LBB Regression Model
David Ricardo
2023-03-29
1 PENDAHULUAN
LBB Regression Model ini menggunakan data pengiriman makanan yang terjadi di India. Ini adalah data layanan kurir dimana restoran, toko, atau perusahaan pengiriman makanan mengantarkan makanan ke pelanggan. Pemesanan biasanya dilakukan melalui situs web atau aplikasi mobile restoran atau penjual bahan makanan, atau melalui perusahaan pemesanan makanan. Barang yang dikirim dapat mencakup makanan pembuka, pendamping, minuman, makanan penutup, atau barang belanjaan dan biasanya dikirim dalam kotak atau tas. Pengantar biasanya akan mengendarai mobil, tetapi di kota-kota besar di mana rumah dan restoran lebih dekat satu sama lain, mereka dapat menggunakan sepeda atau skuter bermotor.
Kita akan menggunakan Model Regresi untuk memprediksi berapa waktu yang dibutuhkan untuk mengirim makanan.
2 SETUP
# clear-up the environment
rm(list = ls())
# scientific notation
options(scipen = 999)
# chunk options
knitr::opts_chunk$set(
fig.align = "center",
message = FALSE,
warning = FALSE,
comment = "#>"
)Library yang digunakan :
library(ggplot2)
library(dplyr)
library(geosphere)
library(tidyverse)
library(GGally)
library(caret)3 IMPORT DATA
delivery_food_1 <- read.csv("data/train.csv")
delivery_food_2 <- read.csv("data/test.csv")
delivery_food <- bind_rows(delivery_food_1,delivery_food_2)4 CEK NA
anyNA(delivery_food)#> [1] TRUEmissing_values <- colSums(is.na(delivery_food))
print(missing_values)#> ID Delivery_person_ID
#> 0 0
#> Delivery_person_Age Delivery_person_Ratings
#> 2345 2415
#> Restaurant_latitude Restaurant_longitude
#> 0 0
#> Delivery_location_latitude Delivery_location_longitude
#> 0 0
#> Order_Date Time_Orderd
#> 0 0
#> Time_Order_picked Weatherconditions
#> 0 0
#> Road_traffic_density Vehicle_condition
#> 0 0
#> Type_of_order Type_of_vehicle
#> 0 0
#> multiple_deliveries Festival
#> 1231 0
#> City Time_taken.min.
#> 0 113995 HAPUS NA
delivery_food_clean <- na.omit(delivery_food)6 DATA WRANGLING
delivery_food_clean <- delivery_food_clean %>%
mutate(
Time_Orderd = as.POSIXct(Time_Orderd, format = "%H:%M:%S"),
Time_Order_picked = as.POSIXct(Time_Order_picked, format = "%H:%M:%S"),
Order_preparation = as.numeric(difftime(Time_Order_picked, Time_Orderd, units = "mins")),
Distance = distHaversine(cbind(Restaurant_longitude, Restaurant_latitude), cbind(Delivery_location_longitude, Delivery_location_latitude)),
Delivery_time = as.numeric(gsub("\\(min\\) ",'',Time_taken.min.)),
Weatherconditions = as.factor(Weatherconditions),
Road_traffic_density = as.factor(Road_traffic_density),
Vehicle_condition = as.factor(Vehicle_condition),
Type_of_order = as.factor(Type_of_order),
Type_of_vehicle = as.factor(Type_of_vehicle),
multiple_deliveries = as.numeric(multiple_deliveries),
Festival = as.factor(Festival),
City = as.factor(City)
)
delivery_food_clean <- delivery_food_clean %>%
dplyr::select(
Delivery_person_Age,
Delivery_person_Ratings,
Weatherconditions,
Road_traffic_density,
Vehicle_condition,
Type_of_order,
Type_of_vehicle,
multiple_deliveries,
Festival,
City,
Order_preparation,
Distance,
Delivery_time
)
delivery_food_clean <- na.omit(delivery_food_clean)7 OUTLIER
Terdapat outlier pada kolom Distance dan Order_preparation.
boxplot(delivery_food_clean$Distance, horizontal = T)
boxplot(delivery_food_clean$Order_preparation, horizontal = T)
8 SUBSET
Kita akan menghilangkan Order_preparation yang bernilai negatif dan Distance di atas 1.000.000
delivery_food_clean <- delivery_food_clean[delivery_food_clean$Order_preparation > 0 & delivery_food_clean$Distance <= 1000000,]9 EXPLANATORY DATA ANALYSIS
summary(delivery_food_clean)#> Delivery_person_Age Delivery_person_Ratings Weatherconditions
#> Min. :20.00 Min. :2.500 conditions Cloudy :6972
#> 1st Qu.:25.00 1st Qu.:4.500 conditions Fog :7121
#> Median :30.00 Median :4.700 conditions NaN : 0
#> Mean :29.57 Mean :4.635 conditions Sandstorms:6898
#> 3rd Qu.:35.00 3rd Qu.:4.900 conditions Stormy :7044
#> Max. :39.00 Max. :5.000 conditions Sunny :6738
#> conditions Windy :6929
#> Road_traffic_density Vehicle_condition Type_of_order
#> High : 4194 0:13910 Buffet :10314
#> Jam :13418 1:13859 Drinks :10410
#> Low :13716 2:13933 Meal :10475
#> Medium :10374 3: 0 Snack :10503
#> NaN : 0
#>
#>
#> Type_of_vehicle multiple_deliveries Festival
#> bicycle : 0 Min. :0.0000 NaN : 201
#> electric_scooter : 3368 1st Qu.:0.0000 No :40657
#> motorcycle :24391 Median :1.0000 Yes : 844
#> scooter :13943 Mean :0.7456
#> 3rd Qu.:1.0000
#> Max. :3.0000
#>
#> City Order_preparation Distance Delivery_time
#> Metropolitian :31241 Min. : 5.00 Min. : 1467 Min. :10.00
#> NaN : 1063 1st Qu.: 5.00 1st Qu.: 4663 1st Qu.:19.00
#> Semi-Urban : 152 Median :10.00 Median : 9229 Median :26.00
#> Urban : 9246 Mean : 9.96 Mean : 9718 Mean :26.45
#> 3rd Qu.:15.00 3rd Qu.:13697 3rd Qu.:33.00
#> Max. :15.00 Max. :20993 Max. :54.00
#> str(delivery_food_clean)#> 'data.frame': 41702 obs. of 13 variables:
#> $ Delivery_person_Age : num 37 34 23 38 32 22 33 35 22 36 ...
#> $ Delivery_person_Ratings: num 4.9 4.5 4.4 4.7 4.6 4.8 4.7 4.6 4.8 4.2 ...
#> $ Weatherconditions : Factor w/ 7 levels "conditions Cloudy",..: 6 5 4 6 1 1 2 1 5 2 ...
#> $ Road_traffic_density : Factor w/ 5 levels "High ","Jam ",..: 1 2 3 4 1 2 2 4 2 2 ...
#> $ Vehicle_condition : Factor w/ 4 levels "0","1","2","3": 3 3 1 1 2 1 2 3 1 3 ...
#> $ Type_of_order : Factor w/ 4 levels "Buffet ","Drinks ",..: 4 4 2 1 4 1 3 3 1 4 ...
#> $ Type_of_vehicle : Factor w/ 4 levels "bicycle ","electric_scooter ",..: 3 4 3 3 4 3 4 3 3 3 ...
#> $ multiple_deliveries : num 0 1 1 1 1 1 1 1 1 3 ...
#> $ Festival : Factor w/ 3 levels "NaN ","No ","Yes ": 2 2 2 2 2 2 2 2 2 2 ...
#> $ City : Factor w/ 4 levels "Metropolitian ",..: 4 1 4 1 1 4 1 1 1 1 ...
#> $ Order_preparation : num 15 5 15 10 15 10 15 5 10 15 ...
#> $ Distance : num 3029 20206 1554 7799 6217 ...
#> $ Delivery_time : num 24 33 26 21 30 26 40 32 34 46 ...
#> - attr(*, "na.action")= 'omit' Named int [1:91] 2233 2713 2756 3350 4397 4833 5012 5284 5522 5985 ...
#> ..- attr(*, "names")= chr [1:91] "2388" "2905" "2950" "3585" ...Berikut adalah keterangan untuk setiap kolom : -
Delivery_person_Age: Usia Kurir
- Delivery_person_Ratings: Rating Kurir
- Weatherconditions: Keadaan Cuaca
- Road_traffic_density: Keadaan Lalu Lintas
- Vehicle_condition: Keadaan Kendaraan
- Type_of_order: Jenis Pemesanan
- Type_of_vehicle: Jenis Kendaraaan
- multiple_deliveries: Pengiriman Multiple
- Festival : Apakah ada Festival
- City: Jenis Kota
- Order_preparation: Durasi Persiapan Paket
- Distance: Jarak Antara Restoran ke Tujuan
- Delivery_time: Waktu Pengiriman dari Restoran ke
Tujuan
Berikut adalah korelasi antar variable:
ggcorr(delivery_food_clean, label = TRUE, label_size = 2.9, hjust = 1, layout.exp = 2)
Terlihat bahwa, variable yang paling mempengaruhi Delivery_time adalah
multiple_deliveries, Distance, dan Delivert_person_Age
10 MODEL SINGLE REGRESI LINEAR
Kita akan membuat regresi linear dengan variable prediktor multiple_deliveries karena variable tersebut memiliki korelasi positif tertinggi dengan variable Delivery_time.
model_regresi_single <- lm(Delivery_time ~ multiple_deliveries, delivery_food_clean)
summary(model_regresi_single)#>
#> Call:
#> lm(formula = Delivery_time ~ multiple_deliveries, data = delivery_food_clean)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -18.070 -6.708 -0.708 5.292 32.292
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 21.70754 0.06946 312.51 <0.0000000000000002 ***
#> multiple_deliveries 6.36199 0.07383 86.17 <0.0000000000000002 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 8.651 on 41700 degrees of freedom
#> Multiple R-squared: 0.1511, Adjusted R-squared: 0.1511
#> F-statistic: 7425 on 1 and 41700 DF, p-value: < 0.00000000000000022plot(delivery_food_clean$multiple_deliveries, delivery_food_clean$Delivery_time)
abline(model_regresi_single$coefficients[1],model_regresi_single$coefficients[2])
Dapat dilihat bahwa, adjusted R-squared hanya memiliki nilai 0.1511. Berarti variable multiple_deliveries tidak cukup untuk menjelaskan. Harus menambahkan variable lain untuk meningkatkan kualitas model.
11 STEPWISE FOR FEATURE SELECTION
Kita dapat menggunakan stepwise regression dengan metode backward untuk menentukan variable apa saja yang dapat meningkatkan kualitas model.
model_backward <- lm(Delivery_time ~ ., delivery_food_clean)
model_backward <- step(model_backward, direction = "backward")#> Start: AIC=146981
#> Delivery_time ~ Delivery_person_Age + Delivery_person_Ratings +
#> Weatherconditions + Road_traffic_density + Vehicle_condition +
#> Type_of_order + Type_of_vehicle + multiple_deliveries + Festival +
#> City + Order_preparation + Distance
#>
#> Df Sum of Sq RSS AIC
#> - Type_of_order 3 58 1413604 146977
#> - Order_preparation 1 9 1413554 146979
#> - Type_of_vehicle 2 80 1413626 146979
#> <none> 1413546 146981
#> - City 3 42401 1455947 148207
#> - Festival 2 73881 1487427 149102
#> - multiple_deliveries 1 100301 1513847 149838
#> - Distance 1 108181 1521727 150054
#> - Vehicle_condition 2 124630 1538176 150501
#> - Weatherconditions 5 180593 1594139 151985
#> - Delivery_person_Age 1 196896 1610442 152417
#> - Delivery_person_Ratings 1 203377 1616923 152585
#> - Road_traffic_density 3 335809 1749355 155864
#>
#> Step: AIC=146976.7
#> Delivery_time ~ Delivery_person_Age + Delivery_person_Ratings +
#> Weatherconditions + Road_traffic_density + Vehicle_condition +
#> Type_of_vehicle + multiple_deliveries + Festival + City +
#> Order_preparation + Distance
#>
#> Df Sum of Sq RSS AIC
#> - Order_preparation 1 8 1413612 146975
#> - Type_of_vehicle 2 80 1413683 146975
#> <none> 1413604 146977
#> - City 3 42420 1456024 148204
#> - Festival 2 73907 1487510 149098
#> - multiple_deliveries 1 100264 1513868 149832
#> - Distance 1 108203 1521807 150050
#> - Vehicle_condition 2 124658 1538262 150497
#> - Weatherconditions 5 180627 1594231 151981
#> - Delivery_person_Age 1 196913 1610517 152413
#> - Delivery_person_Ratings 1 203344 1616947 152579
#> - Road_traffic_density 3 335835 1749439 155860
#>
#> Step: AIC=146974.9
#> Delivery_time ~ Delivery_person_Age + Delivery_person_Ratings +
#> Weatherconditions + Road_traffic_density + Vehicle_condition +
#> Type_of_vehicle + multiple_deliveries + Festival + City +
#> Distance
#>
#> Df Sum of Sq RSS AIC
#> - Type_of_vehicle 2 80 1413692 146973
#> <none> 1413612 146975
#> - City 3 42422 1456034 148202
#> - Festival 2 73912 1487524 149096
#> - multiple_deliveries 1 100267 1513879 149831
#> - Distance 1 108216 1521828 150049
#> - Vehicle_condition 2 124672 1538284 150496
#> - Weatherconditions 5 180622 1594234 151979
#> - Delivery_person_Age 1 196937 1610549 152412
#> - Delivery_person_Ratings 1 203353 1616965 152578
#> - Road_traffic_density 3 335829 1749441 155858
#>
#> Step: AIC=146973.3
#> Delivery_time ~ Delivery_person_Age + Delivery_person_Ratings +
#> Weatherconditions + Road_traffic_density + Vehicle_condition +
#> multiple_deliveries + Festival + City + Distance
#>
#> Df Sum of Sq RSS AIC
#> <none> 1413692 146973
#> - City 3 42401 1456093 148200
#> - Festival 2 73941 1487633 149095
#> - multiple_deliveries 1 100242 1513934 149828
#> - Distance 1 108276 1521967 150049
#> - Weatherconditions 5 180619 1594310 151977
#> - Vehicle_condition 2 188818 1602510 152197
#> - Delivery_person_Age 1 196902 1610593 152409
#> - Delivery_person_Ratings 1 203434 1617126 152578
#> - Road_traffic_density 3 335782 1749474 155854model_regresi_multiple <- lm(formula = Delivery_time ~ Delivery_person_Age + Delivery_person_Ratings +
Weatherconditions + Road_traffic_density + Vehicle_condition +
multiple_deliveries + Festival + City + log(Distance), data = delivery_food_clean)
summary(model_regresi_multiple)#>
#> Call:
#> lm(formula = Delivery_time ~ Delivery_person_Age + Delivery_person_Ratings +
#> Weatherconditions + Road_traffic_density + Vehicle_condition +
#> multiple_deliveries + Festival + City + log(Distance), data = delivery_food_clean)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -19.434 -4.098 -0.171 3.825 28.375
#>
#> Coefficients:
#> Estimate Std. Error t value
#> (Intercept) 28.917671 0.761067 37.996
#> Delivery_person_Age 0.381217 0.005078 75.071
#> Delivery_person_Ratings -7.345587 0.094375 -77.834
#> Weatherconditionsconditions Fog 0.034173 0.099031 0.345
#> Weatherconditionsconditions Sandstorms -2.760842 0.100109 -27.578
#> Weatherconditionsconditions Stormy -2.776258 0.099521 -27.896
#> Weatherconditionsconditions Sunny -6.227119 0.100951 -61.685
#> Weatherconditionsconditions Windy -2.660398 0.099927 -26.623
#> Road_traffic_densityJam 0.602088 0.114402 5.263
#> Road_traffic_densityLow -6.131794 0.105612 -58.060
#> Road_traffic_densityMedium -2.391960 0.116122 -20.599
#> Vehicle_condition1 -4.576217 0.071439 -64.058
#> Vehicle_condition2 -4.554126 0.071289 -63.882
#> multiple_deliveries 2.897467 0.052612 55.072
#> FestivalNo 6.452198 0.417555 15.452
#> FestivalYes 15.843985 0.468761 33.800
#> CityNaN -2.524589 0.183733 -13.741
#> CitySemi-Urban 9.745056 0.482464 20.199
#> CityUrban -1.853113 0.070376 -26.332
#> log(Distance) 2.211046 0.045274 48.837
#> Pr(>|t|)
#> (Intercept) < 0.0000000000000002 ***
#> Delivery_person_Age < 0.0000000000000002 ***
#> Delivery_person_Ratings < 0.0000000000000002 ***
#> Weatherconditionsconditions Fog 0.73
#> Weatherconditionsconditions Sandstorms < 0.0000000000000002 ***
#> Weatherconditionsconditions Stormy < 0.0000000000000002 ***
#> Weatherconditionsconditions Sunny < 0.0000000000000002 ***
#> Weatherconditionsconditions Windy < 0.0000000000000002 ***
#> Road_traffic_densityJam 0.000000142 ***
#> Road_traffic_densityLow < 0.0000000000000002 ***
#> Road_traffic_densityMedium < 0.0000000000000002 ***
#> Vehicle_condition1 < 0.0000000000000002 ***
#> Vehicle_condition2 < 0.0000000000000002 ***
#> multiple_deliveries < 0.0000000000000002 ***
#> FestivalNo < 0.0000000000000002 ***
#> FestivalYes < 0.0000000000000002 ***
#> CityNaN < 0.0000000000000002 ***
#> CitySemi-Urban < 0.0000000000000002 ***
#> CityUrban < 0.0000000000000002 ***
#> log(Distance) < 0.0000000000000002 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 5.877 on 41682 degrees of freedom
#> Multiple R-squared: 0.6084, Adjusted R-squared: 0.6083
#> F-statistic: 3409 on 19 and 41682 DF, p-value: < 0.00000000000000022Metode step-wise regression ini akan menghasilkan formula optimum berdasarkan nilai AIC yang terendah, dimana semakin rendah nilai AIC tersebut, maka nilai observasi yang tidak tertangkap semakin kecil.
Bila dibandingkan dengan model awal yang hanya menggunakan variabel multiple_deliveries, model regresi yang menggunakan variabel prediktor Delivery_person_Age, Delivery_person_Ratings, Weatherconditionsconditions, Road_traffic_density, Vehicle_condition, multiple_deliveries, Festival, City, dan Distance memiliki R-squared 0.6083. Jauh lebih tinggi dibandingkan model sebelumnya yaitu 0.1511.
12 PREDICTION INTERVAL
range(delivery_food_clean$Delivery_time)#> [1] 10 54RMSE(pred = model_regresi_multiple$fitted.values, obs = delivery_food_clean$Delivery_time)#> [1] 5.875458Kesimpulan: RMSE cukup tinggi. Sekitar 11% dari rentang variable target. Artinya Model yang dihasilkan oleh stepwise selection pun belum cukup baik.
13 ASUMSI LINEAR REGRESSION
13.1 Linearity
plot(model_backward, which = 1)
abline(h = 10, col = "green")
abline(h = -10, col = "green")
Kesimpulan: karena garis merah masih ada di dalam cakupan toleransi
kita, sehingga model_backward adalabh model yang linear.
13.2 Normality of Residuals
hist(model_backward$residuals)
ks.test(model_backward$residuals, "pnorm")#>
#> Asymptotic one-sample Kolmogorov-Smirnov test
#>
#> data: model_backward$residuals
#> D = 0.35861, p-value < 0.00000000000000022
#> alternative hypothesis: two-sidedKesimpulan: p-value yang lebih kecil dari 0.05 menunjukkan bahwa data tidak terdistribusi normal.
13.3 Homoscedasticity of Residuals
plot(x = model_backward$fitted.values, y = model_backward$residuals)
abline(h = 0, col = "red")
library(lmtest)
bptest(model_backward)#>
#> studentized Breusch-Pagan test
#>
#> data: model_backward
#> BP = 1194.2, df = 19, p-value < 0.00000000000000022Kesimpulan: karena nilai p-value dari BPtest < 0.05, sehingga model ini tidak memenuhi asumsi homoscedasticity of residual
13.4 No Multicollinearity
library(car)
vif(model_backward)#> GVIF Df GVIF^(1/(2*Df))
#> Delivery_person_Age 1.035848 1 1.017766
#> Delivery_person_Ratings 1.053100 1 1.026206
#> Weatherconditions 1.025008 5 1.002473
#> Road_traffic_density 1.294919 3 1.044016
#> Vehicle_condition 1.033807 2 1.008347
#> multiple_deliveries 1.102213 1 1.049863
#> Festival 1.068981 2 1.016816
#> City 1.047122 3 1.007704
#> Distance 1.268914 1 1.126461Kesimpulan: Dari uji VIF, prediktor di model_backward lolos uji asumsi multicolinearity (tidak ada nilai VIF > 10)
14 KESIMPULAN DAN SARAN
Berdasarkan model yang telah dieksplorasi, bahwa prediksi durasi pengiriman atas data delivery makanan ini tidak dapat diselesaikan dengan metode regresi linear. Mungkin perlu tambahan prediktor berupa kategori cluster setiap lokasi restoran dan lokasi tujuan pengiriman. Jadi seluruh kota ditentukan cluster, dimana lokasi restoran dan lokasi tujuan akan di-mapping ke cluster tersebut.