The main objective of this study is to set up a reliable model to predict the corresponding change in the store profitability, with an increase in the employee tenure.
There are other factors too on which the store profitability could depend on such as site-location, population of the locality, pedestrian access, and number of competitors in the region, and it is not clear whether empoyee tenure and financial performance have a linear relationship or not.There is also no clarity regarding the course of action implemented to retain employees, like increasing wages, implementing bonus plans, instituting new training programs etc.
Setting up, reading and describing the data.
setwd("~/Downloads/Prof Sameer Mathur")
store<-read.csv("Store24.csv")
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
library(psych)
describe(store)
## vars n mean sd median trimmed mad
## store 1 75 38.00 21.79 38.00 38.00 28.17
## Sales 2 75 1205413.12 304531.31 1127332.00 1182031.25 288422.04
## Profit 3 75 276313.61 89404.08 265014.00 270260.34 90532.00
## MTenure 4 75 45.30 57.67 24.12 33.58 29.67
## CTenure 5 75 13.93 17.70 7.21 10.60 6.14
## Pop 6 75 9825.59 5911.67 8896.00 9366.07 7266.22
## Comp 7 75 3.79 1.31 3.63 3.66 0.82
## Visibility 8 75 3.08 0.75 3.00 3.07 0.00
## PedCount 9 75 2.96 0.99 3.00 2.97 1.48
## Res 10 75 0.96 0.20 1.00 1.00 0.00
## Hours24 11 75 0.84 0.37 1.00 0.92 0.00
## CrewSkill 12 75 3.46 0.41 3.50 3.47 0.34
## MgrSkill 13 75 3.64 0.41 3.59 3.62 0.45
## ServQual 14 75 87.15 12.61 89.47 88.62 15.61
## min max range skew kurtosis se
## store 1.00 75.00 74.00 0.00 -1.25 2.52
## Sales 699306.00 2113089.00 1413783.00 0.71 -0.09 35164.25
## Profit 122180.00 518998.00 396818.00 0.62 -0.21 10323.49
## MTenure 0.00 277.99 277.99 2.01 3.90 6.66
## CTenure 0.89 114.15 113.26 3.52 15.00 2.04
## Pop 1046.00 26519.00 25473.00 0.62 -0.23 682.62
## Comp 1.65 11.13 9.48 2.48 11.31 0.15
## Visibility 2.00 5.00 3.00 0.25 -0.38 0.09
## PedCount 1.00 5.00 4.00 0.00 -0.52 0.11
## Res 0.00 1.00 1.00 -4.60 19.43 0.02
## Hours24 0.00 1.00 1.00 -1.82 1.32 0.04
## CrewSkill 2.06 4.64 2.58 -0.43 1.64 0.05
## MgrSkill 2.96 4.62 1.67 0.27 -0.53 0.05
## ServQual 57.90 100.00 42.10 -0.66 -0.72 1.46
Getting an insight on important variables of the dataset:-
mean(store$Profit)
## [1] 276313.6
sd(store$Profit)
## [1] 89404.08
mean(store$MTenure)
## [1] 45.29644
sd(store$MTenure)
## [1] 57.67155
mean(store$CTenure)
## [1] 13.9315
sd(store$CTenure)
## [1] 17.69752
Sorting and subsetting on R
mpg_asc <- mtcars[order(-mtcars$mpg),] # Sorting mpg in the descending order
mpg_asc[1:5,]
## mpg cyl disp hp drat wt qsec vs am gear carb
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
# Using the same methods on the current dataset:-
max_prof <- store[order(-store$Profit),]
max_prof[1:10,]
## store Sales Profit MTenure CTenure Pop Comp Visibility
## 74 74 1782957 518998 171.09720 29.519510 10913 2.319850 3
## 7 7 1809256 476355 62.53080 7.326488 17754 3.377900 2
## 9 9 2113089 474725 108.99350 6.061602 26519 2.637630 2
## 6 6 1703140 469050 149.93590 11.351130 16926 3.184613 3
## 44 44 1807740 439781 182.23640 114.151900 20624 3.628561 3
## 2 2 1619874 424007 86.22219 6.636550 8630 4.235555 4
## 45 45 1602362 410149 47.64565 9.166325 17808 3.472609 5
## 18 18 1704826 394039 239.96980 33.774130 3807 3.994713 5
## 11 11 1583446 389886 44.81977 2.036961 21550 3.272398 2
## 47 47 1665657 387853 12.84790 6.636550 23623 2.422707 2
## PedCount Res Hours24 CrewSkill MgrSkill ServQual
## 74 4 1 0 3.50 4.405556 94.73878
## 7 5 1 1 3.94 4.100000 81.57837
## 9 4 1 1 3.22 3.583333 100.00000
## 6 4 1 0 3.58 4.605556 94.73510
## 44 4 0 1 4.06 4.172222 86.84327
## 2 3 1 1 3.20 3.556667 94.73510
## 45 3 1 1 3.58 4.622222 100.00000
## 18 3 1 1 3.18 3.866667 97.36939
## 11 5 1 1 3.43 3.200000 100.00000
## 47 5 1 1 4.23 3.950000 99.80105
min_prof <- store[order(store$Profit),]
min_prof[1:10,]
## store Sales Profit MTenure CTenure Pop Comp Visibility
## 57 57 699306 122180 24.3485700 2.956879 3642 2.973376 3
## 66 66 879581 146058 115.2039000 3.876797 1046 6.569790 2
## 41 41 744211 147327 14.9180200 11.926080 9701 4.364600 2
## 55 55 925744 147672 6.6703910 18.365500 10532 6.389294 4
## 32 32 828918 149033 36.0792600 6.636550 9697 4.641468 3
## 13 13 857843 152513 0.6571813 1.577002 14186 4.435671 3
## 54 54 811190 159792 6.6703910 3.876797 3747 3.756011 3
## 52 52 1073008 169201 24.1185600 3.416838 14859 6.585143 3
## 61 61 716589 177046 21.8184200 13.305950 3014 3.263994 3
## 37 37 1202917 187765 23.1985000 1.347023 8870 4.491863 3
## PedCount Res Hours24 CrewSkill MgrSkill ServQual
## 57 2 1 1 3.35 2.956667 84.21266
## 66 3 1 1 4.03 3.673333 80.26675
## 41 3 1 1 3.03 3.672222 81.13993
## 55 3 1 1 3.49 3.477778 76.31346
## 32 3 1 0 3.28 3.550000 73.68654
## 13 2 1 1 4.10 3.000000 76.30609
## 54 2 1 1 3.08 3.933333 65.78734
## 52 3 1 1 3.83 3.833333 94.73510
## 61 1 1 1 3.07 3.126667 73.68654
## 37 3 1 1 3.38 4.016667 73.68654
Scatter plots
plot(store$MTenure,store$Profit,cex = 0.6,
main = "Profit vs MTenure",
col = "black",
)
abline(lm(store$Profit~store$MTenure),col = "red")
abline(h = mean(store$Profit),col = "blue", lty = "dotted")
plot(store$CTenure,store$Profit,cex = 0.6,
main = "Profit vs CTenure",
col = "black"
)
abline(lm(store$Profit~store$MTenure),col = "red")
abline(h = mean(store$Profit),col = "blue", lty = "dotted")
Correlation matrix and Corrgram
cor(store[,])
## store Sales Profit MTenure CTenure
## store 1.00000000 -0.22693400 -0.19993481 -0.05655216 0.019930097
## Sales -0.22693400 1.00000000 0.92387059 0.45488023 0.254315184
## Profit -0.19993481 0.92387059 1.00000000 0.43886921 0.257678895
## MTenure -0.05655216 0.45488023 0.43886921 1.00000000 0.243383135
## CTenure 0.01993010 0.25431518 0.25767890 0.24338314 1.000000000
## Pop -0.28936691 0.40348147 0.43063326 -0.06089646 -0.001532449
## Comp 0.03194023 -0.23501372 -0.33454148 0.18087179 -0.070281327
## Visibility -0.02648858 0.13065638 0.13569207 0.15651731 0.066506016
## PedCount -0.22117519 0.42391087 0.45023346 0.06198608 -0.084112627
## Res -0.03142976 -0.16672402 -0.15947734 -0.06234721 -0.340340876
## Hours24 0.02687986 0.06324716 -0.02568703 -0.16513872 0.072865022
## CrewSkill 0.04866273 0.16402179 0.16008443 0.10162169 0.257154817
## MgrSkill -0.07218804 0.31163056 0.32284842 0.22962743 0.124045346
## ServQual -0.32246921 0.38638112 0.36245032 0.18168875 0.081156172
## Pop Comp Visibility PedCount Res
## store -0.289366908 0.03194023 -0.02648858 -0.221175193 -0.03142976
## Sales 0.403481471 -0.23501372 0.13065638 0.423910867 -0.16672402
## Profit 0.430633264 -0.33454148 0.13569207 0.450233461 -0.15947734
## MTenure -0.060896460 0.18087179 0.15651731 0.061986084 -0.06234721
## CTenure -0.001532449 -0.07028133 0.06650602 -0.084112627 -0.34034088
## Pop 1.000000000 -0.26828355 -0.04998269 0.607638861 -0.23693726
## Comp -0.268283553 1.00000000 0.02844548 -0.146325204 0.21923878
## Visibility -0.049982694 0.02844548 1.00000000 -0.141068116 0.02194756
## PedCount 0.607638861 -0.14632520 -0.14106812 1.000000000 -0.28437852
## Res -0.236937265 0.21923878 0.02194756 -0.284378520 1.00000000
## Hours24 -0.221767927 0.12957478 0.04692587 -0.275973353 -0.08908708
## CrewSkill 0.282845090 -0.04229731 -0.19745297 0.213672596 -0.15331247
## MgrSkill 0.083554590 0.22407913 0.07348301 0.087475440 -0.03213640
## ServQual 0.123946521 0.01814508 0.20992919 -0.005445552 0.09081624
## Hours24 CrewSkill MgrSkill ServQual
## store 0.02687986 0.04866273 -0.07218804 -0.322469213
## Sales 0.06324716 0.16402179 0.31163056 0.386381121
## Profit -0.02568703 0.16008443 0.32284842 0.362450323
## MTenure -0.16513872 0.10162169 0.22962743 0.181688755
## CTenure 0.07286502 0.25715482 0.12404535 0.081156172
## Pop -0.22176793 0.28284509 0.08355459 0.123946521
## Comp 0.12957478 -0.04229731 0.22407913 0.018145080
## Visibility 0.04692587 -0.19745297 0.07348301 0.209929194
## PedCount -0.27597335 0.21367260 0.08747544 -0.005445552
## Res -0.08908708 -0.15331247 -0.03213640 0.090816237
## Hours24 1.00000000 0.10536295 -0.03883007 0.058325655
## CrewSkill 0.10536295 1.00000000 -0.02100949 -0.033516504
## MgrSkill -0.03883007 -0.02100949 1.00000000 0.356702708
## ServQual 0.05832565 -0.03351650 0.35670271 1.000000000
cor(store$Profit,store$MTenure)
## [1] 0.4388692
cor(store$Profit,store$CTenure)
## [1] 0.2576789
library(corrgram)
par(mfrow = c(1,1))
cols <- colorRampPalette(c("darkgreen","blue"))
corrgram(store,order = FALSE,
upper.panel = panel.pie,
lower.panel = panel.shade,
text.panel = panel.txt,
main = "Corrgram of the dataset",
col.regions = cols
)
Pearson’s correlation tests
cor.test(store$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$CTenure
## t = 2.2786, df = 73, p-value = 0.02562
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.03262507 0.45786339
## sample estimates:
## cor
## 0.2576789
p value for profit vs Mtenure : 8.193e-05
There is a relationship between Profit and Mtenure, and the NULL hyppthesis should be rejected as p-value<0.05
p value for profit vs Ctenure : 0.02562
There is a relationship between Profit and Ctenure, the NULL hypothesis should be rejected as the p-value here is < 0.05
Regression analysis
fit <- lm(store$Profit ~ store$MTenure + store$CTenure + store$Comp + store$Pop + store$PedCount + store$Res + store$Hours24 + store$Visibility)
fit
##
## Call:
## lm(formula = store$Profit ~ store$MTenure + store$CTenure + store$Comp +
## store$Pop + store$PedCount + store$Res + store$Hours24 +
## store$Visibility)
##
## Coefficients:
## (Intercept) store$MTenure store$CTenure store$Comp
## 7610.041 760.993 944.978 -25286.887
## store$Pop store$PedCount store$Res store$Hours24
## 3.667 34087.359 91584.675 63233.307
## store$Visibility
## 12625.447
lm(store$Profit ~ store$MTenure + store$CTenure + store$Comp + store$Pop + store$PedCount + store$Res + store$Hours24 + store$Visibility)$coefficient
## (Intercept) store$MTenure store$CTenure store$Comp
## 7610.041452 760.992734 944.978026 -25286.886662
## store$Pop store$PedCount store$Res store$Hours24
## 3.666606 34087.358789 91584.675234 63233.307162
## store$Visibility
## 12625.447050
summary(fit)
##
## Call:
## lm(formula = store$Profit ~ store$MTenure + store$CTenure + store$Comp +
## store$Pop + store$PedCount + store$Res + store$Hours24 +
## store$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
## store$MTenure 760.993 127.086 5.988 9.72e-08 ***
## store$CTenure 944.978 421.687 2.241 0.028400 *
## store$Comp -25286.887 5491.937 -4.604 1.94e-05 ***
## store$Pop 3.667 1.466 2.501 0.014890 *
## store$PedCount 34087.359 9073.196 3.757 0.000366 ***
## store$Res 91584.675 39231.283 2.334 0.022623 *
## store$Hours24 63233.307 19641.114 3.219 0.001994 **
## store$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
lm(store$Profit ~ store$MTenure + store$CTenure + store$Comp + store$Pop + store$PedCount + store$Res + store$Hours24 + store$Visibility)$coefficient
## (Intercept) store$MTenure store$CTenure store$Comp
## 7610.041452 760.992734 944.978026 -25286.886662
## store$Pop store$PedCount store$Res store$Hours24
## 3.666606 34087.358789 91584.675234 63233.307162
## store$Visibility
## 12625.447050
Intercept and Visibility are the only two variables which are statistically insignificant i.e their p-value > 0.05
From the regression analysis we can see that both the manager’s and the crew member’s tenure has a significant effect on the store profit. An increase of 1 month in both the manager’s and the crew member’s tenure results in an increase in store profit by 760.99 dollars and 944.97 dollars respectively.