In this analysis, we will focus on understanding factors influencing the Final Amount Paid in digital wallet transactions. We will perform an ANOVA test to analyze the effect of different Product Categories on the Final Amount Paid. Additionally, we will build a linear regression model to analyze the relationship between Product Amount and the Final Amount Paid.
# Count the number of unique product categories
n_categories <- length(unique(data$ProductCategory))
n_categories## [1] 0# If there are more than 10 categories, consolidate (for example purposes)
if (n_categories > 10) {
# Example: Consolidating categories into broader groups
data$ProductCategory <- recode(data$ProductCategory,
"Gaming Credits" = "Entertainment",
"Streaming Service" = "Entertainment",
"Flight Booking" = "Travel",
"Bus Ticket" = "Travel",
"Movie Ticket" = "Entertainment",
"Food Delivery" = "Food",
"Grocery Shopping" = "Food",
"Electricity Bill" = "Utilities",
"Gas Bill" = "Utilities",
.default = "Other")
}Running the ANOVA Test
# Run ANOVA
anova_model <- aov(final_amount_paid ~ product_category, data = data)
summary(anova_model)## Df Sum Sq Mean Sq F value Pr(>F)
## product_category 19 2.258e+08 11881877 1.43 0.101
## Residuals 4980 4.138e+10 8310110# Tukey's HSD test for post-hoc analysis
tukey_results <- TukeyHSD(anova_model)
tukey_results## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = final_amount_paid ~ product_category, data = data)
##
## $product_category
## diff lwr upr
## Education Fee-Bus Ticket -29.2838241 -929.2204 870.65271
## Electricity Bill-Bus Ticket 194.8095189 -732.1062 1121.72524
## Flight Booking-Bus Ticket 455.0169726 -508.4513 1418.48528
## Food Delivery-Bus Ticket 335.3949876 -585.4566 1256.24655
## Gaming Credits-Bus Ticket 174.3562758 -772.6721 1121.38468
## Gas Bill-Bus Ticket 700.3637745 -228.3393 1629.06689
## Gift Card-Bus Ticket -121.6183984 -1079.3908 836.15401
## Grocery Shopping-Bus Ticket 21.6476585 -918.3313 961.62661
## Hotel Booking-Bus Ticket 68.4227934 -840.3591 977.20465
## Insurance Premium-Bus Ticket -160.3062478 -1113.6811 793.06861
## Internet Bill-Bus Ticket 605.0683899 -339.9081 1550.04488
## Loan Repayment-Bus Ticket 195.3220234 -737.9615 1128.60558
## Mobile Recharge-Bus Ticket 215.2995247 -721.7682 1152.36728
## Movie Ticket-Bus Ticket 165.8445230 -744.4786 1076.16763
## Online Shopping-Bus Ticket 220.6775333 -714.4845 1155.83953
## Rent Payment-Bus Ticket 263.3025147 -664.5038 1191.10880
## Streaming Service-Bus Ticket 142.8016213 -748.2668 1033.87008
## Taxi Fare-Bus Ticket 354.9167151 -568.4980 1278.33145
## Water Bill-Bus Ticket 381.1788565 -528.3711 1290.72884
## Electricity Bill-Education Fee 224.0933430 -659.0228 1107.20948
## Flight Booking-Education Fee 484.3007967 -437.1071 1405.70871
## Food Delivery-Education Fee 364.6788117 -512.0703 1241.42790
## Gaming Credits-Education Fee 203.6400999 -700.5635 1107.84371
## Gas Bill-Education Fee 729.6475986 -155.3444 1614.63960
## Gift Card-Education Fee -92.3345742 -1007.7849 823.11578
## Grocery Shopping-Education Fee 50.9314826 -845.8861 947.74907
## Hotel Booking-Education Fee 97.7066176 -766.3569 961.77017
## Insurance Premium-Education Fee -131.0224236 -1041.8709 779.82607
## Internet Bill-Education Fee 634.3522141 -267.7021 1536.40649
## Loan Repayment-Education Fee 224.6058476 -665.1916 1114.40333
## Mobile Recharge-Education Fee 244.5833488 -649.1825 1138.34916
## Movie Ticket-Education Fee 195.1283471 -670.5561 1060.81276
## Online Shopping-Education Fee 249.9613574 -641.8062 1141.72888
## Rent Payment-Education Fee 292.5863388 -591.4645 1176.63717
## Streaming Service-Education Fee 172.0854454 -673.3283 1017.49917
## Taxi Fare-Education Fee 384.2005392 -495.2403 1263.64135
## Water Bill-Education Fee 410.4626807 -454.4087 1275.33408
## Flight Booking-Electricity Bill 260.2074537 -687.5686 1207.98355
## Food Delivery-Electricity Bill 140.5854687 -763.8348 1045.00570
## Gaming Credits-Electricity Bill -20.4532431 -951.5124 910.60591
## Gas Bill-Electricity Bill 505.5542556 -406.8589 1417.96744
## Gift Card-Electricity Bill -316.4279173 -1258.4132 625.55740
## Grocery Shopping-Electricity Bill -173.1618604 -1097.0497 750.72600
## Hotel Booking-Electricity Bill -126.3867255 -1018.5150 765.74152
## Insurance Premium-Electricity Bill -355.1157667 -1292.6295 582.39795
## Internet Bill-Electricity Bill 410.2588710 -518.7131 1339.23084
## Loan Repayment-Electricity Bill 0.5125045 -916.5625 917.58750
## Mobile Recharge-Electricity Bill 20.4900058 -900.4358 941.41580
## Movie Ticket-Electricity Bill -28.9649959 -922.6632 864.73322
## Online Shopping-Electricity Bill 25.8680144 -893.1185 944.85458
## Rent Payment-Electricity Bill 68.4929958 -843.0073 979.99333
## Streaming Service-Electricity Bill -52.0078976 -926.0853 822.06953
## Taxi Fare-Electricity Bill 160.1071962 -746.9226 1067.13703
## Water Bill-Electricity Bill 186.3693376 -706.5414 1079.28004
## Food Delivery-Flight Booking -119.6219850 -1061.4682 822.22427
## Gaming Credits-Flight Booking -280.6606968 -1248.1159 686.79451
## Gas Bill-Flight Booking 245.3468019 -704.1774 1194.87102
## Gift Card-Flight Booking -576.6353710 -1554.6102 401.33945
## Grocery Shopping-Flight Booking -433.3693141 -1393.9250 527.18636
## Hotel Booking-Flight Booking -386.5941792 -1316.6432 543.45487
## Insurance Premium-Flight Booking -615.3232204 -1588.9917 358.34530
## Internet Bill-Flight Booking 150.0514173 -815.3953 1115.49812
## Loan Repayment-Flight Booking -259.6949492 -1213.6996 694.30975
## Mobile Recharge-Flight Booking -239.7174479 -1197.4245 717.98958
## Movie Ticket-Flight Booking -289.1724496 -1220.7276 642.38266
## Online Shopping-Flight Booking -234.3394393 -1190.1819 721.50298
## Rent Payment-Flight Booking -191.7144579 -1140.3615 756.93262
## Streaming Service-Flight Booking -312.2153513 -1224.9638 600.53312
## Taxi Fare-Flight Booking -100.1002575 -1044.4527 844.25219
## Water Bill-Flight Booking -73.8381161 -1004.6377 856.96151
## Gaming Credits-Food Delivery -161.0387118 -1086.0609 763.98345
## Gas Bill-Food Delivery 364.9687869 -541.2832 1271.22078
## Gift Card-Food Delivery -457.0133860 -1393.0322 479.00541
## Grocery Shopping-Food Delivery -313.7473291 -1231.5510 604.05637
## Hotel Booking-Food Delivery -266.9721941 -1152.7982 618.85378
## Insurance Premium-Food Delivery -495.7012353 -1427.2198 435.81732
## Internet Bill-Food Delivery 269.6734023 -653.2479 1192.59472
## Loan Repayment-Food Delivery -140.0729641 -1051.0183 770.87236
## Mobile Recharge-Food Delivery -120.0954629 -1034.9174 794.72647
## Movie Ticket-Food Delivery -169.5504646 -1056.9576 717.85663
## Online Shopping-Food Delivery -114.7174543 -1027.5872 798.15228
## Rent Payment-Food Delivery -72.0924729 -977.4254 833.24045
## Streaming Service-Food Delivery -192.5933663 -1060.2374 675.05068
## Taxi Fare-Food Delivery 19.5217275 -881.3101 920.35355
## Water Bill-Food Delivery 45.7838689 -840.8301 932.39786
## Gas Bill-Gaming Credits 526.0074987 -406.8311 1458.84611
## Gift Card-Gaming Credits -295.9746741 -1257.7576 665.80824
## Grocery Shopping-Gaming Credits -152.7086173 -1096.7737 791.35644
## Hotel Booking-Gaming Credits -105.9334823 -1018.9411 807.07411
## Insurance Premium-Gaming Credits -334.6625235 -1292.0663 622.74126
## Internet Bill-Gaming Credits 430.7121142 -518.3290 1379.75319
## Loan Repayment-Gaming Credits 20.9657477 -916.4331 958.36459
## Mobile Recharge-Gaming Credits 40.9432489 -900.2232 982.10974
## Movie Ticket-Gaming Credits -8.5117528 -923.0535 906.02996
## Online Shopping-Gaming Credits 46.3212575 -892.9478 985.59031
## Rent Payment-Gaming Credits 88.9462389 -842.9995 1020.89200
## Streaming Service-Gaming Credits -31.5546545 -926.9324 863.82314
## Taxi Fare-Gaming Credits 180.5604393 -747.0134 1108.13425
## Water Bill-Gaming Credits 206.8225808 -706.9496 1120.59474
## Gift Card-Gas Bill -821.9821729 -1765.7263 121.76200
## Grocery Shopping-Gas Bill -678.7161160 -1604.3972 246.96499
## Hotel Booking-Gas Bill -631.9409810 -1525.9262 262.04421
## Insurance Premium-Gas Bill -860.6700222 -1799.9510 78.61092
## Internet Bill-Gas Bill -95.2953845 -1026.0508 835.46003
## Loan Repayment-Gas Bill -505.0417510 -1423.9233 413.83978
## Mobile Recharge-Gas Bill -485.0642498 -1407.7890 437.66054
## Movie Ticket-Gas Bill -534.5192515 -1430.0712 361.03266
## Online Shopping-Gas Bill -479.6862412 -1400.4756 441.10311
## Rent Payment-Gas Bill -437.0612598 -1350.3792 476.25664
## Streaming Service-Gas Bill -557.5621532 -1433.5348 318.41049
## Taxi Fare-Gas Bill -345.4470594 -1254.3034 563.40928
## Water Bill-Gas Bill -319.1849179 -1213.9509 575.58111
## Grocery Shopping-Gift Card 143.2660569 -811.5763 1098.10846
## Hotel Booking-Gift Card 190.0411918 -734.1060 1114.18839
## Insurance Premium-Gift Card -38.6878494 -1006.7205 929.34479
## Internet Bill-Gift Card 726.6867883 -233.0758 1686.44934
## Loan Repayment-Gift Card 316.9404218 -631.3115 1265.19238
## Mobile Recharge-Gift Card 336.9179231 -615.0587 1288.89458
## Movie Ticket-Gift Card 287.4629214 -638.1999 1213.12578
## Online Shopping-Gift Card 342.2959317 -607.8049 1292.39674
## Rent Payment-Gift Card 384.9209131 -557.9407 1327.78256
## Streaming Service-Gift Card 264.4200197 -642.3140 1171.15404
## Taxi Fare-Gift Card 476.5351135 -462.0054 1415.07566
## Water Bill-Gift Card 502.7972549 -422.1053 1427.69982
## Hotel Booking-Grocery Shopping 46.7751349 -858.9182 952.46851
## Insurance Premium-Grocery Shopping -181.9539063 -1132.3852 768.47739
## Internet Bill-Grocery Shopping 583.4207314 -358.5860 1525.42741
## Loan Repayment-Grocery Shopping 173.6743649 -756.6021 1103.95079
## Mobile Recharge-Grocery Shopping 193.6518662 -740.4209 1127.72467
## Movie Ticket-Grocery Shopping 144.1968645 -763.0430 1051.43673
## Online Shopping-Grocery Shopping 199.0298748 -733.1310 1131.19080
## Rent Payment-Grocery Shopping 241.6548562 -683.1265 1166.43620
## Streaming Service-Grocery Shopping 121.1539628 -766.7644 1009.07233
## Taxi Fare-Grocery Shopping 333.2690566 -587.1063 1253.64441
## Water Bill-Grocery Shopping 359.5311980 -546.9329 1265.99532
## Insurance Premium-Hotel Booking -228.7290412 -1148.3179 690.85982
## Internet Bill-Hotel Booking 536.6455965 -374.2334 1447.52463
## Loan Repayment-Hotel Booking 126.8992300 -771.8434 1025.64182
## Mobile Recharge-Hotel Booking 146.8767312 -755.7949 1049.54834
## Movie Ticket-Hotel Booking 97.4217296 -777.4544 972.29784
## Online Shopping-Hotel Booking 152.2547399 -748.4383 1052.94781
## Rent Payment-Hotel Booking 194.8797213 -698.1738 1087.93323
## Streaming Service-Hotel Booking 74.3788278 -780.4446 929.20223
## Taxi Fare-Hotel Booking 286.4939216 -601.9963 1174.98412
## Water Bill-Hotel Booking 312.7560631 -561.3156 1186.82770
## Internet Bill-Insurance Premium 765.3746377 -189.9995 1720.74879
## Loan Repayment-Insurance Premium 355.6282712 -588.1818 1299.43832
## Mobile Recharge-Insurance Premium 375.6057724 -571.9464 1323.15798
## Movie Ticket-Insurance Premium 326.1507708 -594.9613 1247.26280
## Online Shopping-Insurance Premium 380.9837811 -564.6838 1326.65136
## Rent Payment-Insurance Premium 423.6087625 -514.7855 1362.00299
## Streaming Service-Insurance Premium 303.1078690 -598.9798 1205.19557
## Taxi Fare-Insurance Premium 515.2229628 -418.8295 1449.27542
## Water Bill-Insurance Premium 541.4851043 -378.8629 1461.83307
## Loan Repayment-Internet Bill -409.7463665 -1345.0722 525.57944
## Mobile Recharge-Internet Bill -389.7688652 -1328.8706 549.33290
## Movie Ticket-Internet Bill -439.2238669 -1351.6406 473.19288
## Online Shopping-Internet Bill -384.3908566 -1321.5910 552.80929
## Rent Payment-Internet Bill -341.7658752 -1271.6264 588.09469
## Streaming Service-Internet Bill -462.2667686 -1355.4740 430.94046
## Taxi Fare-Internet Bill -250.1516748 -1175.6304 675.32708
## Water Bill-Internet Bill -223.8895334 -1135.5349 687.75586
## Mobile Recharge-Loan Repayment 19.9775012 -907.3573 947.31226
## Movie Ticket-Loan Repayment -29.4775005 -929.7785 870.82353
## Online Shopping-Loan Repayment 25.3555099 -900.0535 950.76447
## Rent Payment-Loan Repayment 67.9804913 -849.9946 985.95560
## Streaming Service-Loan Repayment -52.5204022 -933.3477 828.30693
## Taxi Fare-Loan Repayment 159.5946916 -753.9416 1073.13099
## Water Bill-Loan Repayment 185.8568331 -713.6625 1085.37613
## Movie Ticket-Mobile Recharge -49.4550017 -953.6783 854.76827
## Online Shopping-Mobile Recharge 5.3780086 -923.8472 934.60324
## Rent Payment-Mobile Recharge 48.0029900 -873.8192 969.82514
## Streaming Service-Mobile Recharge -72.4979034 -957.3338 812.33799
## Taxi Fare-Mobile Recharge 139.6171904 -777.7848 1057.01914
## Water Bill-Mobile Recharge 165.8793318 -737.5656 1069.32426
## Online Shopping-Movie Ticket 54.8330103 -847.4151 957.08115
## Rent Payment-Movie Ticket 97.4579917 -797.1639 992.07984
## Streaming Service-Movie Ticket -23.0429017 -879.5047 833.41886
## Taxi Fare-Movie Ticket 189.0721921 -700.9944 1079.13877
## Water Bill-Movie Ticket 215.3343335 -660.3396 1091.00831
## Rent Payment-Online Shopping 42.6249814 -877.2598 962.50979
## Streaming Service-Online Shopping -77.8759120 -960.6933 804.94148
## Taxi Fare-Online Shopping 134.2391818 -781.2161 1049.69444
## Water Bill-Online Shopping 160.5013232 -740.9668 1061.96942
## Streaming Service-Rent Payment -120.5008934 -995.5227 754.52088
## Taxi Fare-Rent Payment 91.6142004 -816.3257 999.55411
## Water Bill-Rent Payment 117.8763418 -775.9588 1011.71149
## Taxi Fare-Streaming Service 212.1150938 -658.2488 1082.47902
## Water Bill-Streaming Service 238.3772352 -617.2627 1094.01721
## Water Bill-Taxi Fare 26.2621414 -863.0137 915.53799
## p adj
## Education Fee-Bus Ticket 1.0000000
## Electricity Bill-Bus Ticket 0.9999999
## Flight Booking-Bus Ticket 0.9824317
## Food Delivery-Bus Ticket 0.9992996
## Gaming Credits-Bus Ticket 1.0000000
## Gas Bill-Bus Ticket 0.4479335
## Gift Card-Bus Ticket 1.0000000
## Grocery Shopping-Bus Ticket 1.0000000
## Hotel Booking-Bus Ticket 1.0000000
## Insurance Premium-Bus Ticket 1.0000000
## Internet Bill-Bus Ticket 0.7551981
## Loan Repayment-Bus Ticket 0.9999999
## Mobile Recharge-Bus Ticket 0.9999994
## Movie Ticket-Bus Ticket 1.0000000
## Online Shopping-Bus Ticket 0.9999991
## Rent Payment-Bus Ticket 0.9999825
## Streaming Service-Bus Ticket 1.0000000
## Taxi Fare-Bus Ticket 0.9985506
## Water Bill-Bus Ticket 0.9956133
## Electricity Bill-Education Fee 0.9999971
## Flight Booking-Education Fee 0.9480591
## Food Delivery-Education Fee 0.9960031
## Gaming Credits-Education Fee 0.9999996
## Gas Bill-Education Fee 0.2756521
## Gift Card-Education Fee 1.0000000
## Grocery Shopping-Education Fee 1.0000000
## Hotel Booking-Education Fee 1.0000000
## Insurance Premium-Education Fee 1.0000000
## Internet Bill-Education Fee 0.5890439
## Loan Repayment-Education Fee 0.9999973
## Mobile Recharge-Education Fee 0.9999902
## Movie Ticket-Education Fee 0.9999996
## Online Shopping-Education Fee 0.9999856
## Rent Payment-Education Fee 0.9998202
## Streaming Service-Education Fee 0.9999999
## Taxi Fare-Education Fee 0.9927505
## Water Bill-Education Fee 0.9814724
## Flight Booking-Electricity Bill 0.9999896
## Food Delivery-Electricity Bill 1.0000000
## Gaming Credits-Electricity Bill 1.0000000
## Gas Bill-Electricity Bill 0.9165862
## Gift Card-Electricity Bill 0.9997768
## Grocery Shopping-Electricity Bill 1.0000000
## Hotel Booking-Electricity Bill 1.0000000
## Insurance Premium-Electricity Bill 0.9988068
## Internet Bill-Electricity Bill 0.9917641
## Loan Repayment-Electricity Bill 1.0000000
## Mobile Recharge-Electricity Bill 1.0000000
## Movie Ticket-Electricity Bill 1.0000000
## Online Shopping-Electricity Bill 1.0000000
## Rent Payment-Electricity Bill 1.0000000
## Streaming Service-Electricity Bill 1.0000000
## Taxi Fare-Electricity Bill 1.0000000
## Water Bill-Electricity Bill 0.9999999
## Food Delivery-Flight Booking 1.0000000
## Gaming Credits-Flight Booking 0.9999754
## Gas Bill-Flight Booking 0.9999961
## Gift Card-Flight Booking 0.8619947
## Grocery Shopping-Flight Booking 0.9894516
## Hotel Booking-Flight Booking 0.9960357
## Insurance Premium-Flight Booking 0.7748675
## Internet Bill-Flight Booking 1.0000000
## Loan Repayment-Flight Booking 0.9999910
## Mobile Recharge-Flight Booking 0.9999977
## Movie Ticket-Flight Booking 0.9999306
## Online Shopping-Flight Booking 0.9999983
## Rent Payment-Flight Booking 0.9999999
## Streaming Service-Flight Booking 0.9997102
## Taxi Fare-Flight Booking 1.0000000
## Water Bill-Flight Booking 1.0000000
## Gaming Credits-Food Delivery 1.0000000
## Gas Bill-Food Delivery 0.9973388
## Gift Card-Food Delivery 0.9749660
## Grocery Shopping-Food Delivery 0.9997128
## Hotel Booking-Food Delivery 0.9999557
## Insurance Premium-Food Delivery 0.9417494
## Internet Bill-Food Delivery 0.9999725
## Loan Repayment-Food Delivery 1.0000000
## Mobile Recharge-Food Delivery 1.0000000
## Movie Ticket-Food Delivery 1.0000000
## Online Shopping-Food Delivery 1.0000000
## Rent Payment-Food Delivery 1.0000000
## Streaming Service-Food Delivery 0.9999997
## Taxi Fare-Food Delivery 1.0000000
## Water Bill-Food Delivery 1.0000000
## Gas Bill-Gaming Credits 0.9032820
## Gift Card-Gaming Credits 0.9999391
## Grocery Shopping-Gaming Credits 1.0000000
## Hotel Booking-Gaming Credits 1.0000000
## Insurance Premium-Gaming Credits 0.9996055
## Internet Bill-Gaming Credits 0.9887157
## Loan Repayment-Gaming Credits 1.0000000
## Mobile Recharge-Gaming Credits 1.0000000
## Movie Ticket-Gaming Credits 1.0000000
## Online Shopping-Gaming Credits 1.0000000
## Rent Payment-Gaming Credits 1.0000000
## Streaming Service-Gaming Credits 1.0000000
## Taxi Fare-Gaming Credits 1.0000000
## Water Bill-Gaming Credits 0.9999996
## Gift Card-Gas Bill 0.1872813
## Grocery Shopping-Gas Bill 0.5053192
## Hotel Booking-Gas Bill 0.5788559
## Insurance Premium-Gas Bill 0.1225681
## Internet Bill-Gas Bill 1.0000000
## Loan Repayment-Gas Bill 0.9222113
## Mobile Recharge-Gas Bill 0.9479875
## Movie Ticket-Gas Bill 0.8487426
## Online Shopping-Gas Bill 0.9522442
## Rent Payment-Gas Bill 0.9797478
## Streaming Service-Gas Bill 0.7642402
## Taxi Fare-Gas Bill 0.9987506
## Water Bill-Gas Bill 0.9994751
## Grocery Shopping-Gift Card 1.0000000
## Hotel Booking-Gift Card 0.9999999
## Insurance Premium-Gift Card 1.0000000
## Internet Bill-Gift Card 0.4397998
## Loan Repayment-Gift Card 0.9997924
## Mobile Recharge-Gift Card 0.9995301
## Movie Ticket-Gift Card 0.9999301
## Online Shopping-Gift Card 0.9993976
## Rent Payment-Gift Card 0.9968364
## Streaming Service-Gift Card 0.9999733
## Taxi Fare-Gift Card 0.9627633
## Water Bill-Gift Card 0.9293691
## Hotel Booking-Grocery Shopping 1.0000000
## Insurance Premium-Grocery Shopping 1.0000000
## Internet Bill-Grocery Shopping 0.8031854
## Loan Repayment-Grocery Shopping 1.0000000
## Mobile Recharge-Grocery Shopping 0.9999999
## Movie Ticket-Grocery Shopping 1.0000000
## Online Shopping-Grocery Shopping 0.9999998
## Rent Payment-Grocery Shopping 0.9999953
## Streaming Service-Grocery Shopping 1.0000000
## Taxi Fare-Grocery Shopping 0.9993538
## Water Bill-Grocery Shopping 0.9978123
## Insurance Premium-Hotel Booking 0.9999979
## Internet Bill-Hotel Booking 0.8628316
## Loan Repayment-Hotel Booking 1.0000000
## Mobile Recharge-Hotel Booking 1.0000000
## Movie Ticket-Hotel Booking 1.0000000
## Online Shopping-Hotel Booking 1.0000000
## Rent Payment-Hotel Booking 0.9999998
## Streaming Service-Hotel Booking 1.0000000
## Taxi Fare-Hotel Booking 0.9998774
## Water Bill-Hotel Booking 0.9994523
## Internet Bill-Insurance Premium 0.3282489
## Loan Repayment-Insurance Premium 0.9988880
## Mobile Recharge-Insurance Premium 0.9978289
## Movie Ticket-Insurance Premium 0.9995270
## Online Shopping-Insurance Premium 0.9973262
## Rent Payment-Insurance Premium 0.9893836
## Streaming Service-Insurance Premium 0.9997759
## Taxi Fare-Insurance Premium 0.9197548
## Water Bill-Insurance Premium 0.8642528
## Loan Repayment-Internet Bill 0.9925095
## Mobile Recharge-Internet Bill 0.9961093
## Movie Ticket-Internet Bill 0.9784294
## Online Shopping-Internet Bill 0.9966458
## Rent Payment-Internet Bill 0.9992065
## Streaming Service-Internet Bill 0.9551514
## Taxi Fare-Internet Bill 0.9999919
## Water Bill-Internet Bill 0.9999983
## Mobile Recharge-Loan Repayment 1.0000000
## Movie Ticket-Loan Repayment 1.0000000
## Online Shopping-Loan Repayment 1.0000000
## Rent Payment-Loan Repayment 1.0000000
## Streaming Service-Loan Repayment 1.0000000
## Taxi Fare-Loan Repayment 1.0000000
## Water Bill-Loan Repayment 0.9999999
## Movie Ticket-Mobile Recharge 1.0000000
## Online Shopping-Mobile Recharge 1.0000000
## Rent Payment-Mobile Recharge 1.0000000
## Streaming Service-Mobile Recharge 1.0000000
## Taxi Fare-Mobile Recharge 1.0000000
## Water Bill-Mobile Recharge 1.0000000
## Online Shopping-Movie Ticket 1.0000000
## Rent Payment-Movie Ticket 1.0000000
## Streaming Service-Movie Ticket 1.0000000
## Taxi Fare-Movie Ticket 0.9999999
## Water Bill-Movie Ticket 0.9999983
## Rent Payment-Online Shopping 1.0000000
## Streaming Service-Online Shopping 1.0000000
## Taxi Fare-Online Shopping 1.0000000
## Water Bill-Online Shopping 1.0000000
## Streaming Service-Rent Payment 1.0000000
## Taxi Fare-Rent Payment 1.0000000
## Water Bill-Rent Payment 1.0000000
## Taxi Fare-Streaming Service 0.9999985
## Water Bill-Streaming Service 0.9999869
## Water Bill-Taxi Fare 1.0000000Interpretation of ANOVA Results:
Since the p-value is 0.101, which is greater than 0.05, we fail to reject the null hypothesis.This means there is not enough evidence to conclude that the mean Final Amount Paid differs significantly across the 20 product categories. Based on this test, we do not find a statistically significant effect of product category on the Final Amount Paid at the 5% significance level.
Linear Regression Model: To analyze the influence of product_amount on the response variable final_amount_paid, we can build a linear regression model and evaluate its fit.
# Build linear regression model
linear_model <- lm(final_amount_paid ~ product_amount, data = data)
# Summary of the model to evaluate its fit
summary(linear_model)##
## Call:
## lm(formula = final_amount_paid ~ product_amount, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -72.829 -24.777 -0.391 24.482 74.146
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.524e+01 9.010e-01 -28.02 <2e-16 ***
## product_amount 1.000e+00 1.571e-04 6365.63 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 32.04 on 4998 degrees of freedom
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
## F-statistic: 4.052e+07 on 1 and 4998 DF, p-value: < 2.2e-16Residual = ObservedValue − PredictedValue
Interpretation: The residuals represent the differences between the observed values of final_amount_paid and the values predicted by your model. The range of residuals from -72.829 to 74.146 suggests that while most predictions are close to the actual values (as indicated by the median close to zero), there are a few instances where the model significantly over- or under-predicts the final amount paid.
Coefficients:
The estimated intercept of the model is \(-25.24\), indicating that when
product_amount is zero, the predicted
final_amount_paid is \(-25.24\). While this value is not
practically meaningful, it establishes a baseline for the effect of
product_amount. The coefficient for
product_amount is \(1.00\), meaning that for each additional
dollar increase in product_amount, the
final_amount_paid increases by approximately \(1.00\). The associated p-value \(< 2e-16\) indicates this coefficient is
statistically significant, making product_amount a reliable
predictor of final_amount_paid.
Model Fit:
The residual standard error is \(32.04\), suggesting a good fit of the model
to the data. The multiple R-squared value is \(0.9999\), meaning that about \(99.99\%\) of the variance in
final_amount_paid can be explained by
product_amount, and the adjusted R-squared also being \(0.9999\) confirms that the model
effectively accounts for variance even with a single predictor. Finally,
the F-statistic of \(4.052e+07\) with a
p-value \(< 2.2e-16\) indicates that
the model as a whole is statistically significant, reflecting a strong
relationship between product_amount and
final_amount_paid.
Summary of Insights
Strong Relationship: The very high R-squared value indicates a strong relationship between product_amount and final_amount_paid, making product_amount a critical factor for predicting how much a user will pay in the end.
Predictive Power: The coefficient for product_amount suggests that increasing the amount spent on products directly increases the final amount paid by the same amount, which could inform pricing and marketing strategies.
Model Significance: Both the individual predictors and the overall model are statistically significant, which adds confidence to the conclusions drawn from this analysis.
Recommendations Based on the analysis: Consider optimizing the product_amount as it has a direct and significant effect on the final_amount_paid. Pricing strategies that increase the product amount might lead to higher final payments.
Further Investigations: I will investigate other potential explanatory variables (e.g., transaction fees, cashback) to see how they interact with product_amount. Additionally, examining non-linear relationships or interactions between variables might provide deeper insights.