Synopsis

We aim to analyse the data for sales across 75 stores of Store24, to estimate the effect of tenures of manager and crew on the sales, relative to other factors such as site location factors.

Exercise

Using R, read the data into a data frame called store.

store<-read.csv(paste("Store24.csv",sep=""))

Using R, get the summary statistics of the data.

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

1.Use R to measure the mean and standard deviation of Profit.

library(psych)
mean(store$Profit)
## [1] 276313.6
sd(store$Profit)
## [1] 89404.08

2.Use R to measure the mean and standard deviation of MTenure.

library(psych)
mean(store$MTenure)
## [1] 45.29644
sd(store$MTenure)
## [1] 57.67155

3.Use R to measure the mean and standard deviation of CTenure.

library(psych)
mean(store$CTenure)
## [1] 13.9315
sd(store$CTenure)
## [1] 17.69752

4.Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the top 10 most profitable stores.

attach(store)
## The following object is masked _by_ .GlobalEnv:
## 
##     store
newdata<-store[order(-Profit),]
newdata[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)

5.Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the bottom 10 least profitable stores.

attach(store)
## The following object is masked _by_ .GlobalEnv:
## 
##     store
newdata<-store[order(Profit),]
newdata[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
detach(store)

6.Use R to draw a scatter plot of Profit vs. MTenure.

attach(store)
## The following object is masked _by_ .GlobalEnv:
## 
##     store
library(car)
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
scatterplot(Profit~MTenure,data=store,smooth=TRUE,boxplots="xy",reg.line=lm,lwd=1)

7.Use R to draw a scatter plot of Profit vs. CTenure.

attach(store)
## The following object is masked _by_ .GlobalEnv:
## 
##     store
## The following objects are masked from store (pos = 4):
## 
##     Comp, CrewSkill, CTenure, Hours24, MgrSkill, MTenure,
##     PedCount, Pop, Profit, Res, Sales, ServQual, store, Visibility
library(car)
scatterplot(Profit~CTenure,data=store,smooth=TRUE,boxplots="xy",reg.line=lm,lwd=1)

8.Use R to construct a Correlation Matrix for all the variables in the dataset. (Display the numbers up to 2 Decimal places)

res<-cor(store)
round(res,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

9.Use R to measure the correlation between Profit and MTenure. (Display the numbers up to 2 Decimal places)

cor.value<-cor(Profit,MTenure)
round(cor.value,2)
## [1] 0.44

10.Use R to measure the correlation between Profit and CTenure. (Display the numbers up to 2 Decimal places)

cor.value<-cor(Profit,CTenure)
round(cor.value,2)
## [1] 0.26

11.Use R to construct the following Corrgram based on all variables in the dataset.

res<-cor(store)
library(corrgram)
## Warning: package 'corrgram' was built under R version 3.4.3
corrgram(res,upper.panel = panel.pie)

12.Run a Pearson’s Correlation test on the correlation between Profit and MTenure. What is the p-value?

cor.test(Profit,MTenure,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  Profit and 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

The p-value is 8.193e-05.

13.Run a Pearson’s Correlation test on the correlation between Profit and CTenure. What is the p-value?

cor.test(Profit,CTenure,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  Profit and 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

The p-value is 0.02562.

14.Run a regression of Profit on {MTenure, CTenure Comp, Pop, PedCount, Res, Hours24, Visibility}.

fit<-lm(Profit~MTenure + CTenure+Comp+Pop+PedCount+Res+Hours24+Visibility)
summary(fit)
## 
## Call:
## lm(formula = Profit ~ MTenure + CTenure + Comp + Pop + PedCount + 
##     Res + Hours24 + Visibility)
## 
## 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

15.List the explanatory variable(s) whose beta-coefficients are statistically significant (p < 0.05).

MTenure, CTenure, Comp, Pop, PedCount, Res, Hours24 are statistically significant(p<0.05).

16.List the explanatory variable(s) whose beta-coefficients are not statistically significant (p > 0.05).

Visibility is not statistically significant(p>0.05).

17.What is expected change in the Profit at a store, if the Manager’s tenure i.e. number of months of experience with Store24, increases by one month?

fit<-lm(Profit~MTenure + CTenure+Comp+Pop+PedCount+Res+Hours24+Visibility)
coefficients(fit)[2]
##  MTenure 
## 760.9927

Thus, the expected change in Profit at a store, if the Manager’s tenure,i.e. number of months of experience with Store24 increases by one month is 760.9927.

18.What is expected change in the Profit at a store, if the Crew’s tenure i.e. number of months of experience with Store24, increases by one month?

fit<-lm(Profit~MTenure + CTenure+Comp+Pop+PedCount+Res+Hours24+Visibility)
coefficients(fit)[3]
## CTenure 
## 944.978

Thus, the expected change in Profit at a store, if the Crew’s tenure,i.e. number of months of experience with Store24 increases by one month is 944.978.

Executive Summary

In this data analysis our aim was to estimate the direct financial effect of increase the manager’s tenure, as well as the crew’s tenure, on sales. To establish the relation, we also need to consider other factors, due to which the sales may be influenced. While site location factors are usually considered most important in determining sales of any store, in this analysis the impact of the tenure of the manager and the crew, relative to the site location factors in deciding the sales, is to be estimated. It is found that even though the relationship between tenure and sales is completely non-linear, and varies depending even on the quantity of the tenure, the most profitable stores have large tenures of managers as well as crews. Moreover,using Pearson’s correlation test, it is evident that the tenure of manager affects the sales much more positively than tenure of crew. Lastly, carrying out regression analysis yields the outcome that the manager’s tenure affects the sales much more significantly than any other factor. So, it is of utmost importance to optimize the tenure of the manager by increasing salary,allowances, or other schemes.