store.df <-read.csv(paste ("Store24.csv", sep=""))
View(store.df)

TASK 4d

Three very important variables in this analysis are the store Profit, the management tenure (MTenure) and the crew tenure (CTenure). ####Use R to measure the mean and standard deviation of Profit. Rrequired mean is:

mean(store.df$Profit)
## [1] 276313.6

Required standard deviation is:

sd(store.df$Profit)
## [1] 89404.08

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

Rrequired mean is:

mean(store.df$MTenure)
## [1] 45.29644

Required standard deviation is:

sd(store.df$MTenure)
## [1] 57.67155

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

Rrequired mean is:

mean(store.df$CTenure)
## [1] 13.9315

Required standard deviation is:

sd(store.df$CTenure)
## [1] 17.69752

TASK 4e - Sorting and Subsetting data in R

In this TASK, we will learn how to sort a dataframe based on a data column

attach(mtcars)
View(mtcars)
newdata <- mtcars[order(mpg),] # sort by mpg (ascending)
View(newdata)

In the above code, the order() function helps us sort the data in mtcars, based on a data column called mpg. We can sort in ascending order or descending order.

newdata[1:5,] # see the 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
newdata <- mtcars[order(-mpg),] # sort by mpg (descending)
View(newdata)
detach(mtcars)

After sorting, notice how we can view the top 5 cars that have the highest and lowest mpg respectively.

TASK 4f- Replicate Exhibit 1 shown in the case, using R

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

  attach(store.df)
  myStore <- store.df[order(-Profit),]
  myStore[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   6.636550

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

  myStore <- store.df[order(Profit),]
  myStore[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  1.347023

TASK 4g - Scatter Plots

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

  library(car)
  scatterplot(Profit ~ MTenure,
              xlab="MTenure", ylab="Profit",
              main="Scatter Plot of Profit VS MTenure", )

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

  scatterplot(Profit ~ CTenure,
              xlab="CTenure", ylab="Profit",
              main="Scatter Plot of Profit VS CTenure", )

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

  round(cor(store.df),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 - Correlations

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(store.df, order=FALSE, 
         lower.panel=panel.shade, upper.panel=panel.pie,
         text.panel=panel.txt, 
         main="Corrgram of Store Variables"
         )

Critically think about how the Profit is correlated with the other variables (e.g. MTenure, CTenure, Sales, Pop, Comp etc).
Qualitatively discuss the managerially relevant correlations. ###TASK 4l - Pearson’s Correlation Tests ####Run a Pearson’s Correlation test on the correlation between Profit and MTenure. What is the p-value? p-value is: 8.193e-05

 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

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

p-value is: 0.02562

  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 3m - Regression Analysis

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

summary(lm(Profit ~ MTenure + CTenure + Comp + Pop + PedCount + Res + Hours24 + Visibility, data=store.df ))
## 
## Call:
## lm(formula = Profit ~ MTenure + CTenure + Comp + Pop + PedCount + 
##     Res + Hours24 + Visibility, data = store.df)
## 
## 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

Based on TASK 3m, answer the following questions:

List the explanatory variable(s) whose beta-coefficients are statistically significant (p < 0.05).

  1. MTenure

  2. CTenure

  3. Comp

  4. Pop

  5. PedCount

  6. Res

  7. Hours24

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

TASK 4o

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? Profit will be gained of 760.993 if this expected change takes place at a store.

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?

Profit will be of 944.978 if this expected change takes place at a store.

TASK 4p