GB304 Final Project Report Final 2

GENERAL BUSINESS 304
The Culver’s Case
Abstract
The major purpose for this business report is to help our clients, Russ and Vicky, choose
the best location for a new Culver’s franchise restaurant in Carbondale, Illinois, basing on
comprehensive statistical analysis
RenaHuang, YutingYang, Yaoyao Chen,
Zichun He, Tina Zhou, & Pack Zhao
[Email address]May, 10th, 2015

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CONTENTS
Executive Summary.......................................................................................................................................ii
Introduction........................................................................................................................................................1
Building Business Model.............................................................................................................................4
Financial Analysis.........................................................................................................................................29
Recommendation.........................................................................................................................................33
Conclusion.........................................................................................................................................................35
Appendix...................................................................................................................................................38/-1-
Figure 1 - Handling Missing Data.................................................................................................................6
Figure 2 - Normal probability plot of the residuals for the gross sales ....................................26
Figure 3 - Plot of residuals against dummy variable 2 of CFSI suitability rating of the
Culver's restaurant...........................................................................................................................................26
Figure 4 - Plot of residuals against dummy variable 1 of CFSI suitability rating of the
Figure 5 - Plot of residuals against the traffic count around the Culver's restaurant ........26
Figure 6 - Plot of residuals against the population within a one-mile radius of the
Figure 7 - Predicted gross sales..................................................................................................................29
Figure 8 - Startup expenses..........................................................................................................................30
Figure 9 - Location Information.................................................................................................................33

EXECUTIVE SUMMARY
SCOPE AND OBJECTIVE
As a student-run consulting firm, we received a request from our clients, Russ
and Vicky, to make a decision of choosing a site location for a Culver's franchise
restaurant by analyzing a set of data from Culver’s restaurants and relative
financial information.
IMPORTANCE OF THE ANALYSIS
Location is one of the key factors of a restaurant’s success, but it is hard to decide
which location is the best by just looking at demographic
characteristics. Therefore we did statistical analysis of the past data and financial
analysis of other relevant information with the intention to provide the most
accurate and reliable recommendations for our clients.
PREDICTION AND RECOMMENDATION
Along with analysis of the sample data, we utilized our financial knowledge and
business acumen to do further comparisons. Based on our business prediction
model, Site C is the most profitable one, but its startup expenses exceed our
clients' budget. Considering their financial ability, we recommend our clients to
choose the second most profitable location, Site A, instead.

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INTRODUCTION
Culver's is one of the various food chains in the Midwest, which provides
franchise options for individuals. Our clients want to seize this business
opportunity, but they have difficulties selecting the best site for the new
franchise restaurant among three potential locations. To help our clients choose
the most appropriate site, we analyzed the sample data retrieved from 89
current Culver’s restaurants. Besides statistical analysis, we also took other
associated costs into account for site recommendations.
CLIENTS’ PROFILES
Name: Russ (age: 64) and Vicky (age: 60)
Goal: open a Culver's restaurant
Location: Carbondale, Illinois
Workforce Preference: Young students
Post-retirement Plan: actively manage an operation for a decade or more
Financial Ability: $1.2 million to $1.5 million
Acceptable minimum annual sales: $1,000,000

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GENERAL COMPANY DESCRIPTION
Culver's Frozen Custard Restaurant is a family business founded in 1984 in Sauk
City, Wisconsin. It is a fast-food restaurant that cooks meal to order individually.
After the first opening’s great success, Culver’s began to franchise restaurants
through Culver Franchising System, Inc. (CFSI). Following is the information we
found useful for our clients to consider.
Mission Statement: Every guest who chooses Culver's leaves happy.
Founding principles: Freshness and quality, hospitality and service to the
community.
Business Hours: 10:00am-10:00pm (with exceptions serving breakfast as well)
Typical food service areas:
 Indoor seating
 Outdoor seating
 Drive-up service
Competitive Advantages:
 A wide variety of entrees
 ButterBurgers® that are made from fresh ground chuck and serve on a
buttered toasted bun

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 Three daily flavors of custard: vanilla, chocolate, and the "flavor of the
day"
Qualities Culver’s are looking for of their franchise partners:
 Leadership skills to take a team of people and operate a Culver's
according to the high standards.
 Energy and enthusiasm
 Willing to work hard
 Love people and believe that having a great heart is also good business
STATISTICAL METHODS
Our statistical methods have two parts: 1) build the business prediction model;
and 2) analyze the profitability of each site. First we chose indicating variables,
and then filled out the missing data. Next we ran regressions to find the
relationship between gross sales and those relevant variables, and ultimately
picked out the best model. Then we applied this model to predicting gross
revenues of Site A, Site B and Site C. Furthermore, we took startup costs and
operating costs into consideration to find the most appropriate location for the
new Culver's restaurant. More details are in the “Building Business Model” section
and the “Financial Analysis” section.

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BUILDING BUSINESS MODEL
CHOOSINGINDICATING VARIABLES
We have collected the historical data of 89 Culver's Frozen Custard
restaurants from the company, which might be useful for us to build the best
model to predict future sales in the three potential locations. These independent
variables include:
 Operation years (AGE)
 Cost of food (FOOD)
 Cost of paper (PAPER)
 Labor expenses (LABOR)
 Other operating expenses (OTHER OP)
 Gross revenue from sales (GSALES)
 Traffic count (TRAFFIC)
 Population within a one-mile radius (POP1M)
 Population within a five-miles radius (POP5M)
 Per capita income within a one-mile radius (PERCAP1)
 Per capita income within a five-mile radius (PERCAP5)
 Average number of autos per household within a one-mile radius
(AUTO1)
 Average number of autos per household within a five-mile radius
(AUTO5)

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 Percentage of adults married within a one-mile radius (MARRIED1)
 Percentage of adults married within a five-mile radius (MARRIED5)
 CFSI suitability rating (SUIT)
However, not all of these variables are relevant to predict gross sales. We
decided to discard variables PAPER, LABOR, FOOD, AGE and OTHER OP first
because they were irrelevant to the location of a new restaurant.
Therefore, the variables that we decided to keep to further analyze are:
TRAFFIC, POP1M, POP5M, PERCAP1, PERCAP5, AUTO1, AUTO5, MARRIED1,
MARRIED5, and SUIT.
HANDLINGMISSING DATA
The raw data we have contained several missing data, so we decided to handle
missing data first. For Store 11 and 71, the data for POP1M, POP5M, PERCAP1,
PERCAP5, AUTO5, AUTO1, MARRIED1, MARRIED5, and SUIT were all missing.
Considering too many data were missing for these two stores and the whole data
set was relatively big, we decided to eliminate the data of these two stores as a
whole.
Then we moved on to deal with the missing data of TRAFFIC for Store 19, 23, 39,
42, 65, 75, 82, and 83. According to the information we had, this kind of missing
data was called “missing at random”. This means the cases with incomplete data
were different from those with complete data, but the pattern of the missing data

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is traceable and predictable from the known data. Therefore, we decided to deal
with these missing data using hot deck imputation method.
Hot deck imputation is a method to identify the most similar case to the case
with a missing value and substitute the most similar case's Y value for the
missing case's Y value. Based on our intuition, we figured traffic count would be
related to gross sales, population and the number of automobiles, so we sorted
the data from smallest to largest based on TRAFFIC, POP1M and AUTO5. Then
we substituted the missing TRAFFIC data with those from the cases having the
most similar values of GSALES, POP1M and AUTO5.
Figure1 - Handling MissingData
(The cells highlighted in yellow are missing data and those in blue are reference data.)

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BUILDINGTHE MODEL FOR PREDICTION
So far we have identified the 10 relevant variables to perform further data
analysis and have handled with missing data. The relevant explanatory variables
are: TRAFFIC, POP1M, POP5M, PERCAP1, PERCAP5, AUTO1, AUTO5, MARRIED1,
MARRIED5, and SUIT.
Then we used Forward Selection Method and Backward Elimination Method to
obtain the best-fit model. Then based on the best-fit model, we would decide on
the most appropriate model in this scenario and use it to make gross sales
prediction for each site.
Forward Selection Method involves starting with no variables in the model,
testing the addition of each variable using a chosen model comparison criterion
(P-value, R Square/adjusted R Square and Standard Error in our analysis),
adding the variable (if any) that improves the model the most, and repeating this
process until none improves the model.
Backward Elimination Method involves starting with all candidate variables,
testing the deletion of each variable using a chosen model comparison criterion
(P-value, R Square/adjusted R Square and Standard Error in our analysis),
deleting the variable (if any) that improves the model the most by being deleted,
and repeating this process until no further improvement is possible.

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SCATTERPLOTS WITH INTERPRETATION
Here we conducted data analysis to figure out the best model: We plotted scatter
plots between every independent variable and the dependent variable, gross
sales. Scatter plot is a type of chart that displays values for two variables for a set
of data using X and Y axes and coordinates. From a scatter plot, one can get a
basic idea of the relationship between the two variables (See the scatter plots in
Appendix).
From those scatter plots, no distinct outliers could be observed, so we would not
consider the influence of outliers in further analysis. By observing the trend of
each scatter plot, we concluded that, a positive relationship existed between
gross sales and independent variables including TRAFFIC, POP1M, POP5M,
PERCAP1, PERCAP5, AUTO1, and AUTO5. Meanwhile, both MARRIED1 and
MARRIED5 variables had a negative relationship with gross sales. As for variable
SUIT, because it is categorical data, we could not conclude its relationship with
gross sales from the scatter plot.
FINDING THE BEST FIT MODEL WITH TWO METHODS
Forward Selection Method
After looking at the general relationships between each x-variable and gross
sales, we used Forward Selection to build the Model first.

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1) Simple Linear Regression between Each Independent Variable and
Dependent Variable.
By doing simple linear regression of single variables, we got the following
results:
The p-values of variables MARRIED1 and MARRIED5 are both greater
than significance level of 0.05, which indicates that these two variables have no
significant influence on GSALES. Therefore we excluded them from the relevant
independent variables. The rest eight variables all have p-values less
than 0.05, which means that they have significant influence on GSALES.
Therefore, we would take them into the next step’s analysis.
Table 1 - Simple linear regression results for single variables

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Among these eight independent variables, variable TRAFFIC has the highest R
Square and the lowest standard error. Therefore, it was selected as the first
independent variable of our model.
2) Multiple Regression with Two Independent Variables.
After choosing TRAFFIC as the first variable, we combined TRAFFIC with each of
the other independent variables and ran linear regressions between the two
x-variables and gross sales. The results are shown below:
 Regression with an Interaction Terms:
According to the results, the p-values of all interaction terms are greater than
0.05, which means that these interactions are not significant to explain the
dependent variable. Therefore we did not need to include these
interaction terms in our model.
Table 2 - P-values of the interaction terms of two x-variables

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 Regression Model without Interaction Term:
Based on the results, the regression model with independent variables
TRAFFIC and POP1M is significant and has the highest adjusted R square and
the lowest standard error, so we added the second variable POP1M to
our model.
3) Multiple Regression with Three Independent Variables.
After choosing TRAFFIC and POP1M as variables, we combined TRAFFIC
and POP1M with each of the other independent variables and ran linear
regressions between the three x-variables and gross sales. The results are shown
below:
Table 3 - Regression results for two x-variables

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 Regression with an Interaction Term
0.05, which means that all these interactions between each two terms are
not significant to explain the dependent variable. Therefore, we did not need
to include these interaction terms in our model.
 Regression Model without Interaction Terms:
Table 4 - P-values of the interaction terms of three x-variables
Table 5 - Regressionresults for three x-variables

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According to the results, the regression model with independent variables
TRAFFIC, POP1M and AUTO5 is significant and has the highest adjust R
square and the lowest standard error, so we added the third variable, AUTO5,
to our model.
4) Multiple Regression with Four Independent Variables.
After choosing TRAFFIC, POP1M and AUTO5 as our variables, we combined
TRAFFIC, POP1M and AUTO5 with each of the other independent variables
and ran linear regressions between the four x-variables and gross sales.
The results are shown below:
 Regression Model with Interaction Terms:
0.05, which means that these interactions are not significant to explain the
dependent variable. Therefore, we did not need to include these interaction
terms in our model.
Table 6 - P-values of the interaction terms of four x-variables

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 Regression Model Without Interaction Terms:
Based on the results, the regression model with independent variables
TRAFFIC, POP1M, AUTO5 and POP5M is significant and has the highest adjust
R square and the lowest standard error, so we added the
fourth variable POP5M to our model.
5) Multiple Regression with Five Independent Variables.
After choosing TRAFFIC, POP1M, AUTO5 and POP5M as our variables,
we combined TRAFFIC, POP1M, AUTO5 and POP5M with each of the other
independent variable and ran linear regressions between the five x-variables and
gross sales. The results are shown below:
Table 7 - Regressionresults for four x-variables
Table 8 - P-values of the interaction terms of five x-variables

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 Regression Model with Interaction Terms:
0.05, which means that all these interactions between each two terms are
not significant to explain the dependent variable. Therefore, we did not need
to include these interaction terms in our model.
 Regression Model without Interaction Terms:
According to the results, we found that each model had one or two
x-variables with p-values greater than 0.05, so no additional x-variable could
be added to our model to help explain the dependent variable. We ended our
forward selection process here.
6) Conclusion
Through the forward selection process, we were able to find a model with
independent variables TRAFFIC, POP1M, AUTO5 and POP5M to best explain the
Table 9 - Regressionresults for five x-variables

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variation in gross sales, with adjusted R square 57.02% and standard error
101764.9321.
Backward Elimination Method
We then used Backward Elimination Method to validate our model.
1) Multiple Regression with Nine Independent Variables
In the regression model with interaction terms, all the p-values of interaction
terms are greater than alpha 0.05, which indicates that there is no evidence of
interaction. We then moved on to consider model without interaction terms and
got the following results:
Based on the result, the p-values of SUIT, PERCAP1, PERCAP5 and AUTO1 are
greater than the significance level of 0.05, which means that they are
not significant in explaining the variations in the dependent variable.
Table 10 - Regressionresults for nine x-variables

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As PERCAP5 has the highest p-value, being the most insignificant
predictor among these four, we excluded it from our model first.
2) Multiple Regression with Eight Independent Variables
After eliminating PERCAP5, we ran regression with the rest predictors with
interaction terms, all the p -values of interaction terms were greater than the
significance level of 0.05, which indicated there was no evidence of interaction.
We then moved on to consider model without interaction and got the following
results:
Based on the result, the p-values of SUIT, PERCAP1, POP5M and AUTO1 were
greater than 0.05, which meant that they were not significant to explain the
variations in dependent variable. As AUTO1 had the highest p-value, being the
most insignificant predictor, we then excluded it from our model.
Table 11 - Regressionresults for eight x-variables

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3) Multiple Regression with Seven Independent Variables
After eliminating PERCAP5 and AUTO1, we ran regression with the
rest predictors with interaction terms, all the p-values of interaction terms are
greater than the significance level of 0.05, which indicates there is no evidence of
interaction. Then we considered model without interaction and got the following
results:
Based on the result, the p-values of SUIT, PERCAP1 and POP5M are greater than
0.05, which means that they are not significant to explain the variations in
dependent variable. Although SUIT has the highest p value, we could not exclude
this variable because only one of its dummy variable's p-value is greater than
0.05. As PERCAP1 has the second-highest p-value, being the most insignificant
predictor, we then excluded it from our model.
Table 12 - Regressionresults for seven x-variables

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4) Multiple Regression with Six Independent Variables
After eliminating PERCAP5, AUTO1 and PERCAP1, we ran regression with the
rest predictors with interaction terms. All the p-values of interaction terms are
greater than alpha 0.05, which indicates there is no evidence of interaction. We
then considered model without interaction and got the following results:
Based on the result, the p-values of two dummy variables of SUIT are
both greater than 0.05, which means that they are not significant to explain the
variations in dependent variable. Therefore, we excluded it from our model.
Table 13 - Regressionresults for sixx-variables

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5) Multiple Regression with Four Independent Variables
After eliminating PERCAP5, AUTO1, PERCAP1 and SUIT, we ran regression
with the rest predictors with interaction terms.
According to this result, all the p-values of interaction terms are greater than
alpha 0.05, which indicates there is no evidence of interaction. We then moved
on to consider model without interaction and got following results:
Based on the result, the significance F for the overall model and the p-value of
each independent variable are all less than 0.05, which indicates that this is our
Table 15 - Regressionresults for four x-variables
Table 14 - Regressionresults for four x-variables with interaction terms

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best model with all predictors being significant. So we ended our
Backward Elimination process here.
6) Conclusion
Through the backward elimination process, we were able to find a model with
independent variables TRAFFIC, POP1M, AUTO5 and POP5M to best explain the
variation in gross sales, with adjusted R square 57.02% and standard error
101764.9321.
FINDING THE MOST APPROPRIATE MODEL AND JUSTIFICATION
Using the Forward Selection and Backward Elimination method, we have
found the best-fit regression model with independent variables TRAFFIC, POP1M,
AUTO5 and POP5M. Then we tried to find the most appropriate model to select
location and predict gross sales based on the information we know.
Because the data of AUTO5 and POP5M of these three sites are unavailable,
we need to predict AUTO5 and POP5M for each site based on other variables in
order to use the best-fit model on these sites.
Make Predictions for AUTO5 and POP5M:

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We considered POP5M as a dependent variable and used other known
variables as independent variables to find the best regression model to predict
POP5M.
After examining the factors including significance F<0.05, individual p
value<0.05, the highest R Square or adj R Square, and the lowest standard error,
we found that it is best to use POP1M to predict POP5M.
Table 16 - Regressionresults for finding the best x-variables to predict POP5M

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Then we need to predict AUTO5, we did the same process as above:
After examining the factors including significance F<0.05, individual p
value<0.05, the highest R Square or adj R Sqaure, and the lowest standard error,
we found that it is best to use TRAFFIC to predict AUTO5.
Problems if we use other known variables to predict POP5M and AUTO5:
We noticed that the R Square of the regression model between TRAFFIC and
AUTO5 is only 21.72%, which means that only 21.72% of total variations in
dependent variable AUTO 5 is explained by TRAFFIC. Due to the low R Square,
the predicted value of AUTO5 will not be very accurate. The similar situation
applied to POP5M too. In addition, the adjusted R Square for the regression
Table 17 - Regressionresults for finding the best x-variables to predict AUTO5

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model without these two variables is 51.32%, which is only 5.7% lower than the
adjusted R Square for the best-fit model.
We thought using inaccurate data to gain only such small percentage increase in
adjusted R Square was not worthy. Last but not least, there is a parsimony rule of
selecting variables in model building: use as few X variables as
possible. Therefore, we decided to exclude the two unknown independent
variable AUTO5 and POP5M from the best-fit model we got from the model
building process, in order to be align to the rule and to avoid getting an
over-specified model.
This left us with the model that includes two variables, TRAFFIC and
POP1M. Reviewing information about variables and considering that we also
have information of SUIT of each site, which is the CFSI suitability rating about
the comprehensive site analysis, we were wondering if we could add SUIT as an
explanatory variable into this model. Therefore, we ran regression analyses with
and without the two dummy variables of SUIT to see which model would be
better. The regression models are shown below.
Table 18 - Regressionresults using TRAFFIC and POP1M as explanatory variables of GSALES

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Because significance F and p-values of two model are both less than 0.05 (only
one p-value of SUIT is greater than 0.05. In this case, we still treated it as a
significant variable and kept it in the model), these two models are both
appropriate to make predictions for gross sales. However, considering the higher
adjusted R square and the lower standard error, the second model with SUIT as a
variable is more appropriate than the first model.
Therefore, we decided that the regression model with independent variables of
TRAFFIC, POP1M and SUIT is the most appropriate model to predict gross sales
for each site.
CHECKING RESIDUALS
After selecting the best model, we performed a residual analysis to see if the
model violated any assumptions. If any assumption was violated, we might want
to use other methods to build model, such as log transformation. These
assumptions include:
 Linearity
Table 19 - Regressionresults using TRAFFIC, POP1M and SUIT as explanatory variables of GSALES

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 Independence of errors
 Normality of errors
 Equal variances of errors
Figure6 - Plot of residuals against the population withina
one-mile radius of the Culver's restaurant
Figure5 - Plot of residuals against the traffic count
around the Culver's restaurant
Figure4 - Plot of residuals against dummyvariable 1 of CFSI
suitability rating of the Culver's restaurant
Figure3 - Plot of residuals against dummyvariable 2 of
CFSI suitability rating of the Culver's restaurant
Figure2 - Normal probability plotof the residuals for the
gross sales

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From these residual plots, both POP1 and TRAFFIC satisfied the four
assumptions of regression:
1) There was no apparent pattern in the residual plots; the residuals
appeared to be evenly spread above and below 0. Therefore, this
assumption was not violated.
2) When data collected over periods of time sometimes exhibit an
autocorrelation effect among successive observations. In these instances,
there is a relationship between consecutive residuals. Because the
Culver's data were collected during the same time period for each
variable, we did not need to evaluate the independence assumption.
3) According to the normal probability plot of the residuals, the data did not
appear to depart substantially from a normal distribution.
4) There did not appear to be major differences in the variability of the
residuals for different Xi values. Thus, there is no apparent violation in
the assumption of equal variance at each level of X.
Note that the residual plots for dummy variables of variable SUIT cannot be
interpreted.
CHECKING COLLINEARITY
Here we checked if multicollinearity existed. Multicollinearity is a phenomenon
in which two or more predictor variables in a multiple regression model are
highly correlated, meaning that one can be linearly predicted from the

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others. When multicollinearity exists, some x-variables might do a good job at
predicting the Y variable, but these variables do not bring new information to the
regression model, therefore we want to exclude them from the model. We can
detect (Multi)Collinearity when high correlation exists between predictor
variables, when absolute value of r > 0.95.
From the table, we could see that all correlations were less than 0.95 or greater
than -0.95.Therefore we concluded that there was no collinearity between these
variables, and all of them provided new information to the regression model.
LOCATION PREDICTION
Using the model we chose, we predicted the gross revenue of each location. The
results are as following:
Gross Sales Revenue = 493758.5 + 31971.99*Better + 80487.16*Best +
36.28567*TRAFFIC + 64.3183*POP1M
Table 20 - Multicollinearity results for ten relevant variables in predicting gross sales
Table 21 - Predicted gross sales for Site A, B and C

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FINANCIAL ANALYSIS
This section focuses on financial analysis of opening the Culver's Frozen Custard
restaurant at each site. The primary goal is to find the most promising location
among Site A, Site B, and Site C by the financial estimation. To simplify our
analysis, we did not consider the time value of money and the potential growth
rate of annual sales. Additionally, we took our clients' financial ability and
profitability requirements into consideration.
GROSS SALES
We predicted the gross sales of all three sites based on the traffic count, the
population within a one-mile radius, and the CFSI suitability rating: $1,391,607
for Site A, $1,279,961 for Site B, and $1,448,375 for Site C. Our clients only
consider the site with annual sales more than $1 million. Based on our results, all
sites were favorable to our clients.
Figure7 - Predicted gross sales

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START-UP SUMMARY
The Culver's Frozen Custard restaurant has the following start-up costs:
 Initial Lease Payments and Deposits
 Structure and Improvements
 Equipment & Signage
 Other miscellaneous Costs
 Franchise Fee (15-year agreement)
Note that the items mentioned above are depreciable. The difference of the
startup expenses is only due to the initial lease payments and deposits. The
startup costs of all sites are reasonable, which is less than the maximum of
typical initial investment costs ($3,046,000). However, our clients are only able
to obtain $1.2 to $1.55 million from the local bank. Site C ($1,815,000) requires
Figure8 - Startup expenses

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more than $1.55 million to start-up, which is beyond the clients' financial
abilities.
OPERATING COSTS & ANNUAL PROFITS
The operating costs for the Culver's Frozen Custard restaurant include food costs,
paper cost, labor cost, and other operating costs. To eliminate the differences of
operating costs caused by suitability, we used the comparable analysis to
estimate each site's operating costs. Specifically, we concluded each expense as
the percentage of gross sales, and then sort the data by its suitability. For the
suitability rating of 1, the total average operating costs are 94% of the gross sales:
FOOD-31%, PAPER-4%, LABOR-30%, and OTHER OP-29%. For the suitability
rating of 2, the total average operating costs are 91% of the gross sales:
FOOD-30%, PAPER-4%, LABOR-29%, and OTHER OP-28%. As results, annual
profits of each site are as followings: $80,155 for Site A, $73,725 for Site B, and
$132,410 for Site C.
OTHER CONSIDERATIONS
We also compared those three sites using their payback periods. By dividing the
initial investment by the annual profits, we got the results: Site C (6.91 years) has
the shortest payback period. Note that the payback period of Site A (7.05 years)
is similar to Site C. Even though Site C has the highest annual profit, it has the
highest startup expenses as well.

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Our clients have options to renew their franchise agreement every 10 years after
the first 15 years. We recommend that they consider the renew options if the
restaurant operates well in the first 15 years, because the more year the
restaurant operates, the less annual allocation of the start-up expenses will be.
RISKS
There are also risks for the restaurant to generate profits:
1) Workforce: if the local workforce is weak, the restaurant will probably
have higher labor expense, which will lower the annual profits.
2) Competitor: there will probably be a price competition, which will lower
the annual profits.
3) Macroeconomic: if the macroeconomics got better, costumers would
probably spend less money on fast foods, which would lower the annual
profits.
In general, based on our financial analysis mentioned above, we recommend our
clients to choose Site A. If the restaurant at Site A operates well, they can
consider either to renew the franchise agreement or to open another restaurant
at Site C. Note that our clients should pay attention to the changing
circumstances to modify their financial strategies.

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RECOMMENDATION
Each site has different characteristics. The CFSI rates those three sites based on
their unique characteristics: Site A - better, Site B - better, and Site C - best. We
noticed that the suitability rates provided by the CFSI did not take our clients'
preference and goal into account. Thus, we reevaluated those three sites listed
below based on our clients' needs.
Customer Group: All sites have big potential customer bases due to their
location description. The followings shows neighboring groups for each site:
 Site A: 1) high school students; 2) hospital patients and employees
 Site B: drivers
 Site C: 1) middle school students; 2) business office residents; 3)
shoppers
Figure9 - LocationInformation

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Our clients prefer to interact with young students, so both Site A and Site C are
favorable to our clients. Note that the size of each site's customer group is
unknown based on our data.
Workforce: The neighboring groups mentioned above are also indications of the
potential workforce for each site. The major workforce of each site is listed as
followings:
 Site A - students
 Site B - adult employees
 Site C - adult employees
Our clients indicated their preference for labor force - young students. Based on
their preference, Site A is the suitable location to hire young students.
Competitor Pressure: Both Site B and Site C will face intense competitions from
other restaurants: Site B - other 3 fast food restaurants (i.e. McDonald's, A&W,
and Pizza Hut); and Site C - other restaurants at the food court. As results, Site A
has the biggest business viability.
Accessibility: One of the Culvers' competitive advantages is "a wide variety of
entrees." Site C is located within a shopping center, which reduces the likelihood
for providing the out-door seating and the drive-up service. Unlike Site C, both
Site A and Site B are able to provide in-door seating, out-door seating, and
drive-up service.

35
Visibility: Site A is the most visible location. Its speed limit (i.e. 30 mph) will also
help draw drivers' attentions. Site B is the second visible location. Site C is the
least.
In general, Site A is most favorable place for our clients based on the location
descriptions. Both the result from the financial analysis and the result from the
location analysis have demonstrated that Site A is the best.
CONCLUSION
In conclusion, we suggest our client to locate the new Culver's restaurant at Site
A. According to the prediction of gross sale, all of the three location are profitable.
Although Site C has the highest predicted gross sale, after taking other start-up
expenses, such as franchise fee and venue purchase fee, into consideration, we
found that locating at site C was beyond our clients' financial abilities. On the
other hand, Site A has the second highest predicted gross sale, and it is affordable
to our clients. In addition, Site A is the location that suits best for our clients'
interest. Our clients enjoy interacting with young students and they expect to
recruit students as their main labor force. Because Site A is close to a school, this
location is in our clients' favor.

36
For further recommendation, if the restaurant at Site A operates well, our clients
can consider either to renew the franchise agreement or to open another
restaurant.

- 7 -
The P-value of All the Models with and without InteractionTerms
Two independent variables
w/o interaction w/ interaction
Intercept 0.43348 0.40838
TRAFFIC 7.80E-11 0.06915
PERCAP1 0.9735 0.35657
INTERACTION 0.35622
Intercept 0.46665 0.7826
TRAFFIC 1.40E-11 0.19668
PERCAP5 0.76497 0.70195
INTERACTION 0.71604
Intercept 0.37269 0.09544
TRAFFIC 1.20E-10 0.07114
AUTO1 0.23231 0.08876
INTERACTION 0.1111
Intercept 0.01908 0.09005
TRAFFIC 6.90E-09 0.11049
AUTO5 0.01159 0.08357
INTERACTION 0.13908
Intercept 0.05081 0.603399681
TRAFFIC 0.00011 0.357418767
POP1M 0.00057 0.783023942
INTERACTION 0.901200161
Intercept 0.394738756 0.47211
TRAFFIC 8.12381E-11 0.11211
POP5M 0.799642004 0.62557
INTERACTION 0.60635
TRAFFIC+AUTO5
P-value
TRAFFIC+AUTO1
P-value
TRAFFIC+POP1M
P-value
TRAFFIC+POP5M
P-value
TRAFFIC+PEPCAP5
P-value
TRAFFIC+PEPCAP1
P-value

- 8 -
Three independent variables
Intercept 3.04E-02 0.846978729
TRAFFIC 1.01E-04 0.26719108
POP1M 8.72E-05 0.279507846
POP5M 5.38E-02 0.266168787
TRAFFIC*POP1M 0.387549175
POP1M*POP5M 0.586697547
Intercept 3.44E-02 0.999410795
TRAFFIC 8.02E-05 0.872048
POP1M 4.19E-04 0.897980659
PERCAP1 4.00E-01 0.436968105
TRAFFIC*PERCAP1 0.795337162
POP1M*PERCAP1 0.295767129
Intercept 0.065479538 0.646913672
TRAFFIC 0.000170017 0.248403549
POP1M 0.000635673 0.91064369
PERCAP5 0.89357749 0.431038456
Intercept 0.632798025 0.099438507
TRAFFIC 4.67E-04 0.131739557
POP1M 0.00064255 0.750676817
AUTO1 0.250740107 0.084400805
TRAFFIC*AUTO1 0.145827069
POP1M*AUTO1 0.789173958
Intercept 0.034341969 0.123141669
TRAFFIC 0.002491934 0.602748442
POP1M 0.000607895 0.288622784
AUTO5 0.012007974 0.101661674
POP1M*AUTO5 0.264481818
TRAFFIC+POP1M+AUTO5
P-value
TRAFFIC+POP1M+AUTO1
P-value
TRAFFIC+POP1M+PERCAP5
P-value
TRAFFIC+POP1M+PERCAP1
P-value
TRAFFIC+POP1M+POP5M
P-value

- 9 -
Four independent variables
Intercept 1.36E-02 0.498090689
TRAFFIC 3.38E-03 0.848364022
POP1M 2.91E-05 0.697357523
POP5M 1.53E-02 0.222223963
AUTO5 3.67E-03 0.483820834
POP1M*POP5M 0.253422815
POP1M*AUTO5 0.777626544
POP5M*AUTO5 0.188947803
TRAFFIC+POP1M+AUTO5+POP5M
P-value
Intercept 1.81E-02 0.289156326
TRAFFIC 1.41E-03 0.462728048
POP1M 2.22E-04 0.427426298
PERCAP1 1.20E-01 0.659558869
AUTO5 4.79E-03 0.289654461
POP1M*AUTO5 0.402860714
PERCAP1*AUTO5 0.609579772
P-value
TRAFFIC+POP1M+AUTO5+PERCAP1

- 10 -
Intercept 0.033645144 0.195178326
TRAFFIC 0.002536461 0.82575383
POP1M 0.000631115 0.288784438
PERCAP5 0.762702408 0.67600922
AUTO5 0.012028211 0.20348482
POP1M*AUTO5 0.261645024
PERCAP5*AUTO5 0.705505216
P-value
TRAFFIC+POP1M+AUTO5+PERCAP5
Intercept 0.032969686 0.827276931
TRAFFIC 0.002426639 0.998040148
POP1M 6.40E-04 0.102712404
AUTO5 0.022918172 0.632378294
AUTO1 0.620808936 0.848592375
POP1M*AUTO5 0.023192554
POP1M*AUTO1 0.033882256
AUTO5*AUTO1 0.613311427
TRAFFIC+POP1M+AUTO5+AUTO1
P-value

- 11 -
Five independent variables
Intercept 0.008036855 0.588517217
TRAFFIC 0.002120117 0.935748923
POP1M 1.55358E-05 0.966227731
POP5M 0.022599451 0.231623635
AUTO5 0.181806146 0.583749639
PERCAP1 0.001758453 0.99698645
POP1M*POP5M 0.260062713
POP1M*AUTO5 0.938137001
POP5M*AUTO5 0.220951299
AUTO5*PERCAP1 0.963257698
TRAFFIC+POP1M+AUTO5+POP5M+PERCAP1
P-value
Intercept 0.013769273 0.432126455
TRAFFIC 0.003527195 0.64843858
POP1M 3.19406E-05 0.780363724
POP5M 0.016246984 0.255628541
AUTO5 0.811993476 0.454411787
PERCAP5 0.003886997 0.385625986
POP1M*POP5M 0.3389989
POP1M*AUTO5 0.859479362
POP5M*AUTO5 0.227048849
AUTO5*PERCAP5 0.40368779
TRAFFIC+POP1M+AUTO5+POP5M+PERCAP5
P-value

- 12 -
Intercept 0.013220237 0.435918536
TRAFFIC 0.003310179 0.661902071
POP1M 3.22391E-05 0.227489821
POP5M 0.016179132 0.516589135
AUTO5 0.009917151 0.299045728
AUTO1 0.642402171 0.586221726
POP1M*POP5M 0.330263026
POP1M*AUTO5 0.108121193
POP1M*AUTO1 0.060704469
POP5M*AUTO5 0.992942165
POP5M*AUTO1 0.200376619
AUTO5*AUTO1 0.372894793
TRAFFIC+POP1M+AUTO5+POP5M+AUTO1
P-value

- 13 -
All Adjusted R square and Standard Error in Forward Selection
One independent variable R^2 StdError
TRAFFIC 0.45190 115602.52613
POP1M 0.43087 117799.65984
POP5M 0.09197 148794.30237
PERCAP1 0.09037 148925.41929
PERCAP5 0.05351 151912.59198
AUTO1 0.11404 146975.20269
AUTO5 0.24093 136043.50349
MARRID1 0.02077 154517.73000
MARRID5 0.02142 154466.84955
SUIT 0.33622 127972.87754
Two independent variables Adj R^2 StdError
TRAFFIC+POP1M 0.513267 108303.4
TRAFFIC+POP5M 0.43928 116243.8
TRAFFIC+PERCAP1 0.438855 116287.8
TRAFFIC+PERCAP5 0.439448 116226.4
TRAFFIC+AUTO1 0.448354 115299.4
TRAFFIC+AUTO5 0.480083 111934.5
TRAFFIC+SUIT 0.47344 112647.3
Three independent variables Adj R^2 StdError
TRAFFIC+POP1M+POP5M 0.529113 106525.8
TRAFFIC+POP1M+PERCAP1 0.511616 108486.9
TRAFFIC+POP1M+PERCAP5 0.50751 108942.1
TRAFFIC+POP1M+AUTO1 0.515217 108086.3
TRAFFIC+POP1M+AUTO5 0.543671 104866.3
TRAFFIC+POP1M+SUIT 0.532763 106112.2

- 14 -
All Adjusted R square and Standard Error in Backward Elimination
Four independent variables Adj R^2 StdError
TRAFFIC+POP1M+AUTO5+POP5M 0.57026291
3
101764.932
1TRAFFIC+POP1M+AUTO5+PERCA
P1
0.55163457
4
103947.198
1TRAFFIC+POP1M+AUTO5+PERCA
P5
0.53862201
3
105444.799
2TRAFFIC+POP1M+AUTO5+AUTO1 0.53949053
8
105345.504
7TRAFFIC+POP1M+AUTO5+SUIT 0.55776336
3
103234.317
TRAFFIC+POP1M+AUTO5+POP5M+
PERCAP1+PERCAP5+AUTO1+SUIT
P-value Adj R^2 StdError Significance F
Intercept 0.026856118 0.57907521 100716.1188 3.61E-13
SUIT--1 0.21286813 　　　
SUIT--2 0.038320033 　　　
TRAFFIC 0.040929748 　　　
POP1M 5.80345E-05 　　　
POP5M 0.059731892 　　　
PERCAP1 0.144033811 　　　
PERCAP5 0.984763695 　　　
AUTO5 0.008492431 　　　
AUTO1 0.64802495 　　　
+PERCAP1+AUTO1+SUIT
Intercept 0.025873201 0.584469701 100068.6585 8.61489E-14
SUIT--1 0.199058924 　　　
SUIT--2 0.032483762 　　　
TRAFFIC 0.039616272 　　　
POP1M 4.83363E-05 　　　
POP5M 0.058019786 　　　
PERCAP1 0.08320902 　　　
AUTO5 0.006966252 　　　
AUTO1 0.62939005

- 15 -
+PERCAP1+SUIT
Intercept 0.026496734 0.588494882 99582.80379 2.13327E-14
SUIT--1 0.203929082 　　　
SUIT--2 0.032431055 　　　
TRAFFIC 0.040363014 　　　
POP1M 4.33066E-05 　　　
POP5M 0.056125081 　　　
AUTO5 0.002632807 　　　
PERCAP1 0.079199368 　　　
+PERCAP1+SUIT
Intercept 0.044007842 0.577371846 100919.6979 1.98104E-14
SUIT--1 0.279323383 　　　
SUIT--2 0.070466957 　　　
TRAFFIC 0.048119601 　　　
POP1M 0.000098001 　　　
POP5M 0.032096495 　　　
AUTO5 0.007179133 　　　
TRAFFIC+POP1M+AUTO5+POP5M P-value Adj R^2 StdError Significance F
Intercept 0.013610014 0.570262913 101764.9321 3.27079E-15
TRAFFIC 0.003382438 　　　
POP1M 0.000029141 　　　
POP5M 0.015300094 　　　
AUTO5 0.003668162

- 16 -
Regression Analysis of the Final Model
SUMMARY OUTPUT
Multiple R 0.744644163
R Square 0.55449493
Adjusted R Square 0.532762975
Standard Error 106112.2087
Observations 87
ANOVA
df SS MS F Significance F
Regression 4 1.14918E+12 2.87296E+11 25.51518901 9.51338E-14
Residual 82 9.23304E+11 11259800825
Total 86 2.07249E+12
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 493758.5078 167123.8924 2.954445955 0.004087076 161295.8474 826221.1682
1 31971.98741 30955.05052 1.032852051 0.304709787 -29607.46903 93551.44385
2 80487.15826 34575.50525 2.327866438 0.022383888 11705.46405 149268.8525
TRAFFIC 36.28566855 13.98095071 2.595364885 0.011192846 8.473103848 64.09823325
POP1M 64.31830078 18.93507811 3.396780324 0.001053908 26.65039851 101.9862031
Regression Statistics

- 19 -
Collinearity Matrix
Collinearity TRAFFIC POP1M POP5M PERCAP1 PERCAP5 AUTO5 AUTO1 MARRIED1 MARRIED5 SUIT
TRAFFIC 1
POP1M 0.6838116 1
POP5M 0.4234277 0.6406478 1
PERCAP1 0.4436024 0.4600323 0.387156 1
PERCAP5 0.3098713 0.2481092 0.1951778 0.6132598 1
AUTO5 0.466031 0.3518318 0.3219075 0.4066712 0.2902353 1
AUTO1 0.3691286 0.2764955 0.2490518 0.3162532 0.0761126 0.6798959 1
MARRIED1 -0.146772 -0.0442296 0.0848045 -0.0874612 0.0806431 -0.1110432 -0.0689627 1
MARRIED5 -0.195277 -0.2368674 -0.1413524 -0.1719712 -0.0875225 -0.0489086 -0.0697864 -0.0900383 1
SUIT 0.6327749 0.4938176 0.2351384 0.4333737 0.4078884 0.370709 0.2984209 0.0178559 -0.1848175 1

- 20 -
Site Information
Site Price Location
Posted
Speed Limit
Nearby Notes
A 410,000$
in a residental area on a main
street
30 mph
Within Walking Distance:
- a high school
- a small grocery store
- a hospital
B 480,000$
off a freeway ramp on the
edge of Carbondale
45 mph
A Frontage Road
- 2 gas stations w/ convenience
stores
- a McDonald's
- an A&W
- a Pizza Hut
1) the frontage road runs to the
county road leading to the
freeway ramp
2) the frontage road has a
spotlight to make access easier
C 760,000$
at the far end of Carbondale's
new shopping center
N/A
A Shopping Center:
- a food court (including a
Baskin-Robbins ice cream
shop)
Within Waling Distance:
- a middle school
- business offices housing
(about 100 employees)
access from:
1) the street that runs past the
shopping cenrer and dead ends
about a block beyond Site C
2) the end of the shopping
center itself

- 21 -
Predicted Gross Sales Revenue
15,000 5,000 1 1,391,607
16,000 2,700 1 1,279,961
17,000 4,000 2 1,448,375
TRAFFIC POP1M SUIT (1) Predicted GSales (2)
1,150,000
1,200,000
1,250,000
1,300,000
1,350,000
1,400,000
1,450,000
1,500,000
A B C
Predicted Gross Sales

- 22 -
Startup Funding
Startup Costs
A B C
Initial Lease Payments and Deposits 410,000$ 480,000$ 760,000$
Structure and Improvements 600,000 600,000 600,000
Equipment & Signage 300,000 300,000 300,000
Miscellaneous Costs 100,000 100,000 100,000
Franchise Fee (15 yr) 55,000 55,000 55,000
Total 1,465,000 1,535,000 1,815,000
Renew Franchise Agreement (10 yr) 30,000 30,000 30,000

- 23 -
Organization Budget - Example
Numbers of Personnel
A B C
Owners 2 2 2
General Manager (1) 1 1 1
Assistant Manager (2) 2 2 2
Team Member (3) 52 52 52
Total (4) 57 57 57
Site
Personnel Plan -Yearly
A B C
Owners - - -
General Manager (1) 37,158 37,158 37,158 37,158
Assistant Manager (2) 69,278 69,278 69,278 34,639
Team Member (3) - - -
Total (4) 106,436 106,436 106,436
Site Salaries per
person

- 24 -
Comparable Analysis
Comparable Analysis (Suit-1) Comparable Analysis (Suit-2)
Food Paper Labor Other OP Food Paper Labor Other OP
32% 4% 30% 32% 30% 3% 28% 27%
32% 4% 35% 28% 31% 4% 31% 31%
31% 4% 32% 30% 30% 4% 30% 28%
31% 4% 31% 30% 32% 4% 30% 32%
32% 4% 33% 30% 31% 4% 30% 31%
32% 3% 29% 31% 30% 3% 30% 28%
33% 4% 30% 30% 31% 3% 29% 29%
31% 4% 31% 30% 29% 4% 28% 28%
32% 3% 31% 29% 30% 4% 30% 29%
30% 4% 30% 29% 31% 4% 26% 29%
29% 3% 26% 28% 31% 4% 29% 27%
30% 3% 25% 27% 29% 3% 27% 25%
31% 3% 29% 29% 31% 4% 31% 29%
32% 4% 30% 28% 31% 4% 31% 30%
32% 4% 33% 30% 30% 4% 30% 29%
30% 4% 30% 28% 27% 3% 25% 26%
31% 4% 32% 29% 30% 4% 28% 26%
30% 4% 30% 29% 28% 3% 26% 28%
31% 4% 29% 31% 32% 3% 29% 28%
31% 5% 32% 30% 29% 3% 28% 27%
30% 4% 29% 29% 30% 4% 30% 29%
29% 4% 29% 28% 31% 4% 32% 29%
31% 4% 30% 29% 29% 3% 29% 27%
31% 4% 30% 29% 29% 4% 28% 27%
30% 4% 29% 28%
Variable Cost 94% 31% 4% 31% 30%
35% 4% 29% 28%
28% 3% 25% 28%
28% 3% 26% 28%
28% 3% 26% 27%
30% 4% 29% 28%
Variable Cost 91%

- 25 -
Annual Profit
Initial Investment
A B C
Franchise Fee 55,000$ 55,000$ 55,000$
Start-up Costs 100,000 100,000 100,000
Site 410,000 480,000 760,000
Total 565,000$ 635,000$ 915,000$
Renew Franchise Agreement (10 yr) 30,000$
Annual Profit
A B C
Predicted GSales (1) 1,391,607$ 1,279,961$ 1,448,375$
Food (2) (430,900) (396,330) (436,847)
% of Gsales 31% 31% 30%
Paper (3) (53,004.49) (48,752.04) (51,822.65)
% of Gsales 4% 4% 4%
Labor (420,519) (386,782) (417,426)
% of Gsales 30% 30% 29%
Other Operating Costs (4) (407,028) (374,373) (409,870)
% of Gsales 29% 29% 28%
Total Annual Profit 80,155 73,725 132,410

- 26 -
Total Profits
Total Profits after () yr A B C
10 236,554 102,246 409,100
15 637,330 470,870 1,071,150
25 1,408,884 1,178,116 2,365,250
35 2,210,438 1,915,363 3,689,350

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