 -5.820300 0.0000

DAY="Fri" 0.022581 0.016497 1.368836 0.1711

DAY="Mon" -0.161743 0.022540 -7.175943 0.0000

DAY="Thu" -0.144117 0.017906 -8.048730 0.0000

DAY="Tue" -0.155646 0.019781 -7.868260 0.0000

DAY="Wed" -0.152052 0.017707 -8.587311 0.0000

NIGHT="D" 0.032803 0.007686 4.268036 0.0000

(DAY="Sat")*(NIGHT="D") 0.057904 0.015488 3.738729 0.0002(DAY="Sat")*(NIGHT="N") 0.153090 0.017309 8.844725 0.0000

(DAY="Sun")*(NIGHT="N") 0.025112 0.018642 1.347041 0.1780

MONTH=5 0.040327 0.012448 3.239515 0.0012

MONTH=6 0.085631 0.013196 6.489109 0.0000

MONTH=7 0.155233 0.011743 13.21949 0.0000

MONTH=8 0.121272 0.011403 10.63520 0.0000

MONTH=9 0.067639 0.012029 5.622767 0.0000

HTEAM="ANA" 0.622062 0.018021 34.51864 0.0000

HTEAM="ARI" 0.322166 0.017839 18.05966 0.0000


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HTEAM="ATL" 0.397875 0.018222 21.83528 0.0000

HTEAM="BAL" 0.179725 0.020528 8.755269 0.0000

HTEAM="BOS" 0.573980 0.017760 32.31889 0.0000

HTEAM="CHA" 0.316453 0.017275 18.31899 0.0000

HTEAM="CHN" 0.584032 0.018058 32.34246 0.0000

HTEAM="CIN" 0.267118 0.018520 14.42345 0.0000

HTEAM="CLE" 0.127516 0.020854 6.114765 0.0000

HTEAM="COL" 0.489427 0.018070 27.08515 0.0000

HTEAM="DET" 0.494991 0.017841 27.74448 0.0000

HTEAM="HOU" 0.328412 0.018346 17.90098 0.0000

HTEAM="KCA" 0.113186 0.018709 6.049737 0.0000

HTEAM="LAN" 0.741537 0.019935 37.19732 0.0000

HTEAM="MIA" 0.330490 0.021572 15.32020 0.0000

HTEAM="MIL" 0.546247 0.017414 31.36806 0.0000

HTEAM="MIN" 0.494215 0.017512 28.22190 0.0000

HTEAM="NYA" 0.888844 0.017798 49.94021 0.0000

HTEAM="NYN" 0.550848 0.021574 25.53320 0.0000

HTEAM="OAK" 0.002631 0.020818 0.126397 0.8994

HTEAM="PHI" 0.790565 0.018376 43.02083 0.0000

HTEAM="PIT" 0.116813 0.020069 5.820464 0.0000

HTEAM="SDN" 0.305410 0.017342 17.61096 0.0000HTEAM="SEA" 0.252439 0.018677 13.51576 0.0000

HTEAM="SFN" 0.602850 0.017918 33.64538 0.0000

HTEAM="SLN" 0.654934 0.017339 37.77243 0.0000

HTEAM="TBA" 0.107240 0.019856 5.400820 0.0000

HTEAM="TEX" 0.463726 0.020961 22.12300 0.0000

HTEAM="TOR" 0.211442 0.019623 10.77537 0.0000

HTEAM="WAS" 0.270890 0.018908 14.32693 0.0000

AR(1) 0.396197 0.008809 44.97564 0.0000

R-squared 0.675175 Mean dependent var 10.26667

Adjusted R-squared 0.673638 S.D. dependent var 0.394989

S.E. of regression 0.225650 Akaike info criterion -0.134884

Sum squared resid 613.1012 Schwarz criterion -0.099405

Log likelihood 873.9778 Hannan-Quinn criter. -0.122987F-statistic 439.0918 Durbin-Watson stat 2.039759

Prob(F-statistic) 0.000000 Wald F-statistic 147.1499

Prob(Wald F-statistic) 0.000000

Inverted AR Roots .40

!"#$% E( @34,."35 A%"0/ 1B2"3%0 C@A1D +*3 1%F,GA*6 9*4%$

EVIEWS command for OLS semi-log model in #$%&' *:

ls log(attendance) c @expand(year, @dropfirst)



@expand(day, @drop("Mon"), @drop("Tue"), @drop("Wed"), @drop("Thu"), @drop("Fri"),@drop("Sun"))*@expand(night, @drop("N"))

@expand(day, @drop("Mon"), @drop("Tue"), @drop("Wed"), @drop("Thu"), @drop("Fri"),@drop("Sun"))*@expand(night, @drop("D"))

@expand(day, @drop("Mon"), @drop("Tue"), @drop("Wed"), @drop("Thu"), @drop("Fri"),@drop("Sat"))*@expand(night, @drop("D"))


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And we corrected for covariance with Newey-West.

Dependent Variable: ATTENDANCE

Method: ML - Censored Normal (TOBIT) (Quadratic hill climbing)

Date: 04/30/14 Time: 20:54



Right censoring (indicator) series: CAPACITY


Covariance matrix computed using second derivatives

Variable Coefficient Std. Error z-Statistic Prob.

C 18529.80 532.3081 34.81030 0.0000INTER 3441.535 279.6429 12.30689 0.0000

HOLIDAY 4119.488 550.4018 7.484511 0.0000

OPENING 23183.42 843.1406 27.49651 0.0000

NY2 2067.946 814.9742 2.537437 0.0112

BAY2 -768.7924 890.0366 -0.863776 0.3877

CHI2 708.7618 988.9024 0.716716 0.4735

DC2 -3.631945 760.0641 -0.004778 0.9962

LA2 519.1164 893.9740 0.580684 0.5615

YEAR=2009 -2701.138 213.2914 -12.66407 0.0000

YEAR=2010 -2840.467 213.5381 -13.30192 0.0000

YEAR=2011 -2456.163 213.7740 -11.48953 0.0000

YEAR=2012 -2328.046 215.9733 -10.77932 0.0000

DAY="Fri" 1170.963 341.8113 3.425758 0.0006

DAY="Mon" -4836.565 358.4919 -13.49142 0.0000DAY="Thu" -3859.149 306.6237 -12.58595 0.0000

DAY="Tue" -4189.954 343.8090 -12.18687 0.0000

DAY="Wed" -4107.736 303.9955 -13.51249 0.0000

NIGHT="D" 1057.236 247.0709 4.279077 0.0000

(DAY="Sat")*(NIGHT="D") 2411.540 339.7966 7.097011 0.0000

(DAY="Sat")*(NIGHT="N") 5290.438 371.4553 14.24246 0.0000

(DAY="Sun")*(NIGHT="N") 2290.158 703.4261 3.255719 0.0011

MONTH=5 1153.377 240.3484 4.798772 0.0000

MONTH=6 2434.475 278.2535 8.749129 0.0000

MONTH=7 4513.829 246.6223 18.30260 0.0000

MONTH=8 3612.541 240.1137 15.04512 0.0000

MONTH=9 1964.708 238.2791 8.245407 0.0000

HTEAM="ANA" 22741.62 550.4439 41.31505 0.0000

HTEAM="ARI" 8777.128 530.1819 16.55494 0.0000

HTEAM="ATL" 11943.82 531.6618 22.46507 0.0000

HTEAM="BAL" 5394.724 539.6740 9.996263 0.0000

HTEAM="BOS" 29154.72 708.1247 41.17173 0.0000

HTEAM="CHA" 8765.713 537.4913 16.30857 0.0000

HTEAM="CHN" 23174.00 577.4846 40.12921 0.0000

HTEAM="CIN" 7684.867 532.1422 14.44138 0.0000

HTEAM="CLE" 3414.697 531.1509 6.428864 0.0000

HTEAM="COL" 15812.97 533.3251 29.64979 0.0000


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HTEAM="DET" 17231.61 542.8497 31.74287 0.0000

HTEAM="HOU" 9964.019 532.2119 18.72190 0.0000

HTEAM="KCA" 2908.022 531.5844 5.470481 0.0000

HTEAM="LAN" 25057.94 542.1382 46.22057 0.0000

HTEAM="MIA" 9431.093 896.9613 10.51449 0.0000

HTEAM="MIL" 20029.96 546.5815 36.64587 0.0000

HTEAM="MIN" 17819.92 547.1074 32.57116 0.0000

HTEAM="NYA" 29442.87 549.1606 53.61431 0.0000

HTEAM="NYN" 18738.82 550.4079 34.04533 0.0000

HTEAM="OAK" 765.8447 538.9753 1.420927 0.1553

HTEAM="PHI" 35420.06 696.1475 50.88011 0.0000

HTEAM="PIT" 3697.383 532.4180 6.944512 0.0000

HTEAM="SDN" 8282.613 530.7822 15.60454 0.0000

HTEAM="SEA" 6805.123 530.2401 12.83404 0.0000

HTEAM="SFN" 23097.35 567.0065 40.73559 0.0000

HTEAM="SLN" 23197.41 538.9847 43.03909 0.0000

HTEAM="TBA" 3053.152 530.7654 5.752357 0.0000

HTEAM="TEX" 14286.01 533.5162 26.77708 0.0000

HTEAM="TOR" 5967.397 532.5510 11.20530 0.0000

HTEAM="WAS" 7393.712 542.1213 13.63848 0.0000

Error Distribution

SCALE:C(58) 7041.411 52.09958 135.1529 0.0000

Mean dependent var 30859.70 S.D. dependent var 10653.21

Akaike info criterion 16.64864 Schwarz criterion 16.68411


Avg. log likelihood -8.319526

Left censored obs 0 Right censored obs 2469

Uncensored obs 9631 Total obs 12100

!"#$% H( @34,."35 A%"0/ 1B2"3%0 C@A1D +*3 )I 9*4%$

EVIEWS command for CR model in #$%&' 1:

censored(r=capacity, i) attendance c @expand(year, @dropfirst)






@drop("Sun"))*@expand(night, @drop("D"))

@expand(day, @drop("Mon"), @drop("Tue"), @drop("Wed"), @drop("Thu"), @drop("Fri"),@drop("Sat"))*@expand(night, @drop("D"))




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Dependent Variable: LOG(ATTENDANCE)

Method: ML - Censored Normal (TOBIT) (Quadratic hill climbing)

Date: 04/30/14 Time: 20:53



Right censoring (indicator) series: CAPACITY


Covariance matrix computed using second derivatives

Variable Coefficient Std. Error z-Statistic Prob.

C 9.745879 0.020357 478.7583 0.0000

INTER 0.126170 0.010731 11.75700 0.0000

HOLIDAY 0.154002 0.021113 7.294075 0.0000

OPENING 0.815026 0.032859 24.80383 0.0000

NY2 0.067072 0.031497 2.129493 0.0332

BAY2 -0.051313 0.034123 -1.503781 0.1326

CHI2 0.026899 0.038035 0.707226 0.4794

DC2 -0.001405 0.029027 -0.048402 0.9614

LA2 0.004449 0.034360 0.129484 0.8970

YEAR=2009 -0.096225 0.008182 -11.76126 0.0000YEAR=2010 -0.103585 0.008190 -12.64733 0.0000

YEAR=2011 -0.080889 0.008205 -9.858578 0.0000

YEAR=2012 -0.076432 0.008287 -9.223013 0.0000

DAY="Fri" 0.053041 0.013116 4.043895 0.0001

DAY="Mon" -0.196273 0.013735 -14.28995 0.0000

DAY="Thu" -0.153047 0.011752 -13.02325 0.0000

DAY="Tue" -0.167310 0.013175 -12.69864 0.0000

DAY="Wed" -0.159051 0.011650 -13.65237 0.0000

NIGHT="D" 0.050972 0.009469 5.382909 0.0000

(DAY="Sat")*(NIGHT="D") 0.078978 0.013068 6.043736 0.0000

(DAY="Sat")*(NIGHT="N") 0.207139 0.014257 14.52940 0.0000

(DAY="Sun")*(NIGHT="N") 0.067081 0.027011 2.483440 0.0130

MONTH=5 0.055323 0.009194 6.017308 0.0000

MONTH=6 0.109652 0.010652 10.29418 0.0000MONTH=7 0.190371 0.009449 20.14692 0.0000

MONTH=8 0.151895 0.009193 16.52321 0.0000

MONTH=9 0.084862 0.009115 9.310593 0.0000

HTEAM="ANA" 0.888019 0.021064 42.15748 0.0000

HTEAM="ARI" 0.414707 0.020249 20.48000 0.0000

HTEAM="ATL" 0.515558 0.020317 25.37623 0.0000

HTEAM="BAL" 0.231430 0.020606 11.23129 0.0000

HTEAM="BOS" 1.157181 0.027078 42.73508 0.0000

HTEAM="CHA" 0.424679 0.020527 20.68834 0.0000

HTEAM="CHN" 0.923253 0.022164 41.65573 0.0000

HTEAM="CIN" 0.344511 0.020322 16.95223 0.0000

HTEAM="CLE" 0.161893 0.020275 7.984914 0.0000

HTEAM="COL" 0.660508 0.020390 32.39424 0.0000HTEAM="DET" 0.718767 0.020804 34.54928 0.0000

HTEAM="HOU" 0.458283 0.020332 22.54042 0.0000

HTEAM="KCA" 0.144443 0.020291 7.118689 0.0000

HTEAM="LAN" 0.920890 0.020744 44.39280 0.0000

HTEAM="MIA" 0.460859 0.034245 13.45757 0.0000

HTEAM="MIL" 0.813820 0.020989 38.77375 0.0000

HTEAM="MIN" 0.737507 0.020968 35.17231 0.0000

HTEAM="NYA" 1.037362 0.021037 49.31226 0.0000

HTEAM="NYN" 0.751198 0.021099 35.60406 0.0000


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"(

HTEAM="OAK" 0.028266 0.020571 1.374096 0.1694

HTEAM="PHI" 1.318332 0.027081 48.68170 0.0000

HTEAM="PIT" 0.153676 0.020319 7.563264 0.0000

HTEAM="SDN" 0.393128 0.020270 19.39433 0.0000

HTEAM="SEA" 0.321248 0.020245 15.86797 0.0000

HTEAM="SFN" 0.920631 0.021807 42.21760 0.0000

HTEAM="SLN" 0.890679 0.020607 43.22205 0.0000

HTEAM="TBA" 0.149402 0.020256 7.375540 0.0000

HTEAM="TEX" 0.580791 0.020393 28.48060 0.0000

HTEAM="TOR" 0.271014 0.020334 13.32834 0.0000

HTEAM="WAS" 0.357785 0.020700 17.28431 0.0000

Error Distribution

SCALE:C(58) 0.268831 0.001975 136.1434 0.0000

Mean dependent var 10.26671 S.D. dependent var 0.394993

Akaike info criterion 0.427297 Schwarz criterion 0.462773


Avg. log likelihood -0.208855

Left censored obs 0 Right censored obs 2469

Uncensored obs 9631 Total obs 12100

!"#$% J( @34,."35 A%"0/ 1B2"3%0 C@A1D +*3 )I 1%F,GA*6 9*4%$

EVIEWS command for CR semi-log model in #$%&' 2:

censored(r=capacity, i) log(attendance) c @expand(year, @dropfirst)






@drop("Sun"))*@expand(night, @drop("D"))


@drop("Sat"))*@expand(night, @drop("D"))




13/14


")

!"#$% K( L"$4 !%0/ +*3 9*.4"50 >0M !:2304"50 @++

N,623% '( O..2"$ O//%.4".-% C;PPQG;P';D


14/14


"*

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mlb baseball attendance

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