getwd()
## [1] "C:/Users/Mohit gupta/Documents/r assignment"
setwd( "C:/Users/Mohit gupta/Documents/r assignment")
store<- read.csv(paste("store24.csv" , sep=''))
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

The mean and standard deviation of Profit.

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

the mean and standard deviation of MTenure.

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

the mean and standard deviation of CTenure.

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

the top 10 most profitable stores.

top10<- store[ order(-store$Profit),]
top10[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

The bottom 10 least profitable stores.

bottom10<- store[ order(store$Profit),]
bottom10[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

a scatter plot of Profit vs. MTenure

plot( x= store$MTenure, y=store$Profit , main = "scatter plot of Profit vs. MTenure", xlab = "M tenure", ylab = "Profit")
abline( lm(store$Profit ~store$MTenure) , col= "green")

a scatter plot of Profit vs. CTenure

plot( x= store$CTenure, y=store$Profit , main = "scatter plot of Profit vs. CTenure", xlab = "Ctenure", ylab = "Profit")
abline( lm(store$Profit ~store$CTenure) , col= "green")

a Correlation Matrix for all the variables in the dataset.

library(psych
        )
corr.test(store, use= "complete")
## Call:corr.test(x = store, use = "complete")
## Correlation matrix 
##            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
## Sample Size 
## [1] 75
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##            store Sales Profit MTenure CTenure  Pop Comp Visibility
## store       0.00  1.00   1.00    1.00    1.00 0.89 1.00       1.00
## Sales       0.05  0.00   0.00    0.00    1.00 0.03 1.00       1.00
## Profit      0.09  0.00   0.00    0.01    1.00 0.01 0.26       1.00
## MTenure     0.63  0.00   0.00    0.00    1.00 1.00 1.00       1.00
## CTenure     0.87  0.03   0.03    0.04    0.00 1.00 1.00       1.00
## Pop         0.01  0.00   0.00    0.60    0.99 0.00 1.00       1.00
## Comp        0.79  0.04   0.00    0.12    0.55 0.02 0.00       1.00
## Visibility  0.82  0.26   0.25    0.18    0.57 0.67 0.81       0.00
## PedCount    0.06  0.00   0.00    0.60    0.47 0.00 0.21       0.23
## Res         0.79  0.15   0.17    0.60    0.00 0.04 0.06       0.85
## Hours24     0.82  0.59   0.83    0.16    0.53 0.06 0.27       0.69
## CrewSkill   0.68  0.16   0.17    0.39    0.03 0.01 0.72       0.09
## MgrSkill    0.54  0.01   0.00    0.05    0.29 0.48 0.05       0.53
## ServQual    0.00  0.00   0.00    0.12    0.49 0.29 0.88       0.07
##            PedCount  Res Hours24 CrewSkill MgrSkill ServQual
## store          1.00 1.00    1.00      1.00     1.00     0.37
## Sales          0.01 1.00    1.00      1.00     0.49     0.05
## Profit         0.00 1.00    1.00      1.00     0.37     0.11
## MTenure        1.00 1.00    1.00      1.00     1.00     1.00
## CTenure        1.00 0.22    1.00      1.00     1.00     1.00
## Pop            0.00 1.00    1.00      1.00     1.00     1.00
## Comp           1.00 1.00    1.00      1.00     1.00     1.00
## Visibility     1.00 1.00    1.00      1.00     1.00     1.00
## PedCount       0.00 0.99    1.00      1.00     1.00     1.00
## Res            0.01 0.00    1.00      1.00     1.00     1.00
## Hours24        0.02 0.45    0.00      1.00     1.00     1.00
## CrewSkill      0.07 0.19    0.37      0.00     1.00     1.00
## MgrSkill       0.46 0.78    0.74      0.86     0.00     0.14
## ServQual       0.96 0.44    0.62      0.78     0.00     0.00
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

Correlations

a] the correlation between Profit and MTenure.

b] the correlation between Profit and CTenure.

x<- store[, c("Profit")]
y<- store[, c ("MTenure" , "CTenure")]
test1<-cor(x,y)
round(test1,2)
##      MTenure CTenure
## [1,]    0.44    0.26

The correlation between Profit and MTenure is .44

The correlation between Profit and CTenure is .26

Corrgram based on all variables in the dataset

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

Profits have very strong positively correlated with sales as compared to others. Profits show positive correlation with population and pedestrian foot traffic volume. However, they are strongly negatively correlated to competition.

Pearson’s Correlation Tests

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
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

The p Value of Pearson’s correlation test between :

1] Profit and MTenure is 8.193e-05 2] Profit and CTenure is .02562

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

regtest <- lm(Profit~ MTenure + CTenure + Comp + Pop + PedCount + Res+ Hours24 + Visibility, data = store)
summary(regtest)
## 
## 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

List of the explanatory variables whose beta-coefficients are statistically significant (p < 0.05) is:

1]MTenure 2]CTenure 3]Comp 4]Pop 5]PedCount 6]Res 7]Hours24

List of the explanatory variables whose beta-coefficients are not statistically significant (p < 0.05) is: 1] Visibility

Answer the following questions: 1]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?

2]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?

regtest$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 Profit at a store increases by 760.99, if the Manager’s tenure i.e. number of months of experience with Store24, increases by one month

The Profit at a store increases by 944.98, if the Crew’s tenure i.e. number of months of experience with Store24, increases by one month

Executive Summary

The relationship between employee tenure and store-level performance is been studied for 75 out of 82 stores of New England’s fourth largest convenience store retailer “store24”. It is found that profits of the stores vary a lot (high standard deviation (i.e. approx. 89000) probably due to a lot of factors affecting it. Also, manager and crew tenures have high deviations. Top 10 profitable stores have experienced staff suggesting some relationship between employee tenure and store level performance as observed through the scatterplot between manager tenure and profits. Manager tenure and profits have a low positive correlation (.44). The same results are observed for crew tenure and profits (.26). Further, regression analysis with profits as dependent variable and MTenure, CTenure Comp, Pop, PedCount, Res, Hours24, Visibility as independent variables depicted that profits are dependent on MTenure, CTenure, Comp, Pop, PedCount, Res and Hours24 (beta coefficients are satistically significant.). Out of these all except competition positively impact profits.