store <- read.csv(paste("Store24.csv", sep = ""))
str(store)
## 'data.frame':    75 obs. of  14 variables:
##  $ store     : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Sales     : int  1060294 1619874 1099921 1053860 1227841 1703140 1809256 1378482 2113089 1080979 ...
##  $ Profit    : int  265014 424007 222735 210122 300480 469050 476355 361115 474725 278625 ...
##  $ MTenure   : num  0 86.22 23.89 0 3.88 ...
##  $ CTenure   : num  24.8 6.64 5.03 5.37 6.87 ...
##  $ Pop       : int  7535 8630 9695 2797 20335 16926 17754 20824 26519 16381 ...
##  $ Comp      : num  2.8 4.24 4.49 4.25 1.65 ...
##  $ Visibility: int  3 4 3 4 2 3 2 4 2 4 ...
##  $ PedCount  : int  3 3 3 2 5 4 5 3 4 3 ...
##  $ Res       : int  1 1 1 1 0 1 1 1 1 1 ...
##  $ Hours24   : int  1 1 1 1 1 0 1 1 1 0 ...
##  $ CrewSkill : num  3.56 3.2 3.8 2.06 3.65 3.58 3.94 3.98 3.22 3.54 ...
##  $ MgrSkill  : num  3.15 3.56 4.12 4.1 3.59 ...
##  $ ServQual  : num  86.8 94.7 78.9 100 68.4 ...

Q 2c

summary(store)
##      store          Sales             Profit          MTenure      
##  Min.   : 1.0   Min.   : 699306   Min.   :122180   Min.   :  0.00  
##  1st Qu.:19.5   1st Qu.: 984579   1st Qu.:211004   1st Qu.:  6.67  
##  Median :38.0   Median :1127332   Median :265014   Median : 24.12  
##  Mean   :38.0   Mean   :1205413   Mean   :276314   Mean   : 45.30  
##  3rd Qu.:56.5   3rd Qu.:1362388   3rd Qu.:331314   3rd Qu.: 50.92  
##  Max.   :75.0   Max.   :2113089   Max.   :518998   Max.   :277.99  
##     CTenure              Pop             Comp          Visibility  
##  Min.   :  0.8871   Min.   : 1046   Min.   : 1.651   Min.   :2.00  
##  1st Qu.:  4.3943   1st Qu.: 5616   1st Qu.: 3.151   1st Qu.:3.00  
##  Median :  7.2115   Median : 8896   Median : 3.629   Median :3.00  
##  Mean   : 13.9315   Mean   : 9826   Mean   : 3.788   Mean   :3.08  
##  3rd Qu.: 17.2156   3rd Qu.:14104   3rd Qu.: 4.230   3rd Qu.:4.00  
##  Max.   :114.1519   Max.   :26519   Max.   :11.128   Max.   :5.00  
##     PedCount         Res          Hours24       CrewSkill    
##  Min.   :1.00   Min.   :0.00   Min.   :0.00   Min.   :2.060  
##  1st Qu.:2.00   1st Qu.:1.00   1st Qu.:1.00   1st Qu.:3.225  
##  Median :3.00   Median :1.00   Median :1.00   Median :3.500  
##  Mean   :2.96   Mean   :0.96   Mean   :0.84   Mean   :3.457  
##  3rd Qu.:4.00   3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:3.655  
##  Max.   :5.00   Max.   :1.00   Max.   :1.00   Max.   :4.640  
##     MgrSkill        ServQual     
##  Min.   :2.957   Min.   : 57.90  
##  1st Qu.:3.344   1st Qu.: 78.95  
##  Median :3.589   Median : 89.47  
##  Mean   :3.638   Mean   : 87.15  
##  3rd Qu.:3.925   3rd Qu.: 99.90  
##  Max.   :4.622   Max.   :100.00

Q 2d

library(psych)
describe(store)[3:5,3:4]
##              mean       sd
## Profit  276313.61 89404.08
## MTenure     45.30    57.67
## CTenure     13.93    17.70

Mean of profit= 276313.61 SD of profit= 89404.08

Mean of MTenure= 45.30 SD of MTenure= 57.67

Mean of CTenure= 13.93 SD of CTenure= 17.70

Q 2f

Top 10 profitable stores

attach(store)
## The following object is masked _by_ .GlobalEnv:
## 
##     store
ascprofit <- store[order(Profit),]
ascprofit[1:10,1:5]
##    store   Sales Profit     MTenure   CTenure
## 57    57  699306 122180  24.3485700  2.956879
## 66    66  879581 146058 115.2039000  3.876797
## 41    41  744211 147327  14.9180200 11.926080
## 55    55  925744 147672   6.6703910 18.365500
## 32    32  828918 149033  36.0792600  6.636550
## 13    13  857843 152513   0.6571813  1.577002
## 54    54  811190 159792   6.6703910  3.876797
## 52    52 1073008 169201  24.1185600  3.416838
## 61    61  716589 177046  21.8184200 13.305950
## 37    37 1202917 187765  23.1985000  1.347023

10 least profitable stores

descprofit <- store[order(-store$Profit),]
descprofit[1:10,1:5] 
##    store   Sales Profit   MTenure    CTenure
## 74    74 1782957 518998 171.09720  29.519510
## 7      7 1809256 476355  62.53080   7.326488
## 9      9 2113089 474725 108.99350   6.061602
## 6      6 1703140 469050 149.93590  11.351130
## 44    44 1807740 439781 182.23640 114.151900
## 2      2 1619874 424007  86.22219   6.636550
## 45    45 1602362 410149  47.64565   9.166325
## 18    18 1704826 394039 239.96980  33.774130
## 11    11 1583446 389886  44.81977   2.036961
## 47    47 1665657 387853  12.84790   6.636550
detach(store)

Q 2g

library(car)
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
scatterplot(Profit~MTenure, data=store, main="Scatterplot of Profit vs. MTenure",pch=16)

Q 2h

scatterplot(Profit~CTenure, data=store, main="Scatterplot of Profit vs. CTenure",pch=16)

Q. 2i

round(cor(store),2)
##            store Sales Profit MTenure CTenure   Pop  Comp Visibility
## store       1.00 -0.23  -0.20   -0.06    0.02 -0.29  0.03      -0.03
## Sales      -0.23  1.00   0.92    0.45    0.25  0.40 -0.24       0.13
## Profit     -0.20  0.92   1.00    0.44    0.26  0.43 -0.33       0.14
## MTenure    -0.06  0.45   0.44    1.00    0.24 -0.06  0.18       0.16
## CTenure     0.02  0.25   0.26    0.24    1.00  0.00 -0.07       0.07
## Pop        -0.29  0.40   0.43   -0.06    0.00  1.00 -0.27      -0.05
## Comp        0.03 -0.24  -0.33    0.18   -0.07 -0.27  1.00       0.03
## Visibility -0.03  0.13   0.14    0.16    0.07 -0.05  0.03       1.00
## PedCount   -0.22  0.42   0.45    0.06   -0.08  0.61 -0.15      -0.14
## Res        -0.03 -0.17  -0.16   -0.06   -0.34 -0.24  0.22       0.02
## Hours24     0.03  0.06  -0.03   -0.17    0.07 -0.22  0.13       0.05
## CrewSkill   0.05  0.16   0.16    0.10    0.26  0.28 -0.04      -0.20
## MgrSkill   -0.07  0.31   0.32    0.23    0.12  0.08  0.22       0.07
## ServQual   -0.32  0.39   0.36    0.18    0.08  0.12  0.02       0.21
##            PedCount   Res Hours24 CrewSkill MgrSkill ServQual
## store         -0.22 -0.03    0.03      0.05    -0.07    -0.32
## Sales          0.42 -0.17    0.06      0.16     0.31     0.39
## Profit         0.45 -0.16   -0.03      0.16     0.32     0.36
## MTenure        0.06 -0.06   -0.17      0.10     0.23     0.18
## CTenure       -0.08 -0.34    0.07      0.26     0.12     0.08
## Pop            0.61 -0.24   -0.22      0.28     0.08     0.12
## Comp          -0.15  0.22    0.13     -0.04     0.22     0.02
## Visibility    -0.14  0.02    0.05     -0.20     0.07     0.21
## PedCount       1.00 -0.28   -0.28      0.21     0.09    -0.01
## Res           -0.28  1.00   -0.09     -0.15    -0.03     0.09
## Hours24       -0.28 -0.09    1.00      0.11    -0.04     0.06
## CrewSkill      0.21 -0.15    0.11      1.00    -0.02    -0.03
## MgrSkill       0.09 -0.03   -0.04     -0.02     1.00     0.36
## ServQual      -0.01  0.09    0.06     -0.03     0.36     1.00

Q 2j

round(cor(store)[3,4:5],2)
## MTenure CTenure 
##    0.44    0.26

Q 2k

library(corrgram)
corrgram(store, lower.panel = panel.shade, upper.panel = panel.pie, text.panel = panel.txt, main = "Corrgram of store variables")

2l

Pearson’s Correlation test on the correlation between Profit and MTenure

cor.test(store$Profit,store$MTenure)
## 
##  Pearson's product-moment correlation
## 
## data:  store$Profit and store$MTenure
## t = 4.1731, df = 73, p-value = 8.193e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2353497 0.6055175
## sample estimates:
##       cor 
## 0.4388692

correlation between Profit and MTenure = 0.44, p-value = 0.00008 < 0.05

Pearson’s Correlation test on the correlation between Profit and CTenure

cor.test(store$Profit,store$CTenure)
## 
##  Pearson's product-moment correlation
## 
## data:  store$Profit and store$CTenure
## t = 2.2786, df = 73, p-value = 0.02562
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.03262507 0.45786339
## sample estimates:
##       cor 
## 0.2576789

correlation between Profit and CTenure = 0.26, p-value = 0.026 < 0.05

Q 2m

fit <- lm(Profit ~ MTenure+CTenure+Comp+Pop+PedCount+Res+Hours24+Visibility , data =  store)
summary(fit)
## 
## Call:
## lm(formula = Profit ~ MTenure + CTenure + Comp + Pop + PedCount + 
##     Res + Hours24 + Visibility, data = store)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -105789  -35946   -7069   33780  112390 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   7610.041  66821.994   0.114 0.909674    
## MTenure        760.993    127.086   5.988 9.72e-08 ***
## CTenure        944.978    421.687   2.241 0.028400 *  
## Comp        -25286.887   5491.937  -4.604 1.94e-05 ***
## Pop              3.667      1.466   2.501 0.014890 *  
## PedCount     34087.359   9073.196   3.757 0.000366 ***
## Res          91584.675  39231.283   2.334 0.022623 *  
## Hours24      63233.307  19641.114   3.219 0.001994 ** 
## Visibility   12625.447   9087.620   1.389 0.169411    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 56970 on 66 degrees of freedom
## Multiple R-squared:  0.6379, Adjusted R-squared:  0.594 
## F-statistic: 14.53 on 8 and 66 DF,  p-value: 5.382e-12

F-statistic = 14.53 and p-value = 5.38e-12 < 0.05

fit$coefficients
##   (Intercept)       MTenure       CTenure          Comp           Pop 
##   7610.041452    760.992734    944.978026 -25286.886662      3.666606 
##      PedCount           Res       Hours24    Visibility 
##  34087.358789  91584.675234  63233.307162  12625.447050

The expected change in the Profit at Store24, if the Manager’s tenure increases by one month is 760.993 The expected change in the Profit at Store24, if the Crew’s tenure increases by one month is 944.978

Q 2n

The explanatory variable(s) whose beta-coefficients are statistically significant (p < 0.05):- MTenure , CTenure, Pop , PedCount , Res , Hours24

The explanatory variable(s) whose beta-coefficients are not statistically significant (p > 0.05):- Visibility

SUMMARY

From the analysis of “Store24 (A) Harvard Case Study” we get the following points

Based on regression analysis ->Visibility of Store does not affect the profit of Store (null hypothesis) ->Manager Tenure, No. of competitors and pedastrian foot traffic volume has highest affect on the profit of store ->These regression analysis are correct up to r-square = 63.79% which is good fit Based on correlation matrix and plots ->Profit of store has a very high positive correlation with Sales(0.92) ->Profit has significant positive correlation with Manager Tenure(0.44), Population(0.43), Pedastrian foot traffic(0.45) ->Profit has slight positive correlation with Crew Tenure(0.26), Manager Skill(0.32) and Service Quality(0.36) ->There is also strong positive correlation between Population and Pedastrian foot traffic(0.61) and also slight positive correlation between Manager Skill and Service Quality(0.36) -> Crew Tenure has only a slight negative correlation with location in residential area(-0.34)

Based on Plots ->Most of the crew tenure is slightly less than mean(13.93) and there are only a few outliers (sd = 17.70) ->Manager tenure is more widely distributed around mean(45.30) with many outliers (sd = 57.67) Profit is very closely related to sales.The tenure of the Manager is more dominant in getting more profits than the tenure of the Crew. This is maybe due to the fact that more experienced manager can manage the crew more effectively and thus get more profits.