Summary of the given dataset

setwd("C:/Users/Jaswanth/Downloads")
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

Analysis of the Mean and Standard Deviation of Profit

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

Mean and Standard deviation of CTenure

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

Mean and Standard Deviation of MTenure

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

Most profitable stores

attach(store)
## The following object is masked _by_ .GlobalEnv:
## 
##     store
newdata <- store[order(-Profit),c("store","Profit","MTenure","CTenure")]
newdata[1:10,]
##    store Profit   MTenure    CTenure
## 74    74 518998 171.09720  29.519510
## 7      7 476355  62.53080   7.326488
## 9      9 474725 108.99350   6.061602
## 6      6 469050 149.93590  11.351130
## 44    44 439781 182.23640 114.151900
## 2      2 424007  86.22219   6.636550
## 45    45 410149  47.64565   9.166325
## 18    18 394039 239.96980  33.774130
## 11    11 389886  44.81977   2.036961
## 47    47 387853  12.84790   6.636550

Least profitable stores

bottom <- store[order(Profit),c("store","Profit","MTenure","CTenure")]
bottom[1:10,]
##    store Profit     MTenure   CTenure
## 57    57 122180  24.3485700  2.956879
## 66    66 146058 115.2039000  3.876797
## 41    41 147327  14.9180200 11.926080
## 55    55 147672   6.6703910 18.365500
## 32    32 149033  36.0792600  6.636550
## 13    13 152513   0.6571813  1.577002
## 54    54 159792   6.6703910  3.876797
## 52    52 169201  24.1185600  3.416838
## 61    61 177046  21.8184200 13.305950
## 37    37 187765  23.1985000  1.347023

Scatter Plot of Profit vs. MTenure

library(car)
scatterplot(Profit~MTenure,main = "Scatterplot of Profit vs Mtenure",pch=19)

## Scatter Plot of Profit vs. CTenure

scatterplot(Profit~CTenure,main = "Scatterplot of Profit vs Ctenure",pch=19)

## Correlation Matrix corrected to two decimal places

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

Correlation between Profit and MTenure

round(cor(Profit,MTenure),2)
## [1] 0.44

Correlation between Profit and CTenure

round(cor(Profit,CTenure),2)
## [1] 0.26

Corrgram based on all variables

library(corrplot)
## corrplot 0.84 loaded
corrplot.mixed(main = "Corrgram of store variables",corr = cor(store),lower = "shade",upper="pie")

## Pearsons test between profit and MTenure

cor.test(Profit,MTenure)
## 
##  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

Pearsons test between profit and CTenure

cor.test(Profit,CTenure)
## 
##  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

Regression Analysis

m<-lm(Profit~MTenure)
summary(m)
## 
## Call:
## lm(formula = Profit ~ MTenure)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -177817  -52029   -8635   50871  188316 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 245496.3    11906.4  20.619  < 2e-16 ***
## MTenure        680.3      163.0   4.173 8.19e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 80880 on 73 degrees of freedom
## Multiple R-squared:  0.1926, Adjusted R-squared:  0.1815 
## F-statistic: 17.41 on 1 and 73 DF,  p-value: 8.193e-05
c<-lm(Profit~CTenure)
summary(c)
## 
## Call:
## lm(formula = Profit ~ CTenure)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -139848  -64869   -9022   45057  222393 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 258178.4    12814.4  20.148   <2e-16 ***
## CTenure       1301.7      571.3   2.279   0.0256 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 86970 on 73 degrees of freedom
## Multiple R-squared:  0.0664, Adjusted R-squared:  0.05361 
## F-statistic: 5.192 on 1 and 73 DF,  p-value: 0.02562
comp<-lm(Profit~Comp)
summary(comp)
## 
## Call:
## lm(formula = Profit ~ Comp)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -172707  -65521  -24559   56628  209205 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   362702      30119  12.042  < 2e-16 ***
## Comp          -22807       7520  -3.033  0.00335 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 84830 on 73 degrees of freedom
## Multiple R-squared:  0.1119, Adjusted R-squared:  0.09975 
## F-statistic:   9.2 on 1 and 73 DF,  p-value: 0.003351
pop<-lm(Profit~Pop)
summary(pop)
## 
## Call:
## lm(formula = Profit ~ Pop)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -152198  -52285  -17228   43501  235602 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.123e+05  1.829e+04  11.611  < 2e-16 ***
## Pop         6.513e+00  1.598e+00   4.077 0.000115 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 81240 on 73 degrees of freedom
## Multiple R-squared:  0.1854, Adjusted R-squared:  0.1743 
## F-statistic: 16.62 on 1 and 73 DF,  p-value: 0.000115
pdc<-lm(Profit~PedCount)
summary(pdc)
## 
## Call:
## lm(formula = Profit ~ PedCount)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -131878  -57678   -1538   45741  200501 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   156254      29373   5.320 1.09e-06 ***
## PedCount       40561       9415   4.308 5.06e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 80370 on 73 degrees of freedom
## Multiple R-squared:  0.2027, Adjusted R-squared:  0.1918 
## F-statistic: 18.56 on 1 and 73 DF,  p-value: 5.057e-05
res<-lm(Profit~Res)
summary(res)
## 
## Call:
## lm(formula = Profit ~ Res)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -151243  -62419   -9467   57891  245575 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   345696      51305   6.738 3.18e-09 ***
## Res           -72273      52363  -1.380    0.172    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 88860 on 73 degrees of freedom
## Multiple R-squared:  0.02543,    Adjusted R-squared:  0.01208 
## F-statistic: 1.905 on 1 and 73 DF,  p-value: 0.1717
h24<-lm(Profit~Hours24)
summary(h24)
## 
## Call:
## lm(formula = Profit ~ Hours24)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -153138  -64315  -11246   52884  237458 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   281540      25976   10.84   <2e-16 ***
## Hours24        -6222      28343   -0.22    0.827    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 89980 on 73 degrees of freedom
## Multiple R-squared:  0.0006598,  Adjusted R-squared:  -0.01303 
## F-statistic: 0.0482 on 1 and 73 DF,  p-value: 0.8268
vis<-lm(Profit~Visibility)
summary(vis)
## 
## Call:
## lm(formula = Profit ~ Visibility)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -152838  -63359  -10946   43839  243980 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   226431      43855   5.163 2.02e-06 ***
## Visibility     16196      13840   1.170    0.246    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 89180 on 73 degrees of freedom
## Multiple R-squared:  0.01841,    Adjusted R-squared:  0.004966 
## F-statistic: 1.369 on 1 and 73 DF,  p-value: 0.2457

The explanatory variables whose beta-coefficients are statistically significant (p<0.05) are : MTenure, CTenure ,Comp,Pop,PedCount

The explanatory variables whose beta-coefficients are not statistically significant (p>0.05) are : Res,Hours24 , Visibility

The expected change in Profit with 1 month increase in Mtenure is 680.3

The expected change in Profit with 1 month increase in Ctenure is 1301.7

Executive Summary

From the regression analysis of profit on the tenures of manager and the crew, we can clearly conclude that the financial performance will not be affected so much by the tenures but it may change by other factors.

While regression analysis provides an estimate of the strength of the relationship between store’s profit and the response variable, it does not provide a formal hypothesis test for this relationship. It just determines whether this relationship is statistically significant or not.Even when the two regression equations produce nearly identical predictions, the differing levels of variability affect the precision of these predictions.Narrower intervals indicate more precise predictions.

It’s difficult to understand this situation using numbers alone.