TFI restraunt chain analysis
Vignesh M
1st January 2018
1. INTRODUCTION
TFI is the company behind some of the world???s most well-known brands like Burger King, Sbarro, Popeyes, Usta Donerci, and Arby???s. They employ around 20,000 people in Europe and Asia and make considerable investments on new restaurant sites.The objective is to decide when and where to open a new restaurant site which is considerable profitable and this process is largely subjective.
The problem and the solution :-
It takes huge investments to open up new restaurant sites. Also when a wrong location for a restaurant brand is chosen, the site closes within 18 months and operating losses are incurred.
Finding a mathematical model to increase the effectiveness of investments in new restaurant sites would allow TFI to invest more in other important business areas, like sustainability, innovation, and training for new employees.
2. DATA FIELDS
. Id : Restaurant id. . Open Date : opening date for a restaurant . City : City that the restaurant is in. Note that there are unicode in the names. . City Group : Type of the city. Big cities, or Other. . Type : Type of the restaurant. FC: Food Court, IL: Inline, DT: Drive Thru, MB: Mobile . P1, P2 ??? P37 : There are three categories of these obfuscated data. Demographic data are gathered from third party providers with GIS systems. These include population in any given area, age and gender distribution, development scales. Real estate data mainly relate to the m2 of the location, front facade of the location, car park availability. Commercial data mainly include the existence of points of interest including schools, banks, other QSR operators. . Revenue : The revenue column indicates a (transformed) revenue of the restaurant in a given year and is the target of predictive analysis. Please note that the values are transformed so they don???t mean real dollar values.
3. DATA EXPLORATION
setwd("~/Downloads/Prof Sameer Mathur/Restaurant data")
train<-read.csv("train.csv")
test<-read.csv("test.csv")
str(train)## 'data.frame': 137 obs. of 43 variables:
## $ Id : int 0 1 2 3 4 5 6 7 8 9 ...
## $ Open.Date : Factor w/ 134 levels "01/03/2014","01/07/2000",..: 60 17 21 11 42 16 94 53 78 114 ...
## $ City : Factor w/ 34 levels "Adana","Afyonkarahisar",..: 17 4 11 31 15 4 17 17 2 12 ...
## $ City.Group: Factor w/ 2 levels "Big Cities","Other": 1 1 2 2 2 1 1 1 2 2 ...
## $ Type : Factor w/ 3 levels "DT","FC","IL": 3 2 3 3 3 2 3 3 3 3 ...
## $ P1 : int 4 4 2 6 3 6 2 4 1 6 ...
## $ P2 : num 5 5 4 4.5 4 6 3 5 1 4.5 ...
## $ P3 : num 4 4 2 6 3 4.5 4 4 4 6 ...
## $ P4 : num 4 4 5 6 4 7.5 4 5 4 7.5 ...
## $ P5 : int 2 1 2 4 2 8 1 2 1 6 ...
## $ P6 : int 2 2 3 4 2 10 5 3 2 4 ...
## $ P7 : int 5 5 5 10 5 10 5 5 1 10 ...
## $ P8 : int 4 5 5 8 5 8 5 4 5 10 ...
## $ P9 : int 5 5 5 10 5 8 5 4 5 10 ...
## $ P10 : int 5 5 5 10 5 8 5 4 5 10 ...
## $ P11 : int 3 1 2 8 2 10 2 4 1 2 ...
## $ P12 : int 5 5 5 10 5 8 5 3 5 10 ...
## $ P13 : num 5 5 5 7.5 5 6 5 4 5 7.5 ...
## $ P14 : int 1 0 0 6 2 0 3 0 1 0 ...
## $ P15 : int 2 0 0 4 1 0 4 0 1 0 ...
## $ P16 : int 2 0 0 9 2 0 4 0 2 0 ...
## $ P17 : int 2 0 0 3 1 0 3 0 1 0 ...
## $ P18 : int 4 0 0 12 4 0 4 0 4 0 ...
## $ P19 : int 5 3 1 20 2 5 2 3 1 25 ...
## $ P20 : int 4 2 1 12 2 6 4 5 1 3 ...
## $ P21 : int 1 1 1 6 1 3 1 2 1 3 ...
## $ P22 : int 3 3 1 1 2 1 2 4 1 1 ...
## $ P23 : int 3 2 1 10 1 5 1 2 1 10 ...
## $ P24 : int 1 0 0 2 2 0 5 0 4 0 ...
## $ P25 : int 1 0 0 2 3 0 4 0 4 0 ...
## $ P26 : num 1 0 0 2.5 3 0 4 0 4 0 ...
## $ P27 : num 4 0 0 2.5 5 0 5 0 2 0 ...
## $ P28 : num 2 3 1 2.5 1 7.5 1 3 2 5 ...
## $ P29 : num 3 3 3 7.5 3 5 3 2 3 2.5 ...
## $ P30 : int 5 0 0 25 5 0 4 0 4 0 ...
## $ P31 : int 3 0 0 12 1 0 5 0 5 0 ...
## $ P32 : int 4 0 0 10 3 0 2 0 5 0 ...
## $ P33 : int 5 0 0 6 2 0 2 0 3 0 ...
## $ P34 : int 5 0 0 18 3 0 3 0 4 0 ...
## $ P35 : int 4 0 0 12 4 0 5 0 5 0 ...
## $ P36 : int 3 0 0 12 3 0 4 0 4 0 ...
## $ P37 : int 4 0 0 6 3 0 4 0 5 0 ...
## $ revenue : num 5653753 6923131 2055379 2675511 4316715 ...library(psych)
summary(train)## Id Open.Date City City.Group Type
## Min. : 0 01/07/2000: 2 Istanbul:50 Big Cities:78 DT: 1
## 1st Qu.: 34 02/02/2012: 2 Ankara :19 Other :59 FC:76
## Median : 68 02/23/2010: 2 Izmir : 9 IL:60
## Mean : 68 01/03/2014: 1 Bursa : 5
## 3rd Qu.:102 01/09/2010: 1 Samsun : 5
## Max. :136 01/17/2009: 1 Antalya : 4
## (Other) :128 (Other) :45
## P1 P2 P3 P4
## Min. : 1.000 Min. :1.000 Min. :0.000 Min. :3.000
## 1st Qu.: 2.000 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.000
## Median : 3.000 Median :5.000 Median :4.000 Median :4.000
## Mean : 4.015 Mean :4.409 Mean :4.318 Mean :4.372
## 3rd Qu.: 4.000 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :12.000 Max. :7.500 Max. :7.500 Max. :7.500
##
## P5 P6 P7 P8
## Min. :1.000 Min. : 1.000 Min. : 1.000 Min. : 1.000
## 1st Qu.:1.000 1st Qu.: 2.000 1st Qu.: 5.000 1st Qu.: 4.000
## Median :2.000 Median : 3.000 Median : 5.000 Median : 5.000
## Mean :2.007 Mean : 3.358 Mean : 5.423 Mean : 5.153
## 3rd Qu.:2.000 3rd Qu.: 4.000 3rd Qu.: 5.000 3rd Qu.: 5.000
## Max. :8.000 Max. :10.000 Max. :10.000 Max. :10.000
##
## P9 P10 P11 P12
## Min. : 4.000 Min. : 4.000 Min. : 1.000 Min. : 2.000
## 1st Qu.: 4.000 1st Qu.: 5.000 1st Qu.: 2.000 1st Qu.: 4.000
## Median : 5.000 Median : 5.000 Median : 3.000 Median : 5.000
## Mean : 5.445 Mean : 5.489 Mean : 3.263 Mean : 5.299
## 3rd Qu.: 5.000 3rd Qu.: 5.000 3rd Qu.: 4.000 3rd Qu.: 5.000
## Max. :10.000 Max. :10.000 Max. :10.000 Max. :10.000
##
## P13 P14 P15 P16
## Min. :3.00 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.:5.00 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median :5.00 Median : 0.000 Median : 0.000 Median : 0.000
## Mean :5.08 Mean : 1.416 Mean : 1.387 Mean : 1.942
## 3rd Qu.:5.00 3rd Qu.: 2.000 3rd Qu.: 2.000 3rd Qu.: 3.000
## Max. :7.50 Max. :15.000 Max. :10.000 Max. :15.000
##
## P17 P18 P19 P20
## Min. : 0.000 Min. : 0.000 Min. : 1.000 Min. : 1.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 2.000 1st Qu.: 2.000
## Median : 0.000 Median : 0.000 Median : 3.000 Median : 4.000
## Mean : 1.036 Mean : 1.942 Mean : 4.905 Mean : 4.547
## 3rd Qu.: 1.000 3rd Qu.: 4.000 3rd Qu.: 5.000 3rd Qu.: 5.000
## Max. :15.000 Max. :12.000 Max. :25.000 Max. :15.000
##
## P21 P22 P23 P24
## Min. : 1.00 Min. :1.000 Min. : 1.000 Min. : 0.000
## 1st Qu.: 1.00 1st Qu.:1.000 1st Qu.: 1.000 1st Qu.: 0.000
## Median : 1.00 Median :2.000 Median : 2.000 Median : 0.000
## Mean : 2.27 Mean :2.226 Mean : 3.423 Mean : 1.372
## 3rd Qu.: 3.00 3rd Qu.:3.000 3rd Qu.: 5.000 3rd Qu.: 2.000
## Max. :15.00 Max. :5.000 Max. :25.000 Max. :10.000
##
## P25 P26 P27 P28
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 1.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 2.000
## Median : 0.000 Median : 0.000 Median : 0.000 Median : 2.500
## Mean : 1.212 Mean : 1.471 Mean : 1.146 Mean : 3.223
## 3rd Qu.: 2.000 3rd Qu.: 2.500 3rd Qu.: 2.000 3rd Qu.: 4.000
## Max. :10.000 Max. :12.500 Max. :12.500 Max. :12.500
##
## P29 P30 P31 P32
## Min. :0.000 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.:2.500 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.000
## Median :3.000 Median : 0.00 Median : 0.000 Median : 0.000
## Mean :3.135 Mean : 2.73 Mean : 1.942 Mean : 2.526
## 3rd Qu.:3.000 3rd Qu.: 4.00 3rd Qu.: 3.000 3rd Qu.: 3.000
## Max. :7.500 Max. :25.00 Max. :15.000 Max. :25.000
##
## P33 P34 P35 P36
## Min. :0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.:0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median :0.000 Median : 0.000 Median : 0.000 Median : 0.000
## Mean :1.139 Mean : 2.489 Mean : 2.029 Mean : 2.212
## 3rd Qu.:2.000 3rd Qu.: 3.000 3rd Qu.: 4.000 3rd Qu.: 3.000
## Max. :6.000 Max. :24.000 Max. :15.000 Max. :20.000
##
## P37 revenue
## Min. :0.000 Min. : 1149870
## 1st Qu.:0.000 1st Qu.: 2999068
## Median :0.000 Median : 3939804
## Mean :1.117 Mean : 4453533
## 3rd Qu.:2.000 3rd Qu.: 5166635
## Max. :8.000 Max. :19696939
## attach(train)
dim(train)## [1] 137 43sum(!complete.cases(train))## [1] 0Obeservations:-
The train dataset has ony 137 observations which is pretty small when it comes to building a prediction model so there is no need to split it further into training and validation datasets.
There are no NA values in the train dataset.
In order to check the revenue pattern in the dataset we need to plot histograms. Also the variables P1 to P37 need to be examined for “0” values.
4. DATA VISUALISATION
library(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphalibrary(reshape)
qplot(x = revenue, y = City, data = train, color = City.Group, size = Type)## Warning: Using size for a discrete variable is not advised.
train_plot <- melt(train[,-c(1:5)])## Using as id variablesggplot(train_plot,aes(x = value)) +
facet_wrap(~variable,scales = "free_x") +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
hist(train$revenue)
ggplot(train, aes(x=Type, y=revenue)) +
geom_point(shape=1) +
geom_smooth()## `geom_smooth()` using method = 'loess'
plot(revenue~., data = train)
Obeservations:-
We can see that there are only three big cities in this dataset namelly Istanbul, Izmir and Ankara, and the rest fall under the “other” category. Also the food courts in Istanbul seem to have the maximum revenue as shown in the scatterplot.
The histogram also has some interesting insights. The variables P1 to P37 have a lot of 0 values as shown from P14 to P18 and then P24 onwards upto P37. The revenue also is right skewed.
Food court seems to be the most popular type of restaurant followed by Inline and then just the one drive through.
Tabular arrangement:-
library(plyr)##
## Attaching package: 'plyr'## The following objects are masked from 'package:reshape':
##
## rename, round_anyx <- train[, c(3, 43)]
y <- aggregate(x$revenue, list(City=x$City), mean)
colnames(y)[2] <- "Average Revenue"
z <- count(x, 'City')
x <- merge(y, z, by = "City")
x<-x[,-3]
x4. Correlation:-
library(corrgram)##
## Attaching package: 'corrgram'## The following object is masked from 'package:plyr':
##
## baseballcorrgram(train[,-c(1,2,3)], order=TRUE, lower.panel=panel.shade,upper.panel=panel.cor,text.panel=panel.txt,main="TFI revenue prediction")
Observations:-
The predictor variables P1 to P37 are definitely postitively correlated. Some of the predictor variables positively affect the revenue whereas some affect it negetively as shown in the corrgram.
5. MODELLING
Since we want to predict the revenue that is to be generated in the upcoming restaurant sites, we will build a linear model based on city group, restaurant type and some significant TFI indicators.
Our hypothesis that a certain variable does not affect the revenue can be tested by the one sample t-test.
t <- apply(train[,-c(1:5)], 2, t.test)
fit <- lm(revenue ~ City.Group + Type + P1 + P2 + P7 , data = train)
summary(fit)##
## Call:
## lm(formula = revenue ~ City.Group + Type + P1 + P2 + P7, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4204859 -1515338 -260522 961954 14055457
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2349141 2605036 0.902 0.3688
## City.GroupOther -894084 493568 -1.811 0.0724 .
## TypeFC 1366421 2571129 0.531 0.5960
## TypeIL 744976 2582728 0.288 0.7735
## P1 -143377 169313 -0.847 0.3987
## P2 566516 288910 1.961 0.0520 .
## P7 -95306 187350 -0.509 0.6118
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2497000 on 130 degrees of freedom
## Multiple R-squared: 0.1016, Adjusted R-squared: 0.06016
## F-statistic: 2.451 on 6 and 130 DF, p-value: 0.02808CONCLUSION
Based on the t-tests we can say that the all the predictor values have some effect on the revenue.
The model that is built on the above factors shows that the p value is less than 0.05 which implies that it has a lowere probability of failing.
This model can now be used on the test dataset to predict the revenue and a decision tree model would be the recommended procedure.