Store 24(A):Managing Employee Retention
Zeba Khan
February 12, 2018
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.
store<-read.csv(paste("Store24.csv",sep=","))
View(store)
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. :100.00TASK 4d
1:Use R to measure the mean and standard deviation of Profit
mean(store$Profit)## [1] 276313.6sd(store$Profit)## [1] 89404.082:Use R to measure the mean and standard deviation of MTenure
mean(store$MTenure)## [1] 45.29644sd(store$MTenure)## [1] 57.671553:Use R to measure the mean and standard deviation of CTenure
mean(store$CTenure)## [1] 13.9315sd(store$CTenure)## [1] 17.69752TASK 4e - Sorting and Subsetting data in R
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 4newdata <- mtcars[order(-mpg),] # sort by mpg (descending)
View(newdata)
detach(mtcars)TASK 4f- Replicate Exhibit 1 shown in the case, using R
4:Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the top 10 most profitable stores.
new<-store[order(store$Profit),]
View(new)
new[1:10]## store Sales Profit MTenure CTenure Pop Comp Visibility
## 57 57 699306 122180 24.3485700 2.9568790 3642 2.973376 3
## 66 66 879581 146058 115.2039000 3.8767970 1046 6.569790 2
## 41 41 744211 147327 14.9180200 11.9260800 9701 4.364600 2
## 55 55 925744 147672 6.6703910 18.3655000 10532 6.389294 4
## 32 32 828918 149033 36.0792600 6.6365500 9697 4.641468 3
## 13 13 857843 152513 0.6571813 1.5770020 14186 4.435671 3
## 54 54 811190 159792 6.6703910 3.8767970 3747 3.756011 3
## 52 52 1073008 169201 24.1185600 3.4168380 14859 6.585143 3
## 61 61 716589 177046 21.8184200 13.3059500 3014 3.263994 3
## 37 37 1202917 187765 23.1985000 1.3470230 8870 4.491863 3
## 56 56 916197 189235 4.7974240 2.7268990 13740 4.597269 2
## 49 49 983296 195276 55.4003900 14.6858300 1863 3.713871 4
## 16 16 883864 196277 23.6585300 4.6817250 6872 3.344703 3
## 72 72 848140 196772 126.4745000 27.4496900 3151 3.680586 2
## 71 71 977566 198529 43.8997200 38.3737200 3265 3.856324 2
## 62 62 942915 202641 12.1578600 6.8665300 9820 4.201450 3
## 38 38 991524 203184 15.6080600 1.5770020 6557 4.225993 3
## 15 15 1005627 203951 0.0000000 8.4763860 8684 3.844220 3
## 4 4 1053860 210122 0.0000000 5.3716630 2797 4.253946 4
## 31 31 993597 211885 0.0000000 10.7761800 2578 3.100689 2
## 26 26 898548 211912 0.6571813 20.4353200 9999 4.178195 3
## 36 36 1016950 219292 41.5995800 20.8952800 3218 3.929021 3
## 39 39 979361 221130 34.6991800 5.4866530 8896 5.046338 2
## 64 64 969509 221157 0.0000000 0.8870637 17110 2.378613 4
## 3 3 1099921 222735 23.8885400 5.0266940 9695 4.494666 3
## 40 40 1042664 222913 122.7943000 16.7556500 2521 11.127880 3
## 58 58 989760 227601 4.5674100 4.1067760 8477 3.993874 4
## 27 27 985862 230194 50.1100800 17.4455900 8153 3.719806 3
## 68 68 1018195 236339 17.4481600 2.2669400 9018 3.504810 4
## 51 51 1027035 237344 3.4173430 7.0965090 3126 2.447474 2
## 63 63 1045264 239036 8.2476260 6.8665300 7581 4.136580 3
## 50 50 935257 251013 12.8479000 16.0657100 14653 1.751638 3
## 70 70 1207204 254203 14.9180200 3.8767970 19809 3.122484 3
## 19 19 1127332 261495 3.4173430 16.9856300 4669 2.753616 2
## 14 14 1171491 261571 87.3722600 2.9568790 6898 4.233057 4
## 29 29 924782 263956 19.5182900 23.5400400 11350 5.392077 3
## 42 42 1273855 264072 2.4972890 86.0944600 2106 3.231049 3
## 1 1 1060294 265014 0.0000000 24.8049300 7535 2.797888 3
## 17 17 1095695 265584 31.7090000 3.6468170 14477 2.561704 3
## 24 24 1071307 267354 44.8197700 3.4168380 9069 3.280590 2
## 20 20 1320950 269235 65.0609500 5.9466120 15377 4.148495 3
## 28 28 1141465 273036 23.8885400 16.9856300 14673 3.193422 3
## 23 23 1351972 277414 12.3878700 3.4168380 13797 3.594539 3
## 10 10 1080979 278625 31.4789900 23.1950700 16381 2.270771 4
## 73 73 1115450 279193 41.1395500 6.4065710 6276 4.180132 4
## 25 25 1282886 282124 0.0000000 10.3162200 6183 3.517020 3
## 21 21 1237518 282584 24.1185600 7.2114990 14022 4.020201 3
## 48 48 1243167 284169 31.4789900 8.2464070 8491 4.848749 3
## 33 33 1369092 292745 51.7201700 3.8767970 8177 5.309016 3
## 75 75 1321870 296826 2.2672760 8.7063660 8966 1.886111 4
## 5 5 1227841 300480 3.8773700 6.8665300 20335 1.651364 2
## 65 65 1349972 301641 150.2317000 23.4250500 1075 3.218960 3
## 59 59 1334898 303069 13.3079200 13.7659100 6231 3.301353 3
## 46 46 1339214 315780 6.1775050 5.2566730 9285 3.144458 4
## 35 35 1443230 322624 36.9993100 14.8008200 14361 3.613021 4
## 12 12 1444714 329020 277.9877000 6.6365500 11160 4.903895 4
## 30 30 1874873 333607 73.3414400 23.4250500 1116 3.578323 3
## 43 43 1296711 337233 177.5704000 5.4866530 3495 3.653641 4
## 60 60 1433624 356071 33.5162500 6.4065710 8845 2.719548 3
## 8 8 1378482 361115 0.0000000 56.7720800 20824 2.895114 4
## 67 67 1228052 362067 5.2574510 3.4168380 11552 3.583143 3
## 53 53 1355684 365018 57.2404900 8.2464070 6909 3.156869 2
## 22 22 1433440 367036 18.3682200 25.9548300 8280 4.464360 4
## 69 69 1574290 375393 44.1297300 26.7597500 5050 3.949484 3
## 34 34 1557084 382199 29.1788500 19.7453800 10923 2.361195 4
## 47 47 1665657 387853 12.8479000 6.6365500 23623 2.422707 2
## 11 11 1583446 389886 44.8197700 2.0369610 21550 3.272398 2
## 18 18 1704826 394039 239.9698000 33.7741300 3807 3.994713 5
## 45 45 1602362 410149 47.6456500 9.1663250 17808 3.472609 5
## 2 2 1619874 424007 86.2221900 6.6365500 8630 4.235555 4
## 44 44 1807740 439781 182.2364000 114.1519000 20624 3.628561 3
## 6 6 1703140 469050 149.9359000 11.3511300 16926 3.184613 3
## 9 9 2113089 474725 108.9935000 6.0616020 26519 2.637630 2
## 7 7 1809256 476355 62.5308000 7.3264880 17754 3.377900 2
## 74 74 1782957 518998 171.0972000 29.5195100 10913 2.319850 3
## PedCount Res
## 57 2 1
## 66 3 1
## 41 3 1
## 55 3 1
## 32 3 1
## 13 2 1
## 54 2 1
## 52 3 1
## 61 1 1
## 37 3 1
## 56 3 1
## 49 1 1
## 16 3 1
## 72 1 1
## 71 1 1
## 62 4 1
## 38 2 1
## 15 4 1
## 4 2 1
## 31 2 1
## 26 2 1
## 36 2 1
## 39 4 1
## 64 3 1
## 3 3 1
## 40 4 1
## 58 2 1
## 27 2 1
## 68 2 1
## 51 4 1
## 63 3 1
## 50 4 1
## 70 4 1
## 19 3 1
## 14 2 1
## 29 2 1
## 42 2 1
## 1 3 1
## 17 4 1
## 24 3 1
## 20 2 1
## 28 4 1
## 23 4 1
## 10 3 1
## 73 3 1
## 25 3 1
## 21 3 1
## 48 2 1
## 33 2 1
## 75 4 0
## 5 5 0
## 65 1 1
## 59 3 1
## 46 3 1
## 35 3 1
## 12 4 1
## 30 2 1
## 43 3 1
## 60 4 1
## 8 3 1
## 67 3 1
## 53 2 1
## 22 3 1
## 69 3 1
## 34 4 1
## 47 5 1
## 11 5 1
## 18 3 1
## 45 3 1
## 2 3 1
## 44 4 0
## 6 4 1
## 9 4 1
## 7 5 1
## 74 4 15:Use R to print the {StoreID, Sales, Profit, MTenure, CTenure} of the bottom 10 least profitable stores.
new<-store[order(-store$Profit),]
View(new)
new[1:10]## store Sales Profit MTenure CTenure Pop Comp Visibility
## 74 74 1782957 518998 171.0972000 29.5195100 10913 2.319850 3
## 7 7 1809256 476355 62.5308000 7.3264880 17754 3.377900 2
## 9 9 2113089 474725 108.9935000 6.0616020 26519 2.637630 2
## 6 6 1703140 469050 149.9359000 11.3511300 16926 3.184613 3
## 44 44 1807740 439781 182.2364000 114.1519000 20624 3.628561 3
## 2 2 1619874 424007 86.2221900 6.6365500 8630 4.235555 4
## 45 45 1602362 410149 47.6456500 9.1663250 17808 3.472609 5
## 18 18 1704826 394039 239.9698000 33.7741300 3807 3.994713 5
## 11 11 1583446 389886 44.8197700 2.0369610 21550 3.272398 2
## 47 47 1665657 387853 12.8479000 6.6365500 23623 2.422707 2
## 34 34 1557084 382199 29.1788500 19.7453800 10923 2.361195 4
## 69 69 1574290 375393 44.1297300 26.7597500 5050 3.949484 3
## 22 22 1433440 367036 18.3682200 25.9548300 8280 4.464360 4
## 53 53 1355684 365018 57.2404900 8.2464070 6909 3.156869 2
## 67 67 1228052 362067 5.2574510 3.4168380 11552 3.583143 3
## 8 8 1378482 361115 0.0000000 56.7720800 20824 2.895114 4
## 60 60 1433624 356071 33.5162500 6.4065710 8845 2.719548 3
## 43 43 1296711 337233 177.5704000 5.4866530 3495 3.653641 4
## 30 30 1874873 333607 73.3414400 23.4250500 1116 3.578323 3
## 12 12 1444714 329020 277.9877000 6.6365500 11160 4.903895 4
## 35 35 1443230 322624 36.9993100 14.8008200 14361 3.613021 4
## 46 46 1339214 315780 6.1775050 5.2566730 9285 3.144458 4
## 59 59 1334898 303069 13.3079200 13.7659100 6231 3.301353 3
## 65 65 1349972 301641 150.2317000 23.4250500 1075 3.218960 3
## 5 5 1227841 300480 3.8773700 6.8665300 20335 1.651364 2
## 75 75 1321870 296826 2.2672760 8.7063660 8966 1.886111 4
## 33 33 1369092 292745 51.7201700 3.8767970 8177 5.309016 3
## 48 48 1243167 284169 31.4789900 8.2464070 8491 4.848749 3
## 21 21 1237518 282584 24.1185600 7.2114990 14022 4.020201 3
## 25 25 1282886 282124 0.0000000 10.3162200 6183 3.517020 3
## 73 73 1115450 279193 41.1395500 6.4065710 6276 4.180132 4
## 10 10 1080979 278625 31.4789900 23.1950700 16381 2.270771 4
## 23 23 1351972 277414 12.3878700 3.4168380 13797 3.594539 3
## 28 28 1141465 273036 23.8885400 16.9856300 14673 3.193422 3
## 20 20 1320950 269235 65.0609500 5.9466120 15377 4.148495 3
## 24 24 1071307 267354 44.8197700 3.4168380 9069 3.280590 2
## 17 17 1095695 265584 31.7090000 3.6468170 14477 2.561704 3
## 1 1 1060294 265014 0.0000000 24.8049300 7535 2.797888 3
## 42 42 1273855 264072 2.4972890 86.0944600 2106 3.231049 3
## 29 29 924782 263956 19.5182900 23.5400400 11350 5.392077 3
## 14 14 1171491 261571 87.3722600 2.9568790 6898 4.233057 4
## 19 19 1127332 261495 3.4173430 16.9856300 4669 2.753616 2
## 70 70 1207204 254203 14.9180200 3.8767970 19809 3.122484 3
## 50 50 935257 251013 12.8479000 16.0657100 14653 1.751638 3
## 63 63 1045264 239036 8.2476260 6.8665300 7581 4.136580 3
## 51 51 1027035 237344 3.4173430 7.0965090 3126 2.447474 2
## 68 68 1018195 236339 17.4481600 2.2669400 9018 3.504810 4
## 27 27 985862 230194 50.1100800 17.4455900 8153 3.719806 3
## 58 58 989760 227601 4.5674100 4.1067760 8477 3.993874 4
## 40 40 1042664 222913 122.7943000 16.7556500 2521 11.127880 3
## 3 3 1099921 222735 23.8885400 5.0266940 9695 4.494666 3
## 64 64 969509 221157 0.0000000 0.8870637 17110 2.378613 4
## 39 39 979361 221130 34.6991800 5.4866530 8896 5.046338 2
## 36 36 1016950 219292 41.5995800 20.8952800 3218 3.929021 3
## 26 26 898548 211912 0.6571813 20.4353200 9999 4.178195 3
## 31 31 993597 211885 0.0000000 10.7761800 2578 3.100689 2
## 4 4 1053860 210122 0.0000000 5.3716630 2797 4.253946 4
## 15 15 1005627 203951 0.0000000 8.4763860 8684 3.844220 3
## 38 38 991524 203184 15.6080600 1.5770020 6557 4.225993 3
## 62 62 942915 202641 12.1578600 6.8665300 9820 4.201450 3
## 71 71 977566 198529 43.8997200 38.3737200 3265 3.856324 2
## 72 72 848140 196772 126.4745000 27.4496900 3151 3.680586 2
## 16 16 883864 196277 23.6585300 4.6817250 6872 3.344703 3
## 49 49 983296 195276 55.4003900 14.6858300 1863 3.713871 4
## 56 56 916197 189235 4.7974240 2.7268990 13740 4.597269 2
## 37 37 1202917 187765 23.1985000 1.3470230 8870 4.491863 3
## 61 61 716589 177046 21.8184200 13.3059500 3014 3.263994 3
## 52 52 1073008 169201 24.1185600 3.4168380 14859 6.585143 3
## 54 54 811190 159792 6.6703910 3.8767970 3747 3.756011 3
## 13 13 857843 152513 0.6571813 1.5770020 14186 4.435671 3
## 32 32 828918 149033 36.0792600 6.6365500 9697 4.641468 3
## 55 55 925744 147672 6.6703910 18.3655000 10532 6.389294 4
## 41 41 744211 147327 14.9180200 11.9260800 9701 4.364600 2
## 66 66 879581 146058 115.2039000 3.8767970 1046 6.569790 2
## 57 57 699306 122180 24.3485700 2.9568790 3642 2.973376 3
## PedCount Res
## 74 4 1
## 7 5 1
## 9 4 1
## 6 4 1
## 44 4 0
## 2 3 1
## 45 3 1
## 18 3 1
## 11 5 1
## 47 5 1
## 34 4 1
## 69 3 1
## 22 3 1
## 53 2 1
## 67 3 1
## 8 3 1
## 60 4 1
## 43 3 1
## 30 2 1
## 12 4 1
## 35 3 1
## 46 3 1
## 59 3 1
## 65 1 1
## 5 5 0
## 75 4 0
## 33 2 1
## 48 2 1
## 21 3 1
## 25 3 1
## 73 3 1
## 10 3 1
## 23 4 1
## 28 4 1
## 20 2 1
## 24 3 1
## 17 4 1
## 1 3 1
## 42 2 1
## 29 2 1
## 14 2 1
## 19 3 1
## 70 4 1
## 50 4 1
## 63 3 1
## 51 4 1
## 68 2 1
## 27 2 1
## 58 2 1
## 40 4 1
## 3 3 1
## 64 3 1
## 39 4 1
## 36 2 1
## 26 2 1
## 31 2 1
## 4 2 1
## 15 4 1
## 38 2 1
## 62 4 1
## 71 1 1
## 72 1 1
## 16 3 1
## 49 1 1
## 56 3 1
## 37 3 1
## 61 1 1
## 52 3 1
## 54 2 1
## 13 2 1
## 32 3 1
## 55 3 1
## 41 3 1
## 66 3 1
## 57 2 1TASK 4g - Scatter Plots
6:Use R to draw a scatter plot of Profit vs. MTenure
plot(store$MTenure,store$Profit, col="blue",main="Profit vs. MTenure",ylab="Profit",xlab="Manager Tenure")
abline(h=mean(store$Profit),col="dark blue", lty="dotted")
abline(v=mean(store$MTenure),col="dark blue", lty="dotted")
abline(lm(store$MTenure~store$Profit))
TASK 4h - Scatter Plots (contd.)
Use R to draw a scatter plot of Profit vs. CTenure.
plot(store$CTenure,store$Profit, col="blue",main="Profit vs. CTenure",xlab="Crew Tenure",ylab="Profit")
abline(h=mean(store$Profit),col="dark blue", lty="dotted")
abline(v=mean(store$CTenure),col="dark blue", lty="dotted")
abline(lm(store$CTenure~store$Profit))
TASK 4i - Correlation Matrix
8:Use R to construct a Correlation Matrix for all the variables in the dataset.
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 1.00TASK 4j - Correlations
9:Use R to measure the correlation between Profit and MTenure.
round(cor(store$Profit,store$MTenure),2)## [1] 0.4410:Use R to measure the correlation between Profit and CTenure.
round(cor(store$Profit,store$CTenure),2)## [1] 0.26TASK 4k
11: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 loadedcorrplot(corr=cor(store))
TASK 4l - Pearson’s Correlation Tests
12:Run a Pearson’s Correlation test on the correlation between Profit and MTenure. 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
## 0.4388692The p-value obtained = 0.0000819
13:Run a Pearson’s Correlation test on the correlation between Profit and CTenure. What is the p-value?
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
## 0.2576789The p-value obtained = 0.02562
TASK 3m - Regression Analysis
14:Run a regression of Profit on {MTenure, CTenure Comp, Pop, PedCount, Res, Hours24, Visibility}.
model<-lm(Profit ~ MTenure + CTenure + Comp + Pop + PedCount + Res + Hours24 + Visibility, data=store )
summary(model)##
## 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-12TASK 4n
Based on TASK 3m, answer the following questions:
15:List the explanatory variable(s) whose beta-coefficients are statistically significant (p < 0.05).
model$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 12625.447050Variables p-value MTenure 9.72e-08 CTenure 0.028400
Comp 1.94e-05 Pop 0.014890
PedCount 0.000366 Res 0.022623
Hours24 0.001994
16:List the explanatory variable(s) whose beta-coefficients are not statistically significant (p > 0.05).
Visibility 0.169411
TASK 4o
Based on TASK 2m, answer the following questions:
17: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?
fit <- lm(Profit~MTenure, data=store)
summary(fit)##
## Call:
## lm(formula = Profit ~ MTenure, data = store)
##
## 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-05The regression model is : profit = 245496.3 + 680.3 * MTenure
The expected increase in profit is $680.3 as the manager’s tenure increases by 1.
18: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 <- lm(Profit~CTenure, data=store)
summary(fit)##
## Call:
## lm(formula = Profit ~ CTenure, data = store)
##
## 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: 0.02562The regression model is : Profit = 258178.4 + 1301.7 * CTenure The expected increase in profit is $1301.7 as the crew’s tenure increase by 1 month.
TASK 4p
19:Please prepare an “Executive Summary”.
The following inferences can be drawn from the above regression analysis 1: From the scatter plot, the profit increases slightly as the manager’s tenure increases but there is almost negligible effect of crew’s tenure on profit in most of the cases. 2: From the corrgram, the profit is moderately positively correlated with the manager’s tenure while weakly correlated with crew’s tenure. It is evident that the profit is highly correlated with the area of the population and the hours of operation while it is highly negatively correlated with the number of competitors in the area. 3: From the Pearson’s correlation test, the correlation between profit and crew’s tenure is significantly different from zero. 4: The f-test reveals that all the factors contribute significantly towards profit while the t-test reveals that visibililty, population, type of area and the crew’s tenure aren’t signficant. 5: The model isn’t that reliable since the Adjusted R squared value = 0.594 reveals the addition of more signicant regressors to the model.
Overall, crew’s tenure is not as important as a manager’s tenure in this regard and therefore employee retention might not be a good idea.