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EXECUTIVE SUMMARY
EXECUTIVE SUMMARY
The April 28, 1996, Dallas Momma News's article on the recent increase in
North Texas sporting events and opportunities indicated the possibility that
the non-media revenues at spectator sporting events may decrease due to the
new entertainment options. If this observation is true, and with animosity
toward Major League Baseball still present after the 1994 strike, the Texas
Rangers will be forced to find new ways to maintain or increase profits.
Before increasing ticket, concession, and/or parking prices, the Rangers may
wish to make current operations more efficient and streamlined. The
opportunity exists to derive more profits from food, beer, souvenir, and
program sales by properly adjusting orders so as to meet customer demand, yet
minimize the possibility of overstocking and assuming its associated costs.
Consistently predicting customer demand can be done by using a mixture of
trend analysis, prediction, and common sense.
Historical data on per-capita sales gives a good indication of the demand for
such items by the average Texas Rangers ticket buyer. Performing statistical
analysis on historical data to gauge customer demand and trends has been
widely used in many industries with positive results. By analyzing in-house
attendanceper-capita sales (adjusted by a confidential conversion factor) of
food, beer, souvenirs, and programs from 1990-1992, I believe that game-bygame adjustments in ordering techniques can contribute at least 3% more to net
income resulting from concession, souvenir, and program sales.
I have included a list of the assumptions and constraints that affected this
study. Specific steps to improve per-capita sales can be found in the
section, "Conclusions and Recommendations."
Assumptions and Constraints:
• From the 1990 to 1992 seasons, all home Opening Day games, last home games,
and Nolan Ryan's home games were eliminated from the study. It was felt
that those games would not represent the mentality and habits of the
average regular season person who attends Texas Rangers games.
• The prediction techniques assume that the Rangers can properly estimate
attendance before the game, preferably before ordering items for the game.
The analysis focused on purchases of fans who were in attendance, so the
techniques predict fan behavior once in attendance
• For confidentiality purposes, Mr. McNeill adjusted the per-capita data by a
"conversion factor." Therefore, all values should be adjusted by his
factor to obtain the proper prediction.
• I could not obtain data on lost sales, extra overtime wages attributed to
stocking overstocked food, any regulations requiring certain percentages,
extra disposal costs, or overhead and/or inventory space required due to
overstocking items. While it would be virtually impossible to get
accurate, game-by-game information on these topics, the Costs associated
with these topics should be considered. Along with not ordering food that
will be wasted, saving money in these areas can increase net income.
• I was not able to obtain data indicating the quantity of food ordered per
game versus quantity of food sold per game. Those in charge of that data
may wish to construct a "trade-off" curve using the prediction techniques
found in this report. The curve would show when the costs would exceed the
benefits of ordering more food on a game-by-game basis.
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CONCLUSIONS AND
RECOMMENDATIONS
CONCLUSIONS AND RECOMMENDATIONS
In this section, I will express ways in which the Rangers can reduce costs and
potential lost sales for each of the four categories:
FOOD SALES, MINIMIZE LOST SALES:
• Order 1-2% more food for promotion games than non-promotion games.
• Order 2-3% more food for games when a top-drawing opponent is playing
against the Rangers in good or great weather. Conversely, you can reduce
the normal amount of food ordered by 2-3% when a low-drawing team is
playing in good or great weather.
• Order 5-6% more food on Fridays and Sundays than for games played on
Monday, Tuesday, Wednesday, or Thursday, especially if there is a
promotion. For Saturday games, order 2-3% more than games played on
Monday, Tuesday, Wednesday, or Thursday.
FOOD SALES, REDUCING COSTS:
• Reduce the amount of food ordered by 4-5% for any game when you can predict
poor weather.
• Reduce the amount of food ordered by 2-3% for non-promotion games played
against a last-placed team versus promotion games played against a lastplaced team.
• Reduce the amount of food ordered by 2-3% for weekday games when the
Rangers are playing low-place teams.
• Reduce the amount of food ordered by 4-5% when the Rangers are playing a
weekday game after having lost 3 or more games.
While it is possible to have these options conflict at various points during
the season, the decision maker can take appropriate action by emphasizing
cost-cutting, reducing lost sales, or a "common sense" combination of both.
For additional information on upcoming scenarios, use the regression tree for
food sales. As a supplement to the regression tree, consult the section
entitled "Results of Food_PC Comparisons."
BEER SALES, MINIMIZE LOST SALES:
• On average, fans will spend 16% more on beer for non-promotion weekend
games when the Rangers have lost 2 or more games.
• On average, fans will order 19-20% more on non-promotion nights than on
promotion nights, regardless of whether or not the game is on television.
My theory is that promotion games draw families to the Ballpark, and,
subsequently, beer sales will drop. The decision maker may wish to order
1-2% more beer on promotion nights targeted to an adult crowd.
• Fans will spend the highest amount of money on beer during the Tuesday,
Wednesday, and Thursday games. Non-promotion Tuesday games, with the
Rangers in fourth place (or worse) and/or a losing streak of 2 or more
games, will result in the highest per-capita beer sales.
BEER SALES, REDUCING COSTS:
• Fans will order the least amount of beer on Sundays, Mondays, and promotion
games (especially geared to children and/or families).
• Less beer will be ordered on weekend games as compared with non-weekend
games.
For additional information on different scenarios, consult the regression tree
for per-capita beer sales. As a supplement, you can use the section entitled
"Results of Beer_PC Comparisons."
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CONCLUSIONS AND RECONDATIONS
SOUVENIR SALES, MINIMIZE LOST SALES:
• During good/great weather, televised, weekend games, when the Rangers are
in fourth place (or worse), fans will purchase 7-8% more souvenirs than
similar games except for when the Rangers are in third place.
. Fans will purchase 7-8% more souvenirs on weekend games (Friday through
Sunday) than on weekday games.
• Fans will purchase up to 10% more souvenirs when facing a top-drawing team
on promotion games than on non-promotion games. It can be speculated that
people will spend more on items when originally enticed with a promotion
when facing a top-drawing opponent.
SOUVENIR SALES, REDUCING COSTS:
• On Mondays, when the Rangers are in a losing streak of 3 or more games,
fans will spend up to 25% less on souvenirs than on Mondays when the
Rangers have a win/loss streak of no less than -2 games.
• On good/great weather weekend games, when the Rangers are in third place
(or better), fans will spend up to 25% less on souvenirs when facing a
cellar-dwelling , team as compared with an above-average-drawing team.
. On average, fans will spend up to 13% less on Tuesday games than on Monday
games.
For additional information, consult the regression tree for per-capita
souvenir sales. As a supplement to the regression tree, look at the section
entitled "Results of Nov_PC Comparisons."
PROGRAM SALES, MINIMIZING LOST SALES:
• On good/great weather, non-Monday games when
than a 2-game losing streak, fans bought 25%
when the Rangers were in a losing streak of 3
• On good/great weather, non-promotion Monday
more programs than on promotion games.
• Sundays are the best days to sell programs.
the Rangers were in no worse
more programs on average than
or more games.
games, fans bought up to 23%
PROGRAM SALES, REDUCING COSTS:
• On poor-weather, Monday games, fans spent at least 20% less on programs
than on average Monday games.
• Fans spent up to 9% less on programs during promotion games broadcast on
regular television.
• On cable-broadcast games, fans spent 4% less on programs when a low-drawing
team played versus a top-drawing team.
For additional information, consult the regression tree for per-capita program
sales. As a supplement to the regression tree, look at the section entitled
"Results of Prog ..PC Comparisons."
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TICKET PRICE AND
PER-CAPITA
CONSUMPTION
TIC1ET PRICE AND PER-CAPITA CONSUNPTION
In the April 28, 1996, the Dallas Morning News's Business section reported
that there are over 3.9 million tickets available for the 1996 season. While
it is unlikely that the 3.9 million tickets will be purchased at an average of
over $7.00/ticket (reported in an earlier article), the Rangers current
performance may help the in-house 1996 season attendance surpass pre-season
projections. With the potential increase in attendance, concession sales have
the opportunity to contribute a greater amount to the bottom line.
The data I was given reflects the trends of the average Ranger fan from 1990
to 1992 (excluding Nolan Ryan's games, Opening Day, and the last game of the
season) . I believe that the per-capita sales of food, beer, souvenirs, and
programs have the potential to be higher than those during the 1990 through
1992 seasons. Since the Rangers now play at the Ballpark at Arlington, are
currently playing at a high level, have a wider selection of food items, and
changed the team logo for the 1994 season, the Rangers have established the
foundation for higher per-capita sales than in earlier seasons.
From 1990-1992, every person who attended a game spent an average of
$1.50x(Mr. McNeill's conversion factor) per game on food, beer, souvenirs, and
programs. If Mr. McNeill's conversion factor is greater than "2", and with an
average ticket price of $7.00 to $7.50, the organization can expect at
concession sales of at least 40% of ticket sales. With the Rangers current
performance, food and beer prices that are slightly higher than those at
Arlington Stadium, souvenirs with the new logo, and the possibility of higherthan-expected attendance, it is likely that concession sales could represent a
percentage of ticket sales that is higher than 40%.
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ECONOMIC ANALYSIS
AND SAVINGS
PER YEAR
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ECONOMIC ANALYSIS AND SAVINGS PER YEAR
By adjusting the amount of food, beer, souvenirs, and programs for each game,
the Texas Rangers organization can free up a sizable amount of capital.
Knowing the conditions for upcoming games and ordering items accordingly will
allow the concessions, programs, and souvenirs business units to run more
efficiently and contribute more to the bottom line regardless of the
by cost-cutting or by increasing revenues.
organization's approach:
Incremental adjustments, performed over an entire season, could result in a
possible six-figure improvement in net income.
Presented below are areas in which the Rangers can possibly save money by
reducing costs:
• Neverinitially purchasing items that would be wasted. Although the saved
money never would appear directly on a balance sheet, it should still be
considered as a "savings" or an "opportunity cost." Over the course of a
season, this could amount to several thousand dollars, perhaps as high as
six figures for the 81 regular season, 2 pre-season, and any playoff games.
•Overtime wages would be reduced because less food would have to be stored
and/or disposed of after a game. Since it is difficult to quantify the
actualamount of overtime wages attributed to excess food disposal and
storage, I will not attach a dollar-figure to this facet.
• Disposal costs and any costs associated with donated food would be reduced
due to less waste. Since I was not given any data on this subject, I will
not attach a dollar-figure to this facet as well.
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Since the effort to implement a system to detect lost sales might prove to be
more expensive than the benefits it would bring, I propose using the
regression trees and the comparison tables - as a supplement to the trees - to
reasonably predict turnstile attendance-driven customer demand. The goal is
to accurately predict what the customers will want for a given game, and the
use of reasonable prediction techniques will increase the probability of the
Rangers correctly assessing in-house customer demand. Lost sales will be
reduced from their current levels, as will the costs associated with
overstocking. Due to the costs of obtaining data on lost sales, I cannot put
a dollar-figure on how much sales will increase due to prediction techniques,
but I would estimate that lost sales can be reduced by 5-10% over the course
of a given season.
COMPARISON OF
UNDERSTOCKING VERSUS
OVERSTOCKING
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ISSUES REGARDING TIlE tJNDERSTOCKING OF FOOD, BEER, SOtWENIRS, AND PROGRAZIS
If the Rangers were to fail to meet the demand for food, beer,
. souvenirs, or programs, two potential problems arise:
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The Rangers would fail to acquire its total possible revenue for the
game(s).
Failing to fulfill the needs of every fan may keep a few fans from
attending future games.
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In the first case, the Rangers would not have to make any additional
expenditures. Those in charge of making the decisions could purchase a
slightly greater amount for the next game that is similar to the game in which
the understocking occurred (i.e. the next game that is on a weekend, without a
promotion, against a top-drawing team, etc.).
I believe that people who purchase concessions at a Major League
Baseball game come to the stadium to watch baseball. Unlike a restaurant,
where understocking could tarnish customer relations, most fans will return to
the stadium to watch the game regardless of possible understocking. From
first-hand observations of the Rangers. from 1992 to the present, most fans,
when told that a certain food-item or beer is sold-out, will usually purchase
another item or drink. While it would be relatively impossible to quantify
such occurrences, most fans will purchase the alternative item(s), and their
decisions to return to the stadium are based on factors other than
concessions.
ISSUES THE REGARDING THE OVERSTOCKING OF FOOD, BEER, SOUVENIRS, AND PROGRAMS
If the Rangers were to purchase excess food, beer, souvenirs, and
programs for a game, or series of games, the following costs arise:
The Rangers may have to incur costs to dispose of the items, especially at
the end of the season. Some food items may not be able to be sold at the
next home game because of health regulations. Beer, in opened containers,
may have to be disposed. Souvenirs and novelties may last throughout the
season, or multiple seasons, but the Rangers may obtain a high inventory
carrying cost and potential insurance costs. Finally, programs may need to
be disposed of due to their potential to be outdated.
Extra wages for concession workers, security personnel, and any internal
auditors will increase due to overstocking. If items need extra time to be
stored or prepared for the following game, these wages could translate into
overtime wages as well.
Any items that are disposed not only incur a disposal cost, but they become
"wasted assets," which did not have to be purchased in the first place.
This reduces the amount of available capital overall, and it ties up the
extra capital earlier in the season. The capital could be allocated to
other areas in which the Rangers need to spend.
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These factors show how costs can needlessly increase during the course
of a season. Prediction techniques can reduce the amount of wasted assets
during the course of the season, and also can reduce the number of potential
"lost sales" that would occur if the desired items were sold out. Reducing
the overstocking of items would free up space, capital, and worker hours to
accomplish more of the organization's objectives.
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TECHNIQUES AND
METHODOLOGY
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RATIONALE FOR DECISION-MAKING
MULTIPLE LINEAR REGRESSION:
PROS:
1) Easy to understand
2) Can be done on Excel or Lotus 1-2-3
3) Good for graphs and presentation techniques
CONS: 1) When considering "categorical" variables, such as the days of
the week or promotion versus non-promotion games, some of linear
regression's underlying assumptions are violated
2) It assumes linearity, which is not always the case when
predicting the future
I included an MLR printout because it gives a fairly reasonable prediction of
future food, beer, souvenir, and program sales will be. Since MLR can be done
on Excel or other spreadsheet packages, it can be done by just about anyone in
the organization.
when taking categorical data into consideration, however, MLR has some flaws.
First, by assigning categorical variables, such as the days of the week into
numbers from one to seven, the assumption of a constant variability is
violated. While MLR will still reasonably predict the future with a few
"binary" variables, such as "PROMOTION" = 0 or 1, MLR's accuracy diminishes
when several categorical variables or non-binary categorical variables need to
be considered.
To combat this problem, I performed a "Five-Way Cross-Classification" method.
Of the 185 games from 1990 to 1992 that were analyzed, I removed a separate
20%-section from the data five times. Then I performed MLR on the remaining
148 games. Once I derived the regression formula, I tested its ability to
predict the 20%-section (37 games) that was originally removed.
This "Five-way Cross Classification" method was somewhat accurate in
estimating the remaining data, but other techniques can be used to be more
accurate.
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RATIONALE FOR DECISION-MAKING: ANOVA TABLES
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ANOVA TABLES:
PROS:
1) Allows for categorical data to be analyzed
2) Available on most statistical packages
3) Determines whether or not a variable, or combination of
variables is "significant"
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CONS:
1) Has its roots in Multiple Linear Regression (MLR)
2) Requires further analysis if a "significant" effect is found
3) Does not analyze continuous (normal numerical) variables as
efficiently as MLR
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Analysis of Variance (ANOVA) tables are useful tools in determining which
variables and/or combinations of variables make up the "significant" majority
of an MLR statement. Its underlying assumption is that all of the averages
(means) of the variables are equal to each other; but it points out the
combination of variables (factors) when this assumption is violated. These
violations are the basis of determining which combinations can best be used to
accurately predict the future.
I used the ANOVA methodology to produce an alternative way of handling the
many categorical variables in this analysis. While MLR requires the category
to assume a numerical value, ANOVA considers the category as a "level" and
treats the variable in a better fashion.
The first main drawback to ANOVA in this analysis is that is treat "numerical"
variables (e.g. current win/loss streak) as a level. This differs from MLR
which treats such a variable as a number. By treating a numerical variable as
a level, ANOVA would treat every different numerical value as a level to be
compared with the rest. This could produce "significant effects," when, in
according to MLR, the effects are barely significant.
Thesecond drawback of ANOVA is that it requires multiple comparisons of the
means once a significant effect is detected. Therefore, out of 185 examples,
the difference in just two means could be enough to cause ANOVA to say it
found a significant result, when it the difference may be trivial in the big
picture.
For all of its flaws, ANOVA does give a good indication of what variables need
to be considered when attempting to predict the future and how the Rangers can
cut excess expenditures from its budget.
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RATIONALE FOR DECISION-MZING: REGRESSION TREES
REGRESSION TREES:
PROS:
1)
2)
3)
4)
5)
Takes categorical and numerical variables into consideration
Presented in easy to follow, decision-making format
Uses the software to generate the best "splits" in the data
Models the data, yet still allows for predictability
Hierarchically-based
CONS:
1) Need statistical software packages to derive the trees
2) Programming is difficult and time-consuming
3) Concedes the decision-making to the computer
Of the three predicting techniques used, regression trees give the best
predictions of the future. In addition, the regression tree is structured in
way so a person can follow the tree and come up with a fairly accurate
prediction. The tree takes the most important variables (factors) and
"splits" them according to the computer's decision of what is the best
indicator. Since it accounts for numerical and categorical variables, this
technique gives the user a reasonably accurate picture of future behavior
Regression trees can sometimes "over-model" the data. This means that the tree
will perfectly predict the historical data, but it might not be so accurate
with future data. Therefore, one "prunes" the tree so it can not only
accurately describe the historical data, but it allows the model to predict
the future with a high degree of accuracy. This assumes, of course, that the
original historical data is considered to be indicative future behavior.
The tree allows the user to assess the conditions of upcoming games, and gauge
the probable per-capita amount spent for food, beer, souvenirs, and programs.
If the user knows the current status of inventory, any regulations affecting
in-stadium sales, and any extenuating circumstances, the user can then adjust
his or her orders to meet the requirements for the upcoming games and prevent
both lost sales and needless expenditures.
The main drawbacks in the regression tree analysis are that it takes
significant time to do the initial programming in the software package and it
gives control of the splits to the computer. Therefore, I recommend using the
regression trees, the charts found in this study, and common sense for knowing
when to adjust orders to minimize costs and maximize sales.
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MEAN ABSOLUTE
DEVIATION (M.A.D.)
010
MEAN SQUARED ERROR
(M.S.E.)
MEAN ABSOLUTE DEVIATION AND MEAN SQUARED ERROR
The
two
the
low
Mean absolute deviation (M.A.D.) and the Mean Squared Error (M.S.E.) are
ways to evaluate how accurately a model predicts the historical data. If
historical data is assumed to be indicative of the future, a model with
M.A.D. and low M.S.E. can be considered as useful models.
Mean Absolute Deviation (M.A.D.):
This value is calculated by taking the absolute value of the difference
between the actual data and the predicted data for each observation. Then all
of the M.A.D.'s are added together. Finally, the sum is divided by the total
number of observations. This value indicates the average deviation from the
mean for a prediction model. The M.A.D. for each area of interest (food,
beer, souvenirs, and programs was calculated by the following formula:
Sum of all (Abs(actual value - predicted value)) / 185
MEAN SQUARED ERROR (M.S.E.):
This value indicates the average variability in the prediction model. Unlike
M.A.D., one does not need to take the absolute value of the difference between
the actual value minus the predicted value. M.S.E. is calculated by squaring
the difference between the actual minus the predicted values for each
observation. Then, those values are totaled. Finally, the sum of the values
is divided by the total number of observations to receive an average
variability. The M.S.E. for each area of interest was calculated by the
following formula:
Sum of all [ (actual value - predicted value )2 ] / 185
In both cases, the M.A.D. and the M.S.E. for regression trees were
significantly less than those for multiple linear regression (MLR). This
reinforces the belief that regression trees provide a better representation of
historical data and, also, a better way to predict the future.
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MULTIPLE LINEAR
u REGRESSION PRINTOUTS
SET OF VALUES FOR MULTIPLE LINEAR REGRESSION EQUATIONS
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POSSIBLE VALUES FOR EACH VARIABLE:
• TV_RANK:
"0" for Not Televised
"1" for Over-the-Air
"2" for HSE (Cable)
OPP_RANK:
"1"
"2"
"3"
"4"
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PROMOTION:
"0" for Non-Promotion Game
"1" for Promotion Game
•
WEATHER:
"0" for Poor Weather (Rain, Fog, Sleet, etc.)
"1" for Decent weather
"2" for Outstanding Weather
.
DAYOFWK:
"1"
"2"
"3"
"4"
"5"
"6"
"7"
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STREAK:
"Rangers' current win/loss streak"
* Note: Losing streak is designated as a NEGATIVE number
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POSITION:
"Rangers' current position in the division"
WINS:
"Rangers' current number of wins"
LOSSES:
"Rangers' current number of losses"
* Note: Losses is entered as a POSITIVE number
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for
for
for
for
Poor-Drawing.Team
Average-Drawing Team
Above-Average-Drawing Team
Top-Drawing Team
•
for
for
for
for
for
for
for
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
MULTIPLE LINEAR REGRESSION EQUATIONS
EQUATION FOR "FOOD_PC":
FOOD- PC = _0.001185*TV_RANK + 0.012853*OPP_RANK + 0.003224*PROMOTION +
0.019516*WEATHER + 0.009966*DAYOFWK - 0.01068*STREAK - 0.005511*POSITION +
0.02825*WINS - 0.003267*LOSSES + 0.667777
EQUATION FOR "BEER-PC":
BEER- PC = _0.014904*TV_RANK + 0.000320*OPP_RANK - 0.065958*PROMOTION +
0.008573*WEATHER - 0.014025*DAYOFWK - 0.022967*POSITION - 0.002724*STREAK 0.0039849*WINS + 0.001185*LOSSES + 0.821316
EQUATION FOR "NOV_PC":
NOV_PC = 0.001197*TV_RANK + 0.000597*OPP_RANK - 0.000579*PROMOTION +
0.001569*WEATHER + 0.001149*DAYOFWK + 0.000538*POSITION - 0.0000054*STREAK +
0.000347*W1NS - 0.000439*LOSSES + 0.027925
EQUATION FOR "PROG_PC":
PROG_PC = _0.003516*TV_RANK + 0.010533*0PP_RANK - 0 . 007785*PROMOTION 0.014007*WEATHER + 0.010720*DAYOFWK + 0.005350*POSITION - 0.002076*STREAK +
0.004677*WINS - 0.004676*LOSSES + .133919
04-28-1996
WINKS
A:\WINKS2.DBF
Linear Regression and Correlation 9 independent variables, 185 cases.
Dependent variable is FOOD-PC,
Variable
Coefficient
Intercept
TV-RANK
OPP_ RAN K
PROMOT2
WEATH
DOW--RANK
STREAK
POSIT
WINS
LOSSES
.6677773
-.001185
.0128528
.0032238
.0195157
.009966
-.001068
-.0055109
.0028248
-.0032673
R-Square = 0.185
St. Error
.0371981
.0059865
.0051084
.0108162
.0088294
.0027412
.0020641
.0059666
.001489
.0015298
t-value
p(2 tail)
17.951941
-.1979438
2.5160242
.2980502
2.210301
3.6355714
-.5174062
-.9236224
1.8971166
-2.135821
0.000
0.843
0.013
0.766
0.028
0.000
0.606
0.357
0.059
0.034
Adjusted R-Square = 0.1431
Analysis of Variance to Test Regression Relation
Source
Regression
Error
Total
Sum of Sqs
df
.1914271
.8432487
9
175
1.0346759
Mean Sq
.0212697
.0048186
F
4.4141124
184
A low p-value suggests that the dependent variable FOOD_PC
may be linearly related to independent variable(s).
p-value
0.000
04-28-1996
WINKS
A:\WINKS2.DBF
Linear Regression and Correlation
9
Dependent variable is BEER_PC,
Variable
Coefficient
Intercept
TV_RANK
OPP_RANK
PROMOT2
WEATH
DOW_RANK
POSIT
STREAK
WINS
LOSSES
.8213161
-.0149036
.0003205
-.0659581
.0085732
-.0140253
-.0229665
-.0027242
-.0039849
.0011848
R-Square = 0.547
independent variables, 185
St. Error
.0435813
.0070139
.005985
.0126723
.0103446
.0032116
.0069904
.0024183
.0017445
.0017923
.
cases.
t-value
p(2 tail)
18.845606
-2.124877
.0535517
-5.204885
.8287625
-4.367018
-3.285411
-1.126525
-2.284271
.6610479
0.000
0.035.
0.957
0.000
0.408
0.000
0.001
0.261
0.024
0.509
Source
Sum of Sqs
df
Regression
Error
1.3974559
1.1574859
9
175
Total
2.5549418
184
Mean Sq
.1552729
.0066142
F
23.475666
A low p-value suggests that the dependent variable BEER_PC
p-value
0.000
04-28-1996
WINKS
Linear Regression and Correlation 9 independent variables, 185 cases.
Dependent variable is NOV_PC, Variable
Coefficient
Intercept
TV.-RANK
OPP_RANK
PROMOT2
WEATH
DOW-RANK
POSIT
STREAK
WINS
LOSSES
.1339191
-.0035155
.0105328
-.0077845
-.0140074
.0107202
.0053499
-.0020755
.0046772
-.0046755
R-Square = 0.3026
A:\WINKS2.DBF
St. Error
.0272119
.0043794
.003737
.0079125
.0064591
.0020053
.0043648
.00151
.0010893
.0011191
t-value
p(2 tail)
4.9213393
-.802725
2.8185447
-.9838172
-2.168643
5.3458436
1.2256909
-1.37455
4.2939152
-4.177973
0.000
0.423
0.005
0.327
0.031
0.000
0.222
0.171
0.000
0.000
Sum of Sqs
df
Regression
Error
.1958359
.4512671
9
175
Total
.6471031
184
Source
Mean Sq
.0217595
.0025787
F
8.4382843
A low p-value suggests that the dependent variable NOV_PC
p-value
0.000
04-28-1996
WINKS
I
A:\WINKS2.DBF
Linear Regression and Correlation
9 independent variables, 185 cases.
Dependent variable is PROG_PC,
Variable
Coefficient
Intercept
TV-RANK
OPP_.RANK
PROMOT2
WEATH
DOW-RANK
POSIT
STREAK
WINS
LOSSES
.0279246
.0011974
.0005965
-.0005793
.0015689
.001149
.0005379
-.0000054
.0003465
-.0004393
R-Square = 0.132
St. Error
.0047301
.0007612
.0006496
.0013754
.0011227
.0003486
.0007587
.0002625
.0001893
.0001945
t-value
p(2 tail)
5.9036077
1.573004
.9182882
-.4211607
1.397348
3.2962549
.7089483
-.0206826
1.8300993
-2.258337
0.000
0.118
0.360
0.674
0.164
0.001
0.479
0.984
0.069
0.025
Sum of Sqs
df
Regression
Error
.0020726
.013635
9
175
Total
.0157076
184
Source
Mean Sq
.0002303
.0000779
F
2.9557179
A low p-value suggests that the dependent variable PROG_PC
p-value
0.003
REGRESSION TREE
FOR PER-CAPITA
FOOD SALES
I
AM
0.6878 0.7299
I
i
REGRESSION TREE
FOR PER-CAPITA
BEER SALES
-
-
-
-
-
-
-
-
-
-
-
ml
-
-
-
-
-
-
-
-
51
0.5454 0.6766 0.7001 0.6193
I
REGRESSION TREE
FOR PER-CAPITA
SOUVENIR SALES
0.1
.5
)33
0.2227 0.1815
REGRESSION TREE
FOR PER-CAPITA
PROGRAM SALES
V .V
0.043200.034830.027670.034850.041400.033370.039100.031 430.043540.037880.052670.03963
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
RESULTS OF FOOD PC
COMPARISIONS
Sheeti
TELEVISION COMPARED WITH DAY OF WEEK
TV
H
K
x
SATURDAY SUNDAY
TUESDAY WEDNESDAY i THURSDAY FRIDAY
MONDAY
0.755 0.75691
0.730671 0.71692 0.77135
0.73169 0.708871
0.749
0.7471 0.822751 0.725331
0.67341
0.59
0.7251 0.79667
0.752 0.77633
0.6913
0.709i 0.74289
TELEVISION COMPARED WITH OPPONENT'S DRAWING-RANK.!
TV
H
K
X
ONE
0.72796
O.696
0.73033
FOUR
THREE
TWO
0.764021 0.74206!:
0.722681
0.7362.5i 0.67967.!
0.80511
0.7671
0.704
0.734641
TELEVISION COMPARED WITH PROMOTION
TV
H
K
X
NO PROMOTIOtPROMOTION
0.729661 0.749751
0.7348
0.72275
0.74482 0.73295
OPPONENT'S DRAWING RANK COMPARED WITH PROMOTION 1
RANK NO PROMOTIOPROMOTION
0.71153 0.74152
ONE
0.73907 0.72484
TWO
0.7619
0.75975
THREE
0.71045 0.74627
FOUR
OPPONENT'S DRAWING RANK COMPARED WITH DAY OF WEEK
iTUESDAY WEDNESDAY THURSDAY FRIDAY i SATURDAY SUNDAY
RANK MONDAY
0.69764
0.65225
0.76561
0.7016 1
ONE
07855L 0 . 7277 51 0.74878
0. 754451 0.74425
0.6531
0.708781
0.772
0.69089
0.785561
TWO
0.77358
0.75614 0.782281 0.732461 0.7993
0.72461 0.734861
THREE
0.7375
0.7141,
0.6865 0.750751 0.72367i 0.7525
0.722i
FOUR
Page 1
RESULTS OF BEER PC
COMPARISIONS
Sheeti
TV
H
K
X
TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY
MONDAY
0.6069 0.54307 1 0 . 4 9 7 2- il 0.49171 0.4337
0.47077 0.56561
0.5471 0.424111 0.546
0.693
0.5121 0.61681
0.481111 0.4067
1
0.49111
0.6369i
0.582
.
0.40967 0 . 63071
TELEVISION COMPARED WITH OPPONENT'S DRAWING RANK
TV
H
K
x
ONE
FOUR
THREE
TWO
0.525 0.50827 0.50644!1
0.52353
0.51751 0.51633
0.53914 0.4808!
0.522831 0.56291 0.499231 0.58167
TV
H
K
X
NO PROMOTIOPROMOTION
0.55983 '0.4757
0.55642 1 0.4709
0.586541 0.4552
OPPONENT'S DRAWING RANK COMPARED WITH PROMOTION
RANK
ONE
TWO
THREE
FOUR
0.571831 0.4647
0.590781 0.46821
0.55051 0.46741
0.539181 0.49691
OPPONENT'S DARWING RANK COMPARED WITH DAY OF WEEK
RANK
ONE
TWO
THREE
FOUR
TUESDAY1WEDNESDA'.rl THURSDAY
0.4541 0.59031 0.627911 0.624751
0.404261 0.59181 0.640891 0.60851
0.51
0.5092! 0.6326i 0.57286 11
0.476i 0. 53 81 0 . 6072 51 0.5595 1
MONDAY
1
Page 1
FRIDAY SATURDAY SUNDAY
0.49321 0.447131 0.4143
0.53961 0.508361 0.4099
0.48381 0.453631 0.464
0.4511 0.496
0.4811
I
RESULTS OF NOV PC
COMPARISIONS
Sheeti
TV
H
MONDAY
0.17357_ 0.176081 0.2109 0.222861 0.2186
0.175i 0.2568 .1 0.252671 0.1965
0.1617i
0.1951 0.2227: 0.22411 0.2723
0.208151 0.16631
0.1211 0.15921
0.206331 0.16891
K
X
TV
H
K
x
ITWO
ONE
FOUR
THREE
0.18511 0.1868
0.1981 0.22881
0.216061 0.17861
0.210491 0.20469
0.229371 0.21667
0.22446 0.17433
TV
H
K
X
NO PROMOTIOIPROMOTION
0 . 197 3 91 0.1956 _________
0.20958 0.2271 _________
0.192891 0.2215
OPPONENT'S DRAWING RANK COMPARED WITH PROMOTION
RANK
ONE
TWO
THREE
FOUR
0.18967i 0.2073
0.19015 0.1852
0.21579i 0.2166
0.191271 0.213
RANK
ONE
TWO
THREE
FOUR
MONDAY
0.2276
0 . 2 0 51
0.18581
0.18633
0.15951
0 . 15071
0.18271
0.1865
0.17491 0.14275i 0.22751 0.2145i 0.2388
0.147891 0.17851 0.20991 0.22064 1 0.1981
0.181i 0.19371 0.2266 :10.24373l 0.2516
0.177 0 .217 5 1 0. 2703 31 0.184
0.185
Page 1
RESULTS OF PROG PC
COMPARISIONS
Sheeti
TV
H
K
X
TUESDAY. WEDNESDAY THURSDAY
MONDAY
0.03471 0.03308
0.038691 0.033
0.0361
0.048 0.0372'
0.0271
0.03241
0.03967 0.0318 i
0.03981 0.044791 0.0405
0.04531 0.036891 0.0345
0.03671 0.03591 0.038
TV
H
K
x
ONE
FOUR
THREE
TWO
0.03808 i 0.04031
0.03782 i 0.0363
0.03775
0.039
0.039431 0.0393
0.026
0.035441 0.03441 0.036621
TV
H
K
X
0.037541 0.0381
0.0402511 0.0369
0.036
0.03406
OPPONENT'S DRAWING RINK COMPARED WITH PROMOTION
RANK
ONE
TWO
THREE
FOUR
0.03713 0.0373
0.03563 0.0363
0.037641 0.0378
0.03709 0.0393 i
RANK
ONE
TWO
THREE
FOUR
TUESDAY WEDNESDAY THURSDAY
MONDAY
0.036181 0.03251
0.0406i 0.0334
0.0341
0.034751 0.03311 0.027561
0.0331
0.03921 0.0357i: 0.038141
0.035
0.032
0.044 0.0295
Page 1
0.03931 0.038251 0.0407
0.03741 0.042181 0.0395
0.03661 0.03891 ' 0.0412
0.04
0.044
0.053
i
i
ANOVA PRINTOUTS
(WITH "MEANS") FOR
PER-CAPITA
FOOD SALES
1
The SAS System
12:16 Monday, April 29, 1996
Analysis of Variance Procedure
Class Level Information
Class Levels Values
TV
3 HKX
OPPRANK 4 1234
PROMOT 2 01
TIME
6 1:002:05 6:35 7:05 7:35 8:05
WEATHER 3 012
DAYOFWK 7 Friday Monday Saturday Sunday Thursday Tuesday Wednesda
POSITION 8 01234567
STREAK
15 1234567-1-23-4-5-81314
Number of observations in data set = 185
I
The SAS System
2
12:16 Monday, April 29, 1996
I
1
I
I
Dependent Variable: FOOD
Sum of
DF
Source
Squares
Model
-
I
I
I
I
I
0.12866062 0.00229751
56
Corrected Total
Source
0.90601524 0.00707824 3.08 0.0001
128
Error
Mean
Square F Value Pr> F
184
1.03467586
R-Square
C.V.
0.875651
6.490099
DF
Root MSE
0.0479324
FOOD Mean
0.7385459
Anova SS Mean Square F Value Pr> F
TV
2
0.00265888 0.00132944 0.58 0.5640
0.01454184 6.33 0.0009
OPPRANK
0.04362551
3
1
2.46 0.1221
PROMOT
0.00566305 0.00566305
0.01258067
5.48 0.0004
TIME
5
0.06290335
WEATHER
2
0.01814820 0.00907410 3.95 0.0249
DAYOFWK
6
0.11463061
0.01910510 8.32 0.0001
0.11450014 0.01635716 7.12 0.0001
POSITION
7
14
0.04665402 0.00333243
1.45 0.1613
STREAK
TV*OPPRANK
0.04594577 0.00765763
6
3.33 0.007 1
TV*PROMOT
0.00836328 0.00418164
2
1.82 0.1715
TV*WEATHER
4
0.03679800 0.00919950 4.00 0.0063
TV*DAYOFWK
11
0.06982739 0.00634794 2.76 0.0062
OPPRANK*PROMOT
0.01579802 0.00526601
2.29 0.0880
3
OPPRANK*DAYOFWK
18
0.08569034 0.00476057 2.07 0.0198
OPPRANK*WEATHER
6
0.02797346 0.00466224 2.03 0.0768
OPPRANK*POSITION
14
0.06176733 0.00441195
1.92 00435
OPPRANK*STREAK
24
0.14506788 0.00604449 2.63 0.0015
3
The SAS System
12:16 Monday, April 29, 1996
-------------FOOD------ ----Level of Level of
Mean
SD
DAYOFWK N
TV
•
•
•
•
•
•
H
K
K
K
K
K
K
X
X
X
X
X
X
X
Friday 17 0.77135294
Monday 13 0.73169231
Saturday 14 0.75500000
Sunday 21 0.75690476
Thursday 13 0.7 1692308
Tuesday 16 0.70887500
Wednesda 21 0.73066667
Friday 4 0.82275000
Monday
1 0.59000000
Saturday 9 0.72533333
Sunday 2 0.74900000
Thursday 1 0.74700000
Tuesday 5 0.67340000
Friday
9 0.77633333
3 0.70900000
Monday
Saturday 10 0.72510000
Sunday 6 0.79966667
Thursday 1 0.75200000
Tuesday 9 0.74288889
Wednesda 10 0.69130000
0.07791818
0.06385972
0.06609550
0.08408145
0.08497006
0.06795378
0.07347131
0.06972984
0.07571493
0.02545584
0.07575 157
0.06918996
0.07903797
0.06413952
0.02781 127
0.04084558
0.07479609
----- ------FOOD-----Level of Level of
SD
Mean
TV
OPPRANK N
H
H
H
H
K
K
K
K
X
X
X
X
1
2
3
4
1
2
3
4
1
2
3
4
28
34
37
16
7
4
8
3
18
14
13
3
Level of Level of
PROMOT
TV
H
H
I
11
0
1
56
59
0.72796429
0.72267647
0.76402703
0.74206250
0.69600000
0.80500000
0.73625000
0.67966667
0.73033333
0.73464286
0.76700000
0.70400000
N
0.06538574
0.07509377
0.08275113
0.07090413
0.078723 14
0.11258774
0.06082234
0.08852307
0.08466057
0.06123801
0.04732864
0.048662 10
-------FOOD--------Mean
SD
0.72966071
0.74974576
0.07030409
0.08048379
4
The SAS System
12:16 Monday, April 29, 1996
Level of Level of
TV
PROMOT
K
K
X
X
0
1
0
1
12
10
28
20
-------------FOOD---N
Mean
SD
0.72275000
0.73480000
0.74482143
0.73295000
0.09719813
0.07490854
0.06875025
0.06820980
------------- FOOD - --------Level of Level of
Mean
SD
OPPRANK PROMOT N
1
1
2
2
3
3
4
4
0
1
0
1
0
1
0
1
30
23
27
25
28
30
11
11
0.71153333
0.74152174
0.73907407
0.72484000
0.75975000
0.76190000
0.71045455
0.74627273
0.07289328
0.07239404
0.07 190428
0.08169541
0.06757307
0.07914385
0.07545643
0.06612426
-------------FOOD-----Level of Level of
Mean
OPPRANK DAYOFWK N
1
1
1
I
I
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
Friday 6 0.78550000
0.76560000
Monday
5
Saturday 8 0.72775000
Sunday 9 0.74877778
Thursday 4 0.65225000
Tuesday 10 0.70160000
Wednesda 11 0.69763636
Friday 9 0.78555556
Monday 4 0.65300000
Saturday 11 0.75445455
8 0.74425000
Sunday
Thursday 2 0.77200000
Tuesday 9 0.70877778
Wednesda 9 0.69088889
Friday 11 0.78227273
Monday 5 0.72460000
Saturday 11 0.73245455
Sunday 10 0.79930000
Thursday 7 0.75614286
Tuesday 7 0.73485714
Wednesda 7 0.77357143
Friday 4 0.75075000
SD
0.04668083
0.03686869
0.06926708
0.06877459
0.0685 1946
0.07645507
0.07511494
0.08204132
0.02442676
0.06 13781 1
0.10046144
0.05374012
0.05497676
0.05637474
0.09100669
0.05750913
0.08129251
0.05598621
0.07657769
0.03901038
0.06958174
0.04907392
j
The SAS System
5
12:16 Monday, April 29, 1996
Level of Level of
-------- ---- FOOD ---- ------ OPPRANK DAYOFWK N Mean
SD
4
4
4
4
4
4
Monday
Saturday
Sunday
Thursday
Tuesday
Wednesda
3
3
2
2
4
4
0.72200000
0.72366667
0.75250000
0.68650000
0.71400000
0.73750000
0.12558662
0.04856267
0.02050610
0.03464823
0.10163989
0.08868859
ANOVA PRINTOUTS
(WITH "MEANS") FOR
PER-CAPITA
BEER SALES
The SAS System
12:22 Monday, April 29, 1996
Class Levels Values
TV
3 HKX
OPPRANK 4 1234
PROMOT 2 01
TIME
6 1:00 2:05 6:35 7:05 7:35 8:05
WEATHER 3 012
POSITION 8 01234567
15 1234567-1-2-3-4-5-81314
STREAK
The SAS System
2
12:22 Monday, April 29, 1996
Dependent Variable: BEER
Sum of
Source
DF
Squares
Model
128
Error
56
Corrected Total
Mean
2.55494182 0.01996048 99999.99 0.0001
0.00000000 0.00000000
184
2.55494182
R-Square
C.V.
1.000000
0
Root MSE
0
BEER Mean
0.5207135
DF
Source
Anova SS
Mean Square F Value
Pr> F
TV
0.00799832 0.00399916 99999.99 0.0001
2
0.01782275 0.00594092 99999.99 0.0001
3
OPPRANK
0.43118880 0.43118880 99999.99 0.0001
1
PROMOT
0.05799378 99999.99 0.0001
0.28996891
5
TIME
0.06622234 0.03311117 99999.99 0.0001
WEATHER
2
0.13741093 99999.99 0.0001
0.82446556
DAYOFWK
6
7
0.18056583 0.02579512 99999.99 0.0001
POSITION
0.00957769 99999.99 0.0001
14
0.13408771
STREAK
0.03510690 0.005851 15 99999.99 0.0001
6
TV*OPPRANK
TV*PROMOT
0.01319550 0.00659775 99999.99 0.0001
2
TV*WEATHER
4
0.01427260 0.00356815 99999.99 0.0001
TV*DAYOFWK
0.12486838 0.01135167 99999.99 0.0001
11
OPPRANK*PROMOT
0.023 13489 0.00771163 99999.99 0.0001
3
OPPRANK*DAYOFWK 0.16524190 0.00918011 99999.99 0.0001
18
OPPRANK*WEATHER
0.10849966 0.01808328 99999.99 0.0001
6
OPPR.ANK*POSITION
0.16659311
0.01189951 99999.99 0.0001
14
OPPRANK*STREAK
24
0.14446801
0.00601950 99999.99 0.0001
3
The SAS System
12:22 Monday, April 29, 1996
.------BEER -----------Level of Level of
TV DAYOFWK N Mean
SD
H
H
H
H
H
H
H
K
K
K
K
K
K
X
X
X
X
X
X
X
I
Friday 17 0.49723529
Monday 13 0.47076923
Saturday 14 0.49171429
Sunday 21 0.43371429
Thursday 13 0.54307692
Tuesday 16 0.56556250
Wednesda 21 0.60690476
Friday 4 0.54700000
1 0.5 1200000
Monday
Saturday 9 0.42411111
Sunday
2 0.54600000
Thursday 1 0.69300000
Tuesday 5 0.61680000
Friday
9 0.49111111
Monday 3 0.40966667
Saturday 10 0.48110000
Sunday 6 0.40666667
Thursday 1 0.58200000
Tuesday 9 0.63066667
Wednesda 10 0.63690000
0.07794592
0.06719766
0.08404800
0.07790965
0.11741980
0.11980594
0.14103152
0.08 137567
0.06653278
0.04384062
0.08745685
0.09886031
0.11944176
0.09484660
0.03047403
0.11051357
0.09225984
Level of Level of
TV
OPPRANK
H
H
H
H
K
K
K
K
X
X
X
X
1
2
3
4
1
2
3
4
1
2
3
4
0
1
---------BEERMean
28 0.52353571
34 0.52502941
37 0.50827027
16 0.50643750
7 0.53914286
4 0.48075000
8 0.51750000
3 0.5 1633333
18 0.52283333
14 0.56292857
13 0.49923077
3 0.58166667
Level of Level of
PROMOT
TV
H
H
N
0.12918562
0.11073925
0.11640176
0.11473911
0.11672536
0.09027135
0.13615852
0.05862025
0.12464691
0.12893616
0.13542043
0.07184242
-------------BEER-----------SD
N
Mean
0.55983929
0.47572881
56
59
SD
0.12792111
0.08761747
4
The SAS System
12:22 Monday, April 29, 1996
Level of Level of
TV
PROMOT
K
K
X
X
0
1
0
1
12
10
28
20
-------------BEER-----------N
Mean
SD
0.55641667
0.47090000
0.58653571
0.45520000
- - -
Level of Level of
PROMOT
N
OPPRANK
1
1
2
2
3
3
4
4
0
1
0
1
0
1
0
1
30
23
27
25
28
30
11
11
0.57183333
0.46473913
0.59077778
0.468 16000
0.55050000
0.46740000
0.53918182
0.49690909
0.10077198
0.10537388
0.11944702
0.09188987
BEER -----------Mean
SD
0.12106399
0.10082849
0.101 19035
0.09340890
0.13734075
0.08906162
0.13386099
0.06321622
-BEER-Level of Level of
OPPRANK DAYOFWK N Mean
SD
0.07732636
Friday
6 0.49316667
0.04966387
Monday 5 0.45400000
0.09564284
Saturday 8 0.44712500
1
0.06098975
Sunday
9 0.41433333
1
0.09620248
Thursday 4 0.62475000
1
0.09879614
Tuesday 10 0.59030000
1
0.12645035
Wednesda 11 0.62790909
I
0.06860596
Friday
9 0.53955556
2
0.09097390
Monday 4 0.40425000
2
0.07952518
Saturday 11 0.50836364
2
0.06 190878
Sunday
8 0.40987500
2
0.12657211
Thursday 2 0.60850000
2
0.10784222
Tuesday 9 0.59177778
2
0.09175708
Wednesda 9 0.64088889
2
0.09623390
Friday 11 0.48381818
3
0.08521561
Monday 5 0.50920000
3
0.08361133
Saturday 11 0.45363636
3
0.08366733
Sunday 10 0.46400000
3
0.12592590
Thursday 7 0.50000000
3
0.16105160
Tuesday 7 0.63257143
3
0.15120343
Wednesda 7 0.57285714
3
0.09325949
4
Friday 4 0.48100000
5
The SAS System
12:22 Monday, April 29, 1996
1
------------- BEER -------Level of Level of
OPPRANK DAYOFWK N Mean
I1
•
1
I
4
4
4
4
4
4
Monday
Saturday
Sunday
Thursday
Tuesday
Wednesda
3
3
2
2
4
4
0.47600000
0.45100000
0.49600000
0.55950000
0.53800000
0.60725000
SD
0.05 150728
0.08187185
0.11455130
0.04171930
0.06215572
0.17852427
ANOVA PRINTOUTS'
(WITH "MEANS") FOR
PER-CAPITA
SOUVENIR SALES
I
The SAS System
12:24 Monday, April 29, 1996
Class Levels Values
TV
3 HKX
OPPRANK 4 1234
PROMOT 2 01
TIME
6 1:00 2:05 6:35 7:05 7:35 8:05
WEATHER 3 012
POSITION 8 01234567
STREAK
15 1234567-1-2-3-4-5-81314
2
The SAS System
12:24 Monday, April 29, 1996
•
Dependent Variable: NOV
Sum of
Squares
DF
Source
Error
0.00000000 0.00000000
56
184
Corrected Total
Source
0.64710306 0.00505549 99999.99 0.0001
128
Model
Mean
0.64710306
R-Square
C.V.
1.000000
0
DF
Root MSE
0
NOV Mean
0.201 1459
0.00905096 0.00452548 99999.99 0.0001
TV
2
0.02326348 0.00775449 99999.99 0.0001
OPPRANK
3
0.00250320 0.00250320 99999.99 0.0001
1
PROMOT
0.07941625 0.01588325 99999.99 0.0001
5
TIME
0.03316932 0.01658466 99999.99 0.0001
2
WEATHER
0.13915133 0.02319189 99999.99 0.0001
DAYOFWK
6
0.04544766 0.00649252 99999.99 0.0001
7
POSITION
0.04262941 0.00304496 99999.99 0.0001
STREAK
14
TV*OPPRANK
0.01592358 0.00265393 99999.99 0.0001
6
TV*PROMOT
0.00877430 0.00438715 99999.99 0.0001
2
4 0.02986866 0.007467 16 99999.99 0.0001
TV*WEATHER
TV*DAYOF\7JK
0.02776964 0.00252451 99999.99 0.0001
11
OPPRANK*PROMOT
0.00448810 0.00149603 99999.99 0.0001
3
OPPRANK*DAYOFWK
18 0.03123983 0.00173555 99999.99 0.0001
OPPRANK* WEATHER
6 0.04603930 0.00767322 99999.99 0.0001
OPPRANK*POSITION
14 0.09236970 0.00659784 99999.99 0.0001
24 0.08038931 0.00334955 99999.99 0.0001
OPPRANK*STREAK
3
The SAS System
12:24 Monday, April 29, 1996
-------------NOV------------Level of Level of
Mean
SD
TV
DAYOFWK N
H
H
H
H
H
H
H
K
K
K
K
K
K
X
X
X
X
X
X
X
Friday 17 0.21088235
Monday 13 0.20815385
Saturday 14 0.22285714
Sunday 21 0.21861905
Thursday 13 0.17607692
Tuesday 16 0.16625000
Wednesda 21 0.17357143
Friday 4 0.25675000
Monday
1 0.12100000
Saturday 9 0.25266667
Sunday
2 0.19650000
Thursday 1 0.17500000
Tuesday 5 0.15920000
Friday 9 0.22266667
3 0.20633333
Monday
Saturday 10 0.22410000
Sunday 6 0.27233333
Thursday 1 0.19500000
Tuesday 9 0.16888889
Wednesda 10 0.16170000
0.05008353
0.04930153
0.05064789
0.07281859
0.05882667
0.05414733
0.04232325
0.02677530
0.05023694
0.00353553
0.04921077
0.05074938
0.04650090
0.05993413
0.05670509
0.03708586
0.05241088
-------------NOV------------Level of Level of
SD
Mean
TV
OPPRANK N
H
H
H
H
K
K
K
K
X
X
X
X
1
2
3
4
1
2
3
4
1
2
3
4
28 0.18510714
34 0.18676471
37 0.21048649
16 0.20468750
7 0.19800000
4 0.22875000
8 0.22937500
3 0.21666667
18 0.21605556
14 0.17857143
13 0.22446154
3 0.17433333
0.05149134
0.05178806
0.06868957
0.05247186
0.06208865
0.022721 14
0.06215404
0.10561408
0.07346425
0.04347716
0.05191598
0.04960175
-------------NOV-------Level of Level of
SD
TV PROMOT N Mean
H
H
I
0
1
56 0.19739286
59 0.19562712
0.05300281
0.06322044
4
The SAS System
12:24 Monday, April 29, 1996
I
---- -.. ----- -.-NOV ---------Level of Level of
SD
TV PROMOT N Mean
K
K
X
X
0
1
0
1
12
10
28
20
0.20958333
0.22710000
0.19289286
0.22 145000
0.06108036
0.06290637
0.05137397
0.06978650
---- - ----- NOV.------ -----Level of Level of
SD
Mean
OPPRANK PROMOT N
1
1
2
2
3
3
4
4
0
1
0
1
0
1
0
1
30
23
27
25
28
30
11
11
0.18966667
0.20730435
0.19014815
0.18524000
0.21578571
0.21663333
0.19127273
0.21309091
0.05008774
0.07390377
0.05395276
0.04404948
0.05440681
0.07258597
0.05263856
0.06423310
-------------NOV ------------Level of Level of
Mean
SD
OPPRANK DAYOFWK N
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
Friday 6 0.22750000
Monday 5 0.22760000
Saturday 8 0.21450000
Sunday 9 0.23877778
Thursday 4 0.14275000
Tuesday 10 0.15950000
Wednesda 11 0.17490909
Friday 9 0.20988889
Monday 4 0.20500000
Saturday 11 0.22063636
Sunday
8 0.19812500
Thursday 2 0.17850000
Tuesday 9 0.15066667
Wednesda 9 0.14788889
Friday 11 0.22654545
Monday 5 0.18580000
Saturday 11 0.24372727
Sunday 10 0.25 160000
Thursday 7 0.19671429
Tuesday 7 0.18271429
Wednesda 7 0.18100000
Friday 4 0.21750000
0.06308962
0.05766 108
0.07176350
0.07053151
0.03278592
0.03873342
0.03401310
0.03443996
0.05055030
0.03590062
0.05139049
0.06717514
0.02656596
0.04830746
0.05486231
0.03358124
0.05080372
0.08259970
0.06629911
0.06686732
0.04445222
0.05330729
1
/
I
The SAS System
5
12:24 Monday, April 29, 1996
--- --------- NOV--- --------Level of Level of
SD
Mean
OPPRANK DAYOFWK N
II
-
4
4
4
4
4
4
Monday
Saturday
Sunday
Thursday
Tuesday
Wednesda
3
3
2
2
4
4
0.18633333
0.27033333
0.18400000
0.17700000
0.18650000
0.18500000
0.06987370
0.05901130
0.02121320
0.01838478
0.06538348
0.06582299
I
i
i
i
ANOVA PRINTOUTS
(WITH "MEANS") FOR
PER-CAPITA
PROGRAM SALES
The SAS System
12:21 Monday, April 29, 1996
Class Levels Values
TV
3 HKX
OPPRANK 4 1234
PROMOT 2 01
TIME
6 1:002:056:357:057:35 8:05
WEATHER 3 012
POSITION 8 01234567
STREAK
15 1234567-1-2-3-4-5-81314
2
The SAS System
12:21 Monday, April 29, 1996
Dependent Variable: PROG
Sum of
DF
Squares
Source
Model
Source
2.05 0.0015
0.00276530 0.00004938
56
184
Corrected Total
0.00010111
0.01294233
128
Error
Mean
Square F Value Pr > F
0.01570762
R-Square
C.V.
0.823952
18.92308
DF
Root MSE
0.0070271
PROG Mean
0.0371351
0.00035371
0.00017686 3.58 0.0344
TV
2
0.00011513
0.00003838 0.78 0.5117
OPPRANK
3
0.00001575
0.00001575
0.32 0.5745
1
PROMOT
0.00019200
3.89
0.0043
5
0.00096001
TIME
0.00095203
0.00047601
9.64
0.0003
WEATHER
2
0.00172202
0.00028700
5.81
0.0001
DAYOFWK
6
0.00037426
0.00005347
1.08
0.3867
POSITION
7
0.00058029 0.00004145 0.84 0.6249
14
STREAK
TV*OPPRANK
1.25 0.2965
0.00036966 0.00006161
6
TV*PROMOT
2 0.00009713 0.00004856 0.98 0.3804
TV*WEATHER
4 0.00025501 0.00006375 1.29 0.2846
TV*DAYOFWK 1.42 0.1882
0.00077338 0.00007031
11
OPPRANK*PROMOT 3 0.00001744 0.00000581 0.12 0.9494
OPPRANK*DAYOFWK 18 0.00199654 0.00011092 2.25 0.0110
OPPRANK*WEATHER
6 0.00061112 0.00010185 2.06 0.0723
OPPRANK*POSITION
14
0.00156640 0.00011189 2.27 0.0157
OPPRANK*STREAK
24 0.00218244 0.00009093 1.84 0.0311
3
The SAS System
12:21 Monday, April 29, 1996
- ------- --PROG-------Level of Level of
SD
TV
DAYOFWK N
Mean
H
H
H
H
H
H
H
K
K
K
K
K
K
X
X
X
X
X
X
X
Friday 17 0.03982353
Monday 13 0.03869231
Saturday 14 0.04478571
Sunday 21 0.04052381
Thursday 13 0.03307692
Tuesday 16 0.03300000
Wednesda 21 0.03471429
Friday 4 0.04525000
Monday
1 0.04800000
Saturday 9 0.03688889
Sunday 2 0.03450000
Thursday 1 0.03600000
Tuesday 5 0.03720000
Friday 9 0.03666667
Monday
3 0.03966667
Saturday 10 0.03590000
Sunday
6 0.03800000
Thursday 1 0.02700000
Tuesday 9 0.03177778
Wednesda 10 0.03240000
0.01051924
0.00830045
0.00892859
0.01 102551
0.00653786
0.00675278
0.00904512
0.00427200
0.00592546
0.00070711
0.01013410
0.0088 1760
0.00472582
0.00869802
0.00576194
0.01086022
0.00916758
----- -------- PROG --------Level of Level of
Mean
SD
OPPRANK N
TV
H
H
H
H
K
K
K
K
X
X
X
X
1
2
3
4
1
2
3
4
1
2
3
4
28
34
37
16
7
4
8
3
18
14
13
3
Level of Level of
PROMOT
TV
H
H
0
1
56
59
0.03782143
0.03623529
0.03808108
0.04031250
0.03942857
0.03925000
0.03775000
0.03900000
0.03544444
0.03435714
0.03661538
0.02600000
0.00944792
0.01040122
0.00876983
0.01076859
0.01003090
0.00639661
0.00570088
0.0078 1025
0.00819772
0.00811084
0.00921537
0.0 1200000
-------------PROG -----------SD
N
Mean
0.03753571
0.03801695
0.00979975
0.00963738
4
The SAS System
12:21 Monday, April 29, 1996
Level of Level of
TV
PROMOT
K
K
0
1
X
x
1
12
10
28
20
-------------PROG -----------N
SD
Mean
0.04025000
0.03690000
0.03403571
0.03600000
0.00762919
0.00655659
0.00904099
0.00839 173
-------------PROG-----------of Level of
Mean
SD
OPPRANK PROMOT N
Level
0.00855301
30 0.0.3713333
1
0
0.00985167
23 0.03734783
0.00977103
27 0.03562963
2I10
0.00944599
25 0.03632000
2
1
0.00936587
28 0.03764286
3
0
0.00758257
1
30 0.03776667
3
0.01217748
11 0.03709091
4
0
0.01077117
11 0.03927273
4
1
------------- PROG -----------Level of Level of
Mean
SD
OPPRANK DAYOFWK N
Friday
6 0.03933333
1
Monday 5 0.04060000
1
Saturday 8 0.03825000
1
1
Sunday
9 0.04066667
Thursday 4 0.03250000
1
iTuesday 10 0.03340000
Wednesda 11 0.03618182
2
Friday 9 0.03714114
Monday 4 0.03475000
2
Saturday ii 0.04218182
Sunday
8 0.03950000
2
Thursday 2 0.03400000
2
Tuesday 9 0.03311111
2
Wednesda 9 0.02755556
2
Friday ii 0.03663636
3
Monday 5 0.03920000
3
Saturday 11 0.03890909
3
Sunday 10 0.04120000
Thursday
7 0.03300000
3
Tuesday 7 0.0357 1429
3
Wednesda 7 0.03814286
3
4
Friday 4 0.05300000
0.01051982
0.00829458
0.01170775
0.00653835
0.0059 1608
0.01089546
0.00712486
0.00572519
0.00505800
0.00705433
0.01328802
0.00282843
0.00795997
0.00983757
0.00910245
0.00983362
0.00985347
0.00832399
0.00848528
0.00349830
0.00790419
0.00711805
The SAS System
5
12:21 Monday, April 29, 1996
----- -------- PROG-----------Level of Level of
Mean
SD
OPPRANK DAYOFWK N
4
4
4
4
4
4
Monday
Saturday
Sunday
Thursday
Tuesday
Wednesda
3
3
2
2
4
4
0.04400000
0.04000000
0.02700000
0.03200000
0.02950000
0.03500000
0.00529150
0.00529150
0.01131371
0.00282843
0.01138713
0.00860233
I
i
TECHNICAL APPENDIX:
PRINTOUTS AND BASIC
STATISTICS
I
I
I
Fl
Fl
I
I
I . ......
I
04-28-1996
wmms
A:\WINKS2.DBF
Descriptive Statistics
Variable Name is FOOD-PC
N
Mean
Median
Minimum
Maximum
Sum
=
=
=
=
=
=
Percentiles:
0.0%
0.5%
2.5%
10.0%
25.0%
50.0%
75.0%
90.0%
97.5%
99.5%
100.0%
Missing or Deleted
St. Dev (n-i)
St. Dev (n)
S.E.M.
Variance
Coef. Var.
185
0.73855
0.739
0.554
0.961
136.631
=
=
=
=
=
=
=
=
=
=
=
0.554
0.554
0.5965
0.648
0.6785
0.739
0.787
0.8408
0.8768
0.961
0.961
= 0
= 0.07499
= 0.07478
= 0.00551
= 0.00562
= 0.10153
Tukey Five Number Summary:
Minimum = 0.554
= 0.6785
25th
= 0.739
Median
= 0.787
75th
Maximum = 0.961
Minimum
Quartile
Median
Quartile
Test for normality results:
D = .064
p <= 0.10
Maximum
Five number summary consists of the 0, 25, 50, 75 and 100th percentiles.
Confidence Intervals about the mean:
80
90
95
98
99
%
%
%
%
%
C.I.
C.I.
C.I.
C.I.
C.I.
based
based
based
based
based
on
on
on
on
on
a
a
a
a
a
t
t
t
t
t
critical
critical
critical
critical
critical
value
value
value
value
value
of
of
of
of
of
1.2816 is (0.73148, 0.74561)
1.6449 is (0.72948, 0.74761)
1.96 is (0.72774, 0.74935)
2.3263 is (0.72572, 0.75137)
2.5758 is (0.72434, 0.75275)
I
I
04-28-1996
WINKS
A:\WINKS2.DBF
Descriptive Statistics Variable Name is BEER-PC
N
Mean
Median
Minimum
Maximum
Sum
=
=
=
=
=
=
Percentiles:
0.0%
0.5%
2.5%
10.0%
25.0%
50.0%
75.0%
90.0%
97.5%
99.5%
100.0%
Missing or Deleted = 0
St. Dev (n-i) = 0.11784
St. Dev (n) = 0.11752
S.E.M. = 0.00866
Variance = 0.01389
Coef. Var. = 0.2263
185
0.52071
0.51
0.274
0.861
96.33199
=
=
=
=
=
=
=
=
=
=
=
0.274
0.274
0.3382
0.3842
0.433
0.51
0.60
0.693
0.8097
0.861
0.861
Minimum = 0.274
= 0.433
25th
= 0.51
Median
75th
= 0.60
Maximum = 0.861
Minimum
Quartile
Median
Quartile
p <= 0.01
D = .096
Maximum
80
90
95
98
99
%
%
%
%
%
C.I.
C.I.
C.I.
C.I.
C.I.
based
based
based
based
based
on
on
on
on
on
a
a
a
a
a
t
t
t
t
t
critical
critical
critical
critical
critical
value
value
value
value
value
of
of
of
of
of
1.2816 is (0.50961, 0.53182)
1.6449 is (0.50646, 0.53496)
1.96 is (0.50373, 0.53769)
2.3263 is (0.50056, 0.54087)
2.5758 is (0.4984, 0.54303)
04-28-1996
wis
A:\WINKS2.DBF
Variable Name is NW-PC
Missing or Deleted = 0
St. Dev (n-i) = 0.0593
St. Dev (n) = 0.05914
S.E.M. = 0.00436
Variance = 0.00352
Coef. Var. = 0.29483
= 185
N
= 0.20115
Mean
= 0.194
Median
= 0.087
Minimum
Maximum = 0.457
= 37.21201
Sum
Percentiles:
0.0%
0.5%
2.5%
10.0%
25.0%
50.0%
75.0%
90.0%
97.5%
99.5%
100.0%
=
=
=
=
=
=
=
=
=
=
=
0.087
0.087
0.10455
0.1286
0.1575
0.194
0.237
0.2858
0.3165
0.457
0.457
Minimum
Quartile
Median
Quartile
Maximum
Minimum = 0.087
= 0.1575
25th
Median
= 0.194
= 0.237
75th
Maximum = 0.457
D = .067
p <= 0.05
80
90
95
98
99
%
%
%
%
%
C.I.
C.I.
C.I.
C.I.
C.I.
based
based
based
based
based
on
on
on
on
on
a
a
a
a
a
t
t
t
t
t
critical value of 1.2816 is (0.19556, 0.20673)
04-28-1996
WINKS
I
A:\WINKS2.DBF
Variable Name is PROQ.PC
I
I
I
I
I
N
Mean
Median
Minimum
Maximum
Sum
=
=
=
=
=
=
Percentiles:
0.0%
0.5%
2.5%
10.0%
25.0%
50.0%
75.0%
90.0%
97.5%
99.5%
100.0%
Missing or Deleted
St. Dev (n-i)
St. Dev (n)
S.E.M.
Variance
Coef. Var.
185
0.03714
0.036
0.014
0.065
6.87
=
=
=
= 0.014
= 0.014
0.019
= 0.026
= 0.03
=-0.036
0.043
= 0.05
= 0.057
= 0.065
0.065
= 0
= 0.00924
= 0.00921
= 0.00068
= 0.00009
= 0.2488
Minimum = 0.014
= 0.03
25th
Median
= 0.036
= 0.043
75th
Maximum = 0.065
Minimum
Quartile
Median
Quartile
D = .05
p > 0.20
Maximum
Confidenc e Intervals a: Dout the
80
90
95
98
99
% C.I.
% C.I.
% C.I.
% C.I.
% C.I.
based
based
based
based
based
on a t
on a t
on a t
on a t
on a t
critical
critical
critical
critical
critical
nean:
value
value
value
value
value
of 1.2816
of 1.6449
of 1.96 i
of 2.3263
of 2.5758
is (0.03626, 0.03801) is (0.03602, 0.03825)
3.0358, 0.03847)
is (0.03555, 0.03872) is (0.03539, 0.03888)
04-28-1996
WINKS
A:\WINKS2.DBF
Descriptive Statistics, Summary
Number of records= 185
Statistics from database A:\WINKS2.DBF TV = H
N
MEAN
STD
SEN
MIN
MAX
SUM
115
115
115
115
115
115
.73997
.51669
.19649
.03778
26123.9
22761.7
.07604
.11655
.05822
.00968
8291.0
7906.3
.00709
.01087
.00543
.00090
773.1
737.3
.5840
.3280
.0870
.0170
10969
7221
.9610
.8610
.4570
.0650
42696
38759
85.0960
59.4190
22.5960
4.3450
3004244
2617598
MEAN
STD
SEN
MIN
MAX
SUM
.72823
.51755
.21755
.03873
29779.8
26976.1
.08597
.10944
.06107
.00720
8885.3
8254.2
.01833
.02333
.01302
.00153
1894.4
1759.8
.5650
.3330
.1000
.0230
12000
10623
.9160
.7020
.3300
.0500
40505
38069
16.0210
11.3860
4.7860
.8520
655156
593474
MEAN
STD
SEN
MIN
MAX
SUM
.73987
.53181
.20479
.03485
24207.7
20650.1
.06805
.12606
.06072
.00874
7786.7
7914.8
.00982
.018.20
.00876
.00126
1123.9
1142.4
.5540
.2740
.1070
.0140
10467
6542
.8660
.8340
.3730
.0540
38696
35477
35.5140
25.5270
9.8300
1.6730
1161968
991207
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
TV = K
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
N
22
22
22
22
22
22
TV = X
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
N
48
48
48
48
48
48
04-28-1996
WINKS
A:\WINKS2.DBF
Statistics from database A:\WINKS2.DBF WEATH=0
N
FIELD
12
12
12
12
12
12
FOOD-PC
BEER PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROC_PC
ATTEND
TURNST
WEATH = 1
N
47
47
47
47
47
47
WEATH = 2
N
126
126
126
126
126
126
MEAN
STD
SEM
MIN
MAX
SUM
.70117
.44892
.23958
.03008
23322.3
17897.4
.06400
.10496
.07917
.01009
9504.4
8815.3
.01848
.03030
.02285
.00291
2743.7
2544.8
.6390
.3320
.1460
.0140
12336
7801
.8330
.6440
.3730
.0480
40718
36903
8.4140
5.3870
2.8750
.3610
279868
214769
MEAN
STD
SEM
MIN
MAX
SUN
.73930
.52677
.21332
.03983
27156.6
23671.9
.07164
.13402
.06951
.00846
9025.4
8945.0
.01045
.01955
.01014
.00123
1316.5
1304.8
.6000
.2740
.0950
.0230
11505
8381
.9020
.8510
.4570
.0610
42696
38069
34.7470
24.7580
10.0260
1.8720
1276361
1112580
MEAN
STD
SEM
MIN
MAX
SUN
.74183
.52529
.19294
.03680
25913.8
22816.9
.07670
.11104
.05081
.00910
7961.8
7614.3
.00683
.00989
.00453
.00081
709.3
678.3
.5540
.3330
.0870
.0190
10467
6542
.9610
.8610
.3230
.0650
42273
38759
93.4700
66.1870
24.3110
4.6370
3265139
2874930
04-28-1996
WINKS
A:\WINKS2.DBF
Statistics from database A:\WINKS2.DBF FIELD
FOOD-PC
BEER-PC
NOV.-PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
PROMOT = 0
N
96
96
96
96
96
96
PROMOT = 1
N
89
89
89
89
89
89
MEAN
STD
SEN
MIN
MAX
SUM
.73322
.56720
.19760
.03685
22504.5
19689.2
.07321
.12191
.05323
.00947
7862.9
7875.2
.00747
.01244
.00543
.00097
802.5
803.8
.5540
.3320
.1000
.0140
10467
6542
.9610
.8610
.3230
.0590
41772
37628
70.3890
54.4510
18.9700
3.5380
2160434
1890160
MEAN
STD
SEN
MIN
MAX
SUM
.07686
.08994
.06532
.00903
7083.7
7060.4
.00815
.00953
.00692
.00096
750.9
748.4
.5840
.2740
.0870
.0190
16275
12401
.9020
.7590
.4570
.0650
42696
38759
.74429
.47057
.20497
.03744
29898.1
25978.9
66.2420
41.8810
18.2420
3.3320
2660934
2312119
04-28-1996
WINKS
A:\WINKS2.DBF
Descriptive Statistics, Summary Number of records= 185
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV.-PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD_PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TUBNST
POSIT = 0
N
1
1
1
1
1
1
POSIT=1
N
4
4
4
4
4
4
POSIT=2
N
18
18
18
18
18
18
POSIT = 3
N
77
77
77
77
77
77
POSIT = 4
N
45
45
45
45
45
45
MEAN
STD
SEN
MIN
MAX
SUN
.72200
.78900
.17500
.04700
15293.0
13934.0
.00000
.00000
.00000
.00000
.0
.0
.00000
.00000
.00000
.00000
.0
.0
.7220
.7890
.1750
.0470
15293
13934
.7220
.7890
.1750
.0470
15293
13934
.7220
.7890
.1750
.0470
15293
13934
MEAN
STD
SEN
MIN
MAX
SUN
.74450
.55400
.17775
.03300
29614.3
26141.3
.04238
.14952
.06028
.00548
5386.9
7607.2
.02119
.07476
.03014
.00274
2693.5
3803.6
.6910
.3700
.1150
.0270
24251
15937
.7850
.7020
.2540
.0400
36386
33766
2.9780
2.2160
.7110
.1320
118457
104565
MEAN
STD
SEN
MIN
MAX
SUN
.75233
.54706
.19922
.03928
29895.3
26453.1
.07040
.11124
.04336
.00620
8922.7
8438.4
.01659
.02622
.01022
.00146
2103.1
1989.0
.5540
.3900
.1260
.0310
12909
9620
.8700
.8340
.2880
.0500
42273
35763
13.5420
9.8470
3.5860
.7070
538116
476155
MEAN
STD
SEN
MIN
MAX
SUM
.74299
.52878
.20703
.03699
26209.6
22980.5
.07983
.12132
.06099
.00939
8762.7
8420.3
.00910
.01383
.00695
.00107
998.6
959.6
.5650
.3280
.0970
.0170
10467
6542
.9160
.8610
.4570
.0590
42696
38759
57.2100
40.7160
15.9410
2.8480
2018142
1769498
MEAN
STD
SEN
MIN
MAX
SUN
.76033
.48940
.21438
.03782
26203.5
22665.7
.07335
.11590
.06285
.00980
7739.8
7815.9
.01093
.01728
.00937
.00146
1153.8
1165.1
.6200
.2740
.0870
.0210
13294
9025
.9610
.8090
.3300
.0610
41286
37308
34.2150
22.0230
9.6470
1.7020
1179159
1019956
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
FIELD
-
POSIT =5
N
FOOD-PC'
BEER PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
13
13
13
13
13
13
POSIT = 6
N
18
18
18
18
18
18
POSIT = 7
N
9
9
9
9
9
9
MEAN
STD
SEN
MIN
MAX
SUM
.70846
.56331
.18846
.03562
21578.8
19096.5
.06011
.12704
.05590
.01247
8782.9
9038.4
.01667
.03524
.01550
.00346
2435.9
2506.8
.6290
.3450
.1100
.0140
11505
7801
.7830
.7190
.3230
.0650
40505
38069
9.2100
7.3230
2.4500
.4630
280524
248255
MEAN
STD
SEN
MIN
MAX
SUN
.71561
.48867
.18789
.03678
26631.4
22706.0
.05667
.09750
.05791
.00891
6914.9
6334.4
.01336
.02298
.01365
.00210
1629.9
1493.0
.6260
.3600
.1280
.0190
15932
12340
.8330
.6880
.3730
.0570
41242
37038
12.8810
8.7960
3.3820
.6620
479366
408708
MEAN
STD
SEN
MIN
MAX
SUM
.65256
.51356
.14667
.03433
21367.9
17912.0
.03785
.06324
.03117
.00745
5748.2
5287.3
.01262
.02108
.01039
.00248
1916.1
1762.4
.5900
.3870
.0950
.0260
13619
11004
.7110
.6290
.1900
.0480
30300
25976
5.8730
4.6220
1.3200
.3090
192311
161208
WINKS
A:\WINKS2.DBF
Statistics from database A:\WINKS2.DBF
FIELD
BEER-PC
NOV_PC
FOOD_PC
PROG_PC
ATTEND
OPP_RANK = 1
N
MEAN
STD
SEN
MIN
MAX
SUN
.72455
.52536
.19732
.03723
23936.3
20632.2
.07352
.12388
.06154
.00905
8880.3
8385.8
.01010
.01702
.00845
.00124
1219.8
1151.9
.5540
.3280
.0970
.0170
10467
6542
.8570
.8340
.3730
.0610
42273
37308
38.4010
27.8440
10.4580
1.9730
1268623
1093505
MEAN
STD
SEN
MIN
MAX
SUN
.73223
.53183
.18779
.03596
25130.0
21776.9
.07634
.11469
.04902
.00953
8473.9
8435.1
.01059
.01590
.00680
.00132
1175.1
1169.7
.6130
.2740
.1070
.0170
12273
9025
.9160
.8090
.2900
.0650
41772
38069
38.0760
27.6550
9.7650
1.8700
1306758
1132398
MEAN
STD
SEN
MIN
MAX
SUN
.75640
.50156
.20953
.03700
27603.5
24258.4
.07175
.12176
.05491
.00803
7001.2
6774.7
.00967
.01642
.00740
.00108
944.0
913.5
.6520
.3320
.0870
.0210
14898
11466
.9610
.8610
.3130
.0570
41652
38759
41.6020
27.5860
11.5240
2.0350
1518191
1334213
OPP_RANK = 4
N
MEAN
STD
SEN
MIN
MAX
SUN
.07855
.10321
.07726
.01138
8554.0
8451.4
.01571
.02064
.01545
.00228
1710.8
1690.3
.5900
.3650
.0950
.0140
14507
7801
.9020
.8510
.4570
.0590
42696
37922
18.5520
13.2470
5.4650
.9920
727796
642163
53
53
53
53
53
53
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER_PC
NOV_PC
PROG_PC
TURNST
ATTEND
FIELD
FOOD_PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
OPP_RANK = 2
N
52
52
52
52
52
52
OPP_RANK=3
N
55
55
55
55
55
55
25
25
25
25
25
25
.74208
.52988
.21860
.03968
29111.8
25686.5
I
04-28-1996
WINKS
A:\WINKS2.DBF
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER_PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER_PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER_PC
NOV.-PC
PROG_PC
ATTEND
TURNST
DOW_RANK. = 1
N
17
17
17
17
17
17
MEAN
STD
SEN
MIN
MAX
SUN
.71935
.46241
.20271
.03941
24954.5
21548.3
.07092
.07682
.05037
.00771
6602.7
5913.0
.01720
.01863
.01222
.00187
1601.4
1434.1
.5900
.2740
.1210
.0290
13619
11004
.8400
.6450
.3230
.0520
36430
32422
12.2290
7.8610
3.4460
.6700
424227
366321
MEAN
STD
SEN
MIN
MAX
SUM
.71317
.59363
.16587
.03333
20765.8
17453.6
.06479
.11314
.04733
.00858
6984.2
6280.5
.01183
.02066
.00864
.00157
1275.1
1146.6
.5650
.3320
.0950
.0140
10467
6542
.8440
.8110
.3130
.0500
42273
31898
21.3950
17.8090
4.9760
1.0000
622974
523607
MEAN
STD
SEN
MIN
MAX
SUM
.71797
.61658
.16974
.03397
21461.5
18751.9
.07501
.12656
.04528
.00900
8887.5
8493.7
.01347
.02273
.00813
.00162
1596.2
1525.5
.5540
.3600
.1070
.0170
10969
7221
.8700
.8610
.2680
.0510
41242
37038
22.2570
19.1140
5.2620
1.0530
665305
581308
MEAN
STD
SEM
MIN
MAX
SUM
.72127
.55567
.17727
.03287
25099.6
21675.2
.07950
.11559
.05468
.00631
7284.0
7183.8
.02053
.02985
.01412
.00163
1880.7
1854.9
.5840
.3700
.0870
.0240
11505
8381
.8670
.6980
.2850
.0500
41652
38759
10.8190
8.3350
2.6590
.4930
376494
325128
MEAN
STD
SEN
MIN
MAX
SUN
.77970
.50203
.22053
.03960
28724.7
25869.6
.07398
.08404
.04905
.00957
6895.1
6938.1
.01351
.01534
.00895
.00175
1258.9
1266.7
.6670
.3480
.1420
.0210
15932
12340
.9610
.6880
.3060
.0590
40383
36173
DOW-RANK = 2
N
30
30
30
30
30
30
DOW_RANK = 3
N
31
31
31
31
31
31
DOW_RANK = 4
N
15
15
15
15
15
15
DOW_RANK = 5
N
30
30
30
30
30
30
23.3910
15.0610
6.6160
1.1880
861742
776087
- DOW_RANK = 6
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
FIELD
FOOD-PC
BEER-PC
NOV_PC
PROG_PC
ATTEND
TURNST
MEAN
STD
SEN
MIN
MAX
SUN
.73785
.47006
.23136
.03994
34785.2
30974.4
.06774
.08569
.05347
.00897
4806.0
5019.8
.01179
.01492
.00931
.00156
836.6
873.8
.6330
.3330
.1330
.0220
23632
20445
.8500
.6830
.3300
.0610
42696
38069
24.3490
15.5120
7.6350
1.3180
1147911
1022155
STD
SEN
MIN
MAX
SUM
.07440
.07498
.07014
.00979
6484.7
6857.6
.01382
.01392
.01303
.00182
1204.2
1273.4
.6130
.3280
.1160
.0190
13675
8504
.9020
.6250
.4570
.0650
39895
34170
22.1910
12.6400
6.6180
1.1480
722715
607673
N
FIELD
33
33
33
33
33
33
DOW_RANK=7
N
29
29
29
29
29
29
MEAN
.76521
.43586
.22821
.03959
24921.2
20954.2
DATA FILE
I
WINKS2
V RANK:FOOD-PC 'BEER-PC
H
H
-II
4!
4
0
iWednesday
51
3
ii
41
51
-1
83817:35pm
1!Thursday
51
41
. 11
41
61
-2
3311917:35pm
21 Saturday
31
31
61
61
0
1
2
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201
-9
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I
Page 7
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73!81!
-11 73!82!
I
TEXAS RANGERS
CONCESSION ANALYSIS
Matt Mc Dermott
Senior Design Project
May 2, 1996
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OBJECTIVES
• Analyze per-capita food, beer, souvenir, and
program sales from 1990 through 1992
• Formulate general trends
. Observe any trends that could affect sales,
either positively or negatively
• Discover ways in which the Rangers can
improve net income related to concessions
I
CONSIDERATIONS
I
• The data was reduced by a "confidential"
conversion factor
• Predictions are based on per-capita turnstile
attendance
• Could not acquire data on extra OT wages,
lost sales, disposal costs, or inventory space
• Nolan Ryan games, first/last games of
season removed
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VARIABLES USED
• Television
• Promotion
• Time
• Weather
• Day of Week
• Position
• Win/Loss Streak
• Opponent
• Games over .500
• Per-capita food
demand
• Per-capita beer
demand
• Per-capita souvenir
demand
• Per-capita program
demand
PROBLEMS WITH
UNDERSTOCKING
• Lost sales
• Potential for losing
customers (minimal)
PROBLEMS WITH
OVERSTOCKING
• Purchase of items that
will be thrown away
• Disposal costs
• Extra wages attributed
to excess food
• Potential inventory
carrying costs
1 PREDICTION TECHNIQUES
• Multiple Linear
Regression
• ANOVA & Means
Comparisons
• Regression Trees
//
_
ANOVA
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• Checks for "significant" effects and
interactions
• Runs "means comparisons" tests. This
allows the opportunity to see the averages
for each item compared with one or more
variables
MLR
I
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I
• Looks at each deviation from the overall
average
. Formulates a linear equation based on the
data. This can be used to predict future
events
Returns an "R-squared" value which
informs the reader of the strength of the
equation
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I
BEST TECHNIQUE:
REGRESSION TREES
• Can model categorical and continuous
(numerical) variables
. Hierarchically-based
Presented in decision-making format
Models the data, yet is flexible enough to
reasonably predict the future
M.A.D. & M.S.E.
• FOOD (MLR) = 1.042
• BEER (MLR) =0.134
• NOV (MLR) = 0. 164
• PRO G (MLR) =0.189
• FOOD (REG) = 0.050
=
• BEER (REG) 0.071
• NOV (REG) = 0.098
• PROG (REG) = 0.008
• FOOD (MLR) = 1.437
• BEER (MLR) = 0.023
• NOV (MLR)=0.030
• PROG (MLR) = 0.037
• FOOD (REG) = 0.004
• BEER (REG) = 0.008
• NOV (REG) = 0.018
• PROG (REG) = 0.001
WHAT ANALYSIS SHOWED
• Minor adjustments, or
"fine-tuning", by way
of prediction can
improve net income
from concessions &
programs by 3-4% per
game
• Over 81 regular
season games, this
could result in
tremendous savings
11
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1
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WAYS IN WHICH RANGERS
REDUCE LOST SALES
• Order 1-2% more for
promotion games
• On average, order 5-6%
more food on Fridays and
Sundays
• Order 16% more beer on
non-promotion games
• Order 7-8% more
novelties on weekend
Order 4-5% more
programs on Sundays
NEW WAYS TO CUT COSTS
• Reduce food ordered by 5%
for bad weather & when in a
3+ losing streak
• Reduce beer by 5% on
Sunday & Monday and
promotion games
• Reduce souvenirs by 13% on
a Tuesday with similar
conditions as the Monday
• Reduce programs by 9% for
network-broadcast games
N
,\ \
c-)
Q
Q
I 11/17

121 adultcrowd

Transcription

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