Store24(A)
Ashutosh Kumar
January 15, 2018
TASK 2(a)
Please critically read the Harvard Business School case study Store24 (A): Managing Employee Retention, by Frances X. Frei and Dennis Campbell This case provides a retailing context in which employee retention strategies are explored through analyzing detailed store-level data. Qualitatively identify the crucial issues being faced by the management. Based on your judgment, prepare a list of the most important questions that matter. The key issue of this case study is that the management is considering new strategies to increase manager crew rentention tenure as they believe it might aid to company’s profit. The first and foremost question that arises is that 1) Do increse in manager-crew tenure affect the profit? If so, 2) How much does increased tenure affect profits? Further, the management wants to use the manager-crew tenure data they have been collecting for years to make informed decisions about investing in skill development programs, increasing salaries or giving bonuses. The next question which arises is 3) Does increased salaries and bonuses help to retain the employees? Or the management have to invest in skill development programs? While site-location factors such as population, number of competitors and pedestrain access are traditionally considered as the primary drivers of store success, ‘people factors’, such as employee skill and experience are also crucial factors in optimizing given site’s performance. Hence, we come to the question 4) How much do site-location factors like competitors, population, visibility of the store front etc affect store’s growth? ## TASK 2(b) Play close attention to Exhibit 2 - Variable Names and Descriptions from the case. Understand what each variable means. Go back to the text of the case and relate each variable of Exhibit 2 to the different points of discussion presented in the case. Think about how might a dataset associated with Exhibit 2 help in answering your list of questions from TASK 2a. ## TASK 2(c) Download and review the Store24.csv data file associated with this case. You may open it in Excel for convenience. 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.
store24 <- read.csv(paste("Store24.csv",sep=""))
View(store24)
summary(store24)## 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## 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. :100.00Task2(d)
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.
attach(store24)mean(Profit)## [1] 276313.6## [1] 276313.6
sd(Profit)## [1] 89404.08## [1] 57.67155Use R to measure the mean and standard deviation of CTenure.
mean(CTenure)## [1] 13.9315## [1] 13.9315sd(CTenure)## [1] 17.69752## [1] 17.69752TASK 2(e) - Sortinng and Subsetting data in R
In this TASK, we will learn how to sort a dataframe based on a data column Understand what the following R code does. Copy-Paste it and Execute it in R. attach(mtcars) View(mtcars) newdata <- mtcars[order(mpg),] # sort by mpg (ascending) View(newdata) newdata[1:5,] # see the first 5 rows newdata <- mtcars[order(-mpg),] # sort by mpg (descending) View(newdata) detach(mtcars) R has an inbuilt dataset called mtcars. 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. After sorting, notice how we can view the top 5 cars that have the highest and lowest mpg respectively.
attach(mtcars)
View(mtcars)
newdata <- mtcars[order(mpg),] # sort by mpg (ascending)
View(newdata)
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## 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 4newdata <- mtcars[order(-mpg),] # sort by mpg (descending)
View(newdata)
detach(mtcars)TASK 2f- 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.
top10 <- store24[order(Profit),]
top10[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## 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 1.347023Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the bottom 10 least profitable stores.
bot10 <- store24[order(-Profit),]
bot10[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## 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 6.636550TASK 2g - Scatter Plots
Use R to draw a scatter plot of Profit vs. MTenure.
library(car)
scatterplot(MTenure,Profit,smoother=loessLine,smooth = TRUE, span = 0.6,smoother.args=list(lty=2),spread=FALSE,store24, main="Scatterplot of Profit vs MTenure")
abline(lm(Profit~MTenure),col = "green")
## TASK 2h - Scatter Plots (contd.) Use R to draw a scatter plot of Profit vs. CTenure.
library(car)
scatterplot(CTenure,Profit,smoother=loessLine,smooth = TRUE, span = 0.5,smoother.args=list(lty=2),spread=FALSE,store24,main="Scatterplot of Profit vs CTenure")
abline(lm(Profit~CTenure),col = "green")
## TASK 2i - Correlation Matrix Use R to construct a Correlation Matrix for all the variables in the dataset. (Display the numbers up to 2 Decimal places)
cor_store <- cor(store24)
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## 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 1.00TASK 2j - Correlations
Use R to measure the correlation between Profit and MTenure. (Display the numbers up to 2 Decimal places)
cor(Profit,MTenure)## [1] 0.4388692## [1] 0.4388692Use R to measure the correlation between Profit and CTenure. (Display the numbers up to 2 Decimal places)
cor(Profit,CTenure)## [1] 0.2576789## [1] 0.2576789TASK 2k
Use R to construct the following Corrgram based on all variables in the dataset.
TASK 2l - Pearson’s Correlation Tests
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##
## 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
## 0.4388692Run 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##
## 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
## 0.2576789TASK 2m - Regression Analysis
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=store24)
summary(fit)##
## Call:
## lm(formula = Profit ~ MTenure + CTenure + Comp + Pop + PedCount +
## Res + Hours24 + Visibility, data = store24)
##
## 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##
## Call:
## lm(formula = Profit ~ MTenure + CTenure + Comp + Pop + PedCount +
## Res + Hours24 + Visibility, data = store24)
##
## 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-12TASK 2n
Based on TASK 2m, answer the following questions: List the explanatory variable(s) whose beta-coefficients are statistically significant (p < 0.05).
summary(fit)$coef[summary(fit)$coef[,4] <= 0.05, 4]## MTenure CTenure Comp Pop PedCount
## 9.715897e-08 2.839955e-02 1.938381e-05 1.489046e-02 3.664408e-04
## Res Hours24
## 2.262320e-02 1.993586e-03## MTenure CTenure Comp Pop PedCount
## 9.715897e-08 2.839955e-02 1.938381e-05 1.489046e-02 3.664408e-04
## Res Hours24
## 2.262320e-02 1.993586e-03List the explanatory variable(s) whose beta-coefficients are not statistically significant (p > 0.05).
summary(fit)$coef[summary(fit)$coef[,4] > 0.05, 4]## (Intercept) Visibility
## 0.9096745 0.1694106## (Intercept) Visibility
## 0.9096745 0.1694106TASK 2m
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?
summary(fit)$coefficients["MTenure",1]## [1] 760.9927## [1] 760.9927What is expected change in the Profit at a store, if the Crew’s tenure i.e. number of months of experience with Store24, increases by one month?
summary(fit)$coefficients["CTenure",1]## [1] 944.978## [1] 944.978
TASK 2n
Please prepare an “Executive Summary”. Please add this to the end of your Rmd file. Specifically, please create a qualitative summary of Managerial Insights, based on your data analysis, especially your Regression Analysis. You may write this in paragraph form or in point form. 1. MTenure, CTenure, Comp, Pop, PedCount, Res & Hours24 variables financially make an impact on the profits and the manager need to invest more on these factors. 2. Visibility has p>0.05 and do not make any significant impact on the profits. Hence, the manager should invest less on this factor. 3. The most profitable store is Store 57. The least profitable store is Store 74. With these insights, the manager should try to maintain the momentum with store 57 and other most profitable stores. While, for Store 74 and other least profitting stores, the manager should try to invest in the factors that affect profits as mentioned in point number 1. 4. The correlation between Profit and MTenure is 0.4388 and correlation between Profit and CTenure is 0.2576. For every 100 rupees profit in the company, a manager has a 44 rupees worth of contribution at an average and a crew makes a 26 rupees worth of contribution. We can observe from TASK 2m, that retaining manager and employee for one more month can add significant value to the profits and therefore we can infer that retaining an employee would cost less for the company than losing them.