TASK 4C

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.

stores.df<- read.csv("Store24.csv")
#summary(stores.df)
library(psych)
describe(stores.df[,2:11])[,c(1:4,8,9)]
##            vars  n       mean        sd       min        max
## Sales         1 75 1205413.12 304531.31 699306.00 2113089.00
## Profit        2 75  276313.61  89404.08 122180.00  518998.00
## MTenure       3 75      45.30     57.67      0.00     277.99
## CTenure       4 75      13.93     17.70      0.89     114.15
## Pop           5 75    9825.59   5911.67   1046.00   26519.00
## Comp          6 75       3.79      1.31      1.65      11.13
## Visibility    7 75       3.08      0.75      2.00       5.00
## PedCount      8 75       2.96      0.99      1.00       5.00
## Res           9 75       0.96      0.20      0.00       1.00
## Hours24      10 75       0.84      0.37      0.00       1.00

TASK 4D

4 D1 Use R to measure the mean and standard deviation of Profit.

mean(stores.df$Profit)
## [1] 276313.6
sd(stores.df$Profit)
## [1] 89404.08

4D2-Use R to measure the mean and standard deviation of MTenure.

mean(stores.df$MTenure)
## [1] 45.29644
sd(stores.df$MTenure)
## [1] 57.67155

4D3-Use R to measure the mean and standard deviation of CTenure.

mean(stores.df$CTenure)
## [1] 13.9315
sd(stores.df$CTenure)
## [1] 17.69752

TASK 4e

Sorting and Subsetting data in R

attach(mtcars)
View(mtcars)
newdata <- mtcars[order(mpg),] 
View(newdata)
newdata[1:5,] # 1 out of first 5 rows
##                      mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Cadillac Fleetwood  10.4   8  472 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8  460 215 3.00 5.424 17.82  0  0    3    4
## Camaro Z28          13.3   8  350 245 3.73 3.840 15.41  0  0    3    4
## Duster 360          14.3   8  360 245 3.21 3.570 15.84  0  0    3    4
## Chrysler Imperial   14.7   8  440 230 3.23 5.345 17.42  0  0    3    4

TASK 4f

4 F1Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the top 10 most profitable stores.

attach(stores.df)
newdata <- stores.df[order(-Profit),]
View(newdata)
newdata[1:10,c("store","Sales","Profit","MTenure","CTenure")]
##    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

4 F2-Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the bottom 10 least profitable stores.

attach(stores.df)
## The following objects are masked from stores.df (pos = 3):
## 
##     Comp, CrewSkill, CTenure, Hours24, MgrSkill, MTenure,
##     PedCount, Pop, Profit, Res, Sales, ServQual, store, Visibility
newdata <- stores.df[order(Profit),]
View(newdata)
newdata[10:1,c("store","Sales","Profit","MTenure","CTenure")]
##    store   Sales Profit     MTenure   CTenure
## 37    37 1202917 187765  23.1985000  1.347023
## 61    61  716589 177046  21.8184200 13.305950
## 52    52 1073008 169201  24.1185600  3.416838
## 54    54  811190 159792   6.6703910  3.876797
## 13    13  857843 152513   0.6571813  1.577002
## 32    32  828918 149033  36.0792600  6.636550
## 55    55  925744 147672   6.6703910 18.365500
## 41    41  744211 147327  14.9180200 11.926080
## 66    66  879581 146058 115.2039000  3.876797
## 57    57  699306 122180  24.3485700  2.956879

TASK 4g

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

library(car)
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
scatterplot(stores.df$MTenure,stores.df$Profit,main = "Scatterplot of Profit Vs MTenure",xlab = "MTenure",ylab = "Profit",lwd = 2,smoother = FALSE)
lw1 <- loess(Profit~MTenure,data = stores.df)
j <- order(stores.df$MTenure)
lines(stores.df$MTenure[j],lw1$fitted[j],col="red",lwd = 2,lty="dashed")

##TASK 4h - Scatter Plots (contd.) Use R to draw a scatter plot of Profit vs. CTenure.

library(car)
scatterplot(stores.df$CTenure,stores.df$Profit,main = "Scatterplot of Profit Vs CTenure",xlab = "CTenure",ylab = "Profit",lwd = 2,smoother = FALSE)
lw1 <- loess(Profit~CTenure,data = stores.df)
j <- order(stores.df$CTenure)
lines(stores.df$CTenure[j],lw1$fitted[j],col="red",lwd = 2,lty="dashed")

##Task 4i- Use R to construct a Correlation Matrix for all the variables in the dataset. (Display the numbers up to 2 Decimal places)

cor <- cor(stores.df)
round(cor,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

TASK 4j

Use R to measure the correlation between Profit and MTenure. (Display the numbers up to 2 Decimal places)

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

Use R to measure the correlation between Profit and CTenure. (Display the numbers up to 2 Decimal places)

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

TASK 4k

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

library(corrgram)
corrgram(stores.df,lower.panel = panel.shade,upper.panel=panel.pie,text.panel = panel.txt,main="Corrgram of Store Variables")

##Task 4l 4 L1- Run a Pearson’s Correlation test on the correlation between Profit and MTenure. What is the p-value?

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

4 L2-Run a Pearson’s Correlation test on the correlation between Profit and CTenure. What is the p-value?

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

TASK 4m

4 M1Run a regression of Profit on {MTenure, CTenure Comp, Pop, PedCount, Res,Hours24, Visibility}.

model <- lm(Profit~MTenure+CTenure+Comp+Pop+PedCount+Res+Hours24+Visibility)
model
## 
## Call:
## lm(formula = Profit ~ MTenure + CTenure + Comp + Pop + PedCount + 
##     Res + Hours24 + Visibility)
## 
## Coefficients:
## (Intercept)      MTenure      CTenure         Comp          Pop  
##    7610.041      760.993      944.978   -25286.887        3.667  
##    PedCount          Res      Hours24   Visibility  
##   34087.359    91584.675    63233.307    12625.447
summary(model)
## 
## 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-12

TASK 4n

List the explanatory variable(s) whose beta-coefficients are statistically significant(p < 0.05). 1. MTenure: Average manager tenure during FY-2000 where tenure is defined as the number of months of experience with Store24 2. CTenure: Average crew tenure during FY-2000 where tenure is defined as the number of months of experience with Store24 4. PedCount: 5-point rating on pedestrian foot traffic volume with 5 being the highest 5. CrewSkill: Skill of Crew in the store (rating out of 5) 6. MgrSkill: Skill of Manager in the store (rating out of 5) 7. ServQual: Service Quality

List the explanatory variable(s) whose beta-coefficients are not statistically significant(p > 0.05). 1. Visibility: 5-point rating on visibility of store front with 5 being the highest 2. Pop: Population within a ½ mile radius

TASK 4o

4 O1-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?

model$coefficients[2]
##  MTenure 
## 760.9927

4 O2-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?

model$coefficients[3]
## CTenure 
## 944.978

Task 4p

Executive Summary

From the above corrgram we obtained that Profit is correlated to MTenure, CTenure, Pop, CrewSkill, MgrSkill and ServQual. from the regression analysis that the an increase in Manager’s experience with Store24 can increase the store’s profit by 760.993. from the regression analysis that the an increase in Crew’s experience with Store24 can increase the store’s profit by 944.978.