Store 24
Aditya Satheesh
18 December 2017
Summary of dataset
store.df <- read.csv(paste("Store24.csv", sep=""))
View(store.df)
summary(store.df)## 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. :100.00Mean and Standard deviation
library(psych)
describe(store.df)[3:5,3:5]## mean sd median
## Profit 276313.61 89404.08 265014.00
## MTenure 45.30 57.67 24.12
## CTenure 13.93 17.70 7.21Top 10 least profitable stores
attach(store.df)
newdata <- store.df[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 1.347023Top 10 most profitable stores
attach(store.df)
newdata1 <- store.df[order(-Profit),]
newdata1[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 6.636550Scatterplot of Profit vs MTenure
attach(store.df)
library(car)
scatterplot(MTenure, Profit,main="Profit vs MTenure")
Scatterplot of Profit vs CTenure
scatterplot(CTenure, Profit,main="Profit vs CTenure")
Correlation Matrix
x <- cor(store.df)
round(x,digits=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 1.00Correlation
y<-cor(store.df$Profit,store.df$MTenure)
round(y,digits = 2)## [1] 0.44 z<-cor(store.df$Profit,store.df$CTenure)
round(z,digits = 2)## [1] 0.26The correlation between Profit and MTenure is 0.44 The correlation between Profit and CTenure is 0.26
Corrgram
library(corrgram)
library(ellipse)
corrgram(store.df, method="pearson", upper.panel=panel.pie)
We can see that a postive correlation exists between profit and MTenure, profit and pop, profit and PedCount. A weak postive correlation exists between Profit and CTenure, profit and CrewSkill ,profit and MgrSkill and profit and ServQual. A negative correlation exists between profit and Comp,Res and Hours24
We can see that the correlation between profit and MTenure is stronger than the correlation between profit and CTenure. So keeping this in mind decisions can be taken accordingly to extend tenure in order to improve store performance or not.
Pearson’s Correlation test
cor.test(store.df[,"Profit"],store.df[,"MTenure"])##
## Pearson's product-moment correlation
##
## data: store.df[, "Profit"] and store.df[, "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.df[,"Profit"],store.df[,"CTenure"])##
## Pearson's product-moment correlation
##
## data: store.df[, "Profit"] and store.df[, "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
## 0.2576789The p value for the Pearson’s Correlation Test between profit and MTenure is 8e-05
The p value for the Pearson’s Correlation Test between profit and CTenure is 0.03
Regression Analysis
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-12The explanatory variables that are statistically significant are - MTenure - CTenure - Comp - Pop - PedCount - Res - Hours24
The explanatory variables that are statistically insignificant are - Visibility
We see that there is an expected increase of 760.99 Profit for every one month increase in Manager Tenure.
Profit = 7610.04 + 760.99 x MTenure
We see that there is an expected increase of 944.98 Profit for every one month increase in Crew Tenure.
Profit = 7610.14 + 944.98 x CTenure.
Executive Summary
From running the regression we get
- The regression coefficients of the variables with respect to Profit and whether they are significantly different or not.
- The multiple R-squared(0.638) indicates that the model accounts for 63.8% of the variance in Profits.
- The residual standard error (5700) can be thought of as the average error in predicting profits from the various factors in this model.
- The F statistic tests whether the predictor variables, taken together, predict the response variables above chance levels.
- Once we run the regression analysis we obtain equations for Profit in relation to Mtenure and CTenure as has been mentioned above. We can see from this that the increase in Crew Tenure seems to have a greater impact on profits than increase in Manager Tenure.