Task 2c

Using R, read the data into a data frame called store. Play close attention to Exhibit 3 - Summary Statistics from Sample Stores from the CASE. Using R, get the summary statistics of the data. Confirm that the summary statistics generated from R are consistent with Exhibit 3 from the Case.

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

Task 2d

Three very important variables in this analysis are the store Profit, the management tenure (MTenure) and the crew tenure (CTenure).

mean(store$Profit)
## [1] 276313.6
mean(store$MTenure)
## [1] 45.29644
mean(store$CTenure)
## [1] 13.9315
sd(store$Profit)
## [1] 89404.08
sd(store$MTenure)
## [1] 57.67155
sd(store$CTenure)
## [1] 17.69752

Task 2f

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

newdata<-store[order(-store$Profit),]
newdata[1:10,]
##    store   Sales Profit   MTenure    CTenure   Pop     Comp Visibility
## 74    74 1782957 518998 171.09720  29.519510 10913 2.319850          3
## 7      7 1809256 476355  62.53080   7.326488 17754 3.377900          2
## 9      9 2113089 474725 108.99350   6.061602 26519 2.637630          2
## 6      6 1703140 469050 149.93590  11.351130 16926 3.184613          3
## 44    44 1807740 439781 182.23640 114.151900 20624 3.628561          3
## 2      2 1619874 424007  86.22219   6.636550  8630 4.235555          4
## 45    45 1602362 410149  47.64565   9.166325 17808 3.472609          5
## 18    18 1704826 394039 239.96980  33.774130  3807 3.994713          5
## 11    11 1583446 389886  44.81977   2.036961 21550 3.272398          2
## 47    47 1665657 387853  12.84790   6.636550 23623 2.422707          2
##    PedCount Res Hours24 CrewSkill MgrSkill  ServQual
## 74        4   1       0      3.50 4.405556  94.73878
## 7         5   1       1      3.94 4.100000  81.57837
## 9         4   1       1      3.22 3.583333 100.00000
## 6         4   1       0      3.58 4.605556  94.73510
## 44        4   0       1      4.06 4.172222  86.84327
## 2         3   1       1      3.20 3.556667  94.73510
## 45        3   1       1      3.58 4.622222 100.00000
## 18        3   1       1      3.18 3.866667  97.36939
## 11        5   1       1      3.43 3.200000 100.00000
## 47        5   1       1      4.23 3.950000  99.80105
newdata2<-store[order(store$Profit),]
newdata2[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

Task 2g

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

plot(x=store$MTenure,y=store$Profit,main="Profit vs MTenure",xlab = "Mtenure", ylab = "Profit")

Task 2h

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

plot(x=store$CTenure,y=store$Profit,main="Profit vs CTenure",xlab = "Ctenure", ylab = "Profit")

Task 2i

Use R to construct a Correlation Matrix for all the variables in the dataset.

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

Task 2j

Use R to measure the correlation between Profit and MTenure. Use R to measure the correlation between Profit and CTenure.

cor(store$Profit,store$MTenure)
## [1] 0.4388692
cor(store$Profit,store$CTenure)
## [1] 0.2576789

Task 2k

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

library(corrplot)
## Warning: package 'corrplot' was built under R version 3.4.3
## corrplot 0.84 loaded
corr<-cor(store[,])
corrplot(corr,method=c("circle"),type = c("full"),add=FALSE,col=NULL,bg="white",title = "Corrgram of all variables in the data set",diag=TRUE)

Task 2l

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

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-values are 8.193e-5 and 0.02562 respectively for correlation between Profit and MTenure, and Profit and CTenure. Thus, there exists a relation between Profit and MTenure, as well as Profit and CTenure neglecting the null hypothesis since the p values < 0.05.

Task 2m

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,data = store)
summary(fit)
## 
## 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

Task 2n

Based on TASK 2m, answer the following questions:

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

summary(fit)
## 
## 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
fit$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 explanatory variable(s) whose beta-coefficients are statistically significant (p < 0.05) are MTenure, CTenure, Comp, Pop, PedCount, Res and Hours24.

The explanatory variable(s) whose beta-coefficients are not statistically significant (p > 0.05) are the intercept and Visibility.

Task 2o

Based on TASK 2m, answer the following questions:

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? 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$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 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 is 760.99 dollars according to the coefficient of MTenure obtained from the regression analysis.

The 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 is 944.98 dollars according to the coefficient of CTenure obtained from the regression analysis.