Линеная регрессия на примере данных о такси Нью-Йорка
Ainur Makhmet
21/10/2018
1 Введение
На этой странице Вы найдете объяснение линейной регрессии на примере данных о такси Нью-Йорка.
2 Библиотеки
Загружаем библиотеки.
library(data.table) # библиотека для быстрого чтения данных с csv файла
library(lubridate) # библиотека для работы с данными форматаDate
library(dplyr) # библиотека для data engineering
library(ggplot2) # библиотека для построений графиков
library(caret) # библиотека для создания выборок для обучения и теста
library(xgboost) # библиотека для XGBoost3 Загрузка данных
Читаем данные.
df <- fread("../L9Data/train.csv") # fast read
test_final <- fread("../L9Data/test.csv")
subm <- fread("../L9Data/sample_submission.csv")
# Обзор наименование переменных в искомом дата фрейме
colnames(df) [1] "id" "vendor_id" "pickup_datetime"
[4] "dropoff_datetime" "passenger_count" "pickup_longitude"
[7] "pickup_latitude" "dropoff_longitude" "dropoff_latitude"
[10] "store_and_fwd_flag" "trip_duration" # Обзор наименование переменных в тест файле
colnames(test_final) [1] "id" "vendor_id" "pickup_datetime"
[4] "passenger_count" "pickup_longitude" "pickup_latitude"
[7] "dropoff_longitude" "dropoff_latitude" "store_and_fwd_flag"4 Работа с датами
Обзор формата данных. Здесь показывается как можно конвертировать дату, записанной в формате “character” в дату формата “Date”.
str("2014-01-01") chr "2014-01-01"class("2014-01-01")[1] "character"str(as.Date("01/01/2011")) Date[1:1], format: "1-01-20"str(as.Date("2014-01-01 17:01:01")) Date[1:1], format: "2014-01-01"Для работы с данными следует воспользоваться библотекой lubridate. Рассматриваем сдуеющую расшифровку ymd - year month day mdy - month day year dmy - day month year ymd_hms(df$dropoff_datetime) # возвращает дату в формате год-месц-день_часы-минуты-секунды
Посмотрим на формат данных
str(ymd_hms(df$dropoff_datetime))## POSIXct[1:1458644], format: "2016-03-14 17:32:30" "2016-06-12 00:54:38" ...table((df\(dropoff_datetime-df\)pickup_datetime) == df$trip_duration)
5 Задача
Условие задачи: Определить время поездки на такси. Зависимая переменная (ЗП) - trip_duration
str(df) # Смотрим на тип данныхClasses 'data.table' and 'data.frame': 1458644 obs. of 11 variables:
$ id : chr "id2875421" "id2377394" "id3858529" "id3504673" ...
$ vendor_id : int 2 1 2 2 2 2 1 2 1 2 ...
$ pickup_datetime : chr "2016-03-14 17:24:55" "2016-06-12 00:43:35" "2016-01-19 11:35:24" "2016-04-06 19:32:31" ...
$ dropoff_datetime : chr "2016-03-14 17:32:30" "2016-06-12 00:54:38" "2016-01-19 12:10:48" "2016-04-06 19:39:40" ...
$ passenger_count : int 1 1 1 1 1 6 4 1 1 1 ...
$ pickup_longitude : num -74 -74 -74 -74 -74 ...
$ pickup_latitude : num 40.8 40.7 40.8 40.7 40.8 ...
$ dropoff_longitude : num -74 -74 -74 -74 -74 ...
$ dropoff_latitude : num 40.8 40.7 40.7 40.7 40.8 ...
$ store_and_fwd_flag: chr "N" "N" "N" "N" ...
$ trip_duration : int 455 663 2124 429 435 443 341 1551 255 1225 ...
- attr(*, ".internal.selfref")=<externalptr> 6 Очистка данных
ymd_hms() # преобразует данныеPOSIXct of length 0df$pickup_datetime <- ymd_hms(df$pickup_datetime)
df$dropoff_datetime <- ymd_hms(df$dropoff_datetime)
str(df) # Проверяем формат данныхClasses 'data.table' and 'data.frame': 1458644 obs. of 11 variables:
$ id : chr "id2875421" "id2377394" "id3858529" "id3504673" ...
$ vendor_id : int 2 1 2 2 2 2 1 2 1 2 ...
$ pickup_datetime : POSIXct, format: "2016-03-14 17:24:55" "2016-06-12 00:43:35" ...
$ dropoff_datetime : POSIXct, format: "2016-03-14 17:32:30" "2016-06-12 00:54:38" ...
$ passenger_count : int 1 1 1 1 1 6 4 1 1 1 ...
$ pickup_longitude : num -74 -74 -74 -74 -74 ...
$ pickup_latitude : num 40.8 40.7 40.8 40.7 40.8 ...
$ dropoff_longitude : num -74 -74 -74 -74 -74 ...
$ dropoff_latitude : num 40.8 40.7 40.7 40.7 40.8 ...
$ store_and_fwd_flag: chr "N" "N" "N" "N" ...
$ trip_duration : int 455 663 2124 429 435 443 341 1551 255 1225 ...
- attr(*, ".internal.selfref")=<externalptr> df$id <- NULL # Удаляем переменную не значимую для анализа
df$store_and_fwd_flag <- as.factor(df$store_and_fwd_flag) # Преобразуем данные в факторные данные с двумя уровнями: "N" и "Y"
str(df$store_and_fwd_flag) Factor w/ 2 levels "N","Y": 1 1 1 1 1 1 1 1 1 1 ...sum(is.na(df)) # Подсчитываем колличество NA значений[1] 0boxplot(df$trip_duration) # Строим ящик с усами для того, чтобы увидеть какое распределение зависимой переменной
outliers <- boxplot(df$trip_duration)$out # записываем все выбросы для дальнейшей работы
x = (df[-(which(df$trip_duration %in% outliers)),]) # Удаляем данные из дата фрейма, чьи значения в переменной trip_duration относящийеся к выбросам
nrow(x)/nrow(df) #проверяем соотносимость оставшихся данных от всех изначальных[1] 0.9491171boxplot(x$trip_duration) # Строим ящик с усами для того, чтобы увидеть какое распределение данных зависимой переменной в выборке без выбросов
df <- x # Обновляем нашу выборку6.1 Пункт крутых идеи
Можно долготу и широту сразу преобразовать в расстояние.
Расчленяем данные дат и создаем соответвующие им новые переменные.
df$week <- (lubridate::wday(df$pickup_datetime))
df$hour <- (lubridate::hour(df$pickup_datetime))
df$month <- (lubridate::month(df$pickup_datetime))
df$year <- (lubridate::year(df$pickup_datetime))
df$day <- (lubridate::day(df$pickup_datetime))# Строим график длительности поездки по дням недели
ggplot(df,aes(y=trip_duration,group=week,fill=as.factor(week)))+
geom_boxplot()
# Убираем ненужные пременные
df$pickup_datetime <- NULL
df$dropoff_datetime <- NULL
# Высчитываем координаты посадки x, y, z относительно ядра Земли по формулам
df$x <- cos(df$pickup_latitude)*cos(df$pickup_longitude)
df$y <- cos(df$pickup_latitude)*sin(df$pickup_longitude)
df$z <- sin(df$pickup_latitude)
# Высчитываем координаты конечного пункта поездки x_, y_, z_ относительно ядра Земли по формулам
df$x_ <- cos(df$dropoff_latitude)*cos(df$dropoff_longitude)
df$y_ <- cos(df$dropoff_latitude)*sin(df$dropoff_longitude)
df$z_ <- sin(df$dropoff_latitude)
attach(df) # Сохраняем название переменных дата фрейма в памяти для упрощенного вызова
# Избавляемся от ненужных перемен
df <- select(df,-c(pickup_latitude,pickup_longitude,dropoff_latitude,dropoff_longitude))7 Машинное обучение
Разделяем данные для обучения (train) и тестирования (test) в соотношении 80% для обучения и 20% для теста.
index <- createDataPartition(df$trip_duration,p=0.8,list = F)
tr <- df[index,]
ts <- df[-index,]7.1 Модель №1
# строим можель линейной зависимости между ЗП и всеми остальными переменными
fit <- lm(trip_duration~.,tr)
summary(fit) # анализируем полученную модель ( 0.06457)
Call:
lm(formula = trip_duration ~ ., data = tr)
Residuals:
Min 1Q Median 3Q Max
-12419.1 -326.6 -84.6 256.3 2800.8
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.199e+03 8.268e+01 26.602 <2e-16 ***
vendor_id 1.479e+00 8.657e-01 1.708 0.0877 .
passenger_count 3.900e+00 3.281e-01 11.884 <2e-16 ***
store_and_fwd_flagY 5.794e+01 5.789e+00 10.009 <2e-16 ***
week 7.069e+00 2.061e-01 34.299 <2e-16 ***
hour 2.765e+00 6.401e-02 43.197 <2e-16 ***
month 1.081e+01 2.454e-01 44.065 <2e-16 ***
year NA NA NA NA
day 5.082e-01 4.731e-02 10.741 <2e-16 ***
x 9.865e+02 1.903e+01 51.826 <2e-16 ***
y -5.219e+03 1.391e+02 -37.517 <2e-16 ***
z 1.991e+03 2.665e+01 74.731 <2e-16 ***
x_ 2.699e+03 1.939e+01 139.232 <2e-16 ***
y_ 6.548e+03 1.293e+02 50.643 <2e-16 ***
z_ 9.677e+02 2.283e+01 42.385 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 433.7 on 1107527 degrees of freedom
Multiple R-squared: 0.06384, Adjusted R-squared: 0.06383
F-statistic: 5810 on 13 and 1107527 DF, p-value: < 2.2e-16plot(fit)
head(tr) # Посмотрим как выглядит выборка vendor_id passenger_count store_and_fwd_flag trip_duration week hour
1: 1 1 N 663 1 0
2: 2 1 N 429 4 19
3: 2 1 N 1551 7 7
4: 1 1 N 255 6 23
5: 2 1 N 1225 5 21
6: 2 1 N 1274 3 22
month year day x y z x_ y_
1: 6 2016 12 -0.1515976 -0.9831692 0.10196345 -0.17017986 -0.9793288
2: 4 2016 6 -0.1802777 -0.9762141 0.12044069 -0.18214270 -0.9741555
3: 5 2016 21 -0.1412436 -0.9890444 0.04291223 -0.09459509 -0.9922914
4: 5 2016 27 -0.1703111 -0.9800838 0.10212663 -0.15678110 -0.9817457
5: 3 2016 10 -0.1523078 -0.9836385 0.09621643 -0.14487211 -0.9881509
6: 5 2016 10 -0.1541443 -0.9850599 0.07678911 -0.17290369 -0.9790540
z_
1: 0.10933391
2: 0.13358552
3: 0.08005964
4: 0.10768052
5: 0.05069329
6: 0.10750606prognoz <- predict(fit,ts) # Прогнозируем значения ЗП по построенной моделиWarning in predict.lm(fit, ts): prediction from a rank-deficient fit may be
misleading7.1.1 Анализ эффективности модели
RMSE(prognoz,ts$trip_duration)[1] 433.842# Анализируем распределение ошибки модели
boxplot(prognoz-ts$trip_duration)
qplot(prognoz-ts$trip_duration)
summary(ts$pred)Length Class Mode
0 NULL NULL #Сравниваем распределение значений ЗП
summary(ts$trip_duration) Min. 1st Qu. Median Mean 3rd Qu. Max.
1.0 384.0 632.0 731.3 991.0 2092.0 7.2 Модель №2
Cтроим альтернативную модель для того, чтобы выбрать наиболее эффективную модель. Альтернативная модель строится на основе зависимости ЗП взятой в логарифм от всех остальных переменных.
# Logged dataset
tr_log <- tr
tr_log$trip_duration <- log(tr_log$trip_duration)
fit_log <- lm(trip_duration~.,tr_log)
summary(fit_log)
Call:
lm(formula = trip_duration ~ ., data = tr_log)
Residuals:
Min 1Q Median 3Q Max
-12.9034 -0.4126 0.0763 0.5065 6.5977
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.875e+00 1.350e-01 43.526 < 2e-16 ***
vendor_id 9.234e-03 1.413e-03 6.534 6.42e-11 ***
passenger_count 7.909e-03 5.357e-04 14.764 < 2e-16 ***
store_and_fwd_flagY 4.391e-02 9.450e-03 4.646 3.38e-06 ***
week 1.035e-02 3.365e-04 30.776 < 2e-16 ***
hour 5.064e-03 1.045e-04 48.467 < 2e-16 ***
month 1.399e-02 4.006e-04 34.924 < 2e-16 ***
year NA NA NA NA
day 7.473e-04 7.723e-05 9.676 < 2e-16 ***
x 2.225e-01 3.107e-02 7.159 8.11e-13 ***
y -7.273e+00 2.271e-01 -32.026 < 2e-16 ***
z 2.764e+00 4.350e-02 63.529 < 2e-16 ***
x_ 2.881e+00 3.165e-02 91.041 < 2e-16 ***
y_ 6.852e+00 2.111e-01 32.461 < 2e-16 ***
z_ 1.183e+00 3.727e-02 31.742 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.708 on 1107527 degrees of freedom
Multiple R-squared: 0.02936, Adjusted R-squared: 0.02935
F-statistic: 2577 on 13 and 1107527 DF, p-value: < 2.2e-16# Высчитываем прогнозируемые данные беря экспоненту прогноза
prognoz <- exp(predict(fit_log,ts))Warning in predict.lm(fit_log, ts): prediction from a rank-deficient fit
may be misleadingts$pred <- prognoz
# Смотрим распределение данных
summary(ts$pred) Min. 1st Qu. Median Mean 3rd Qu. Max.
7 554 582 701 615 29024200 # избавляемся от выбросов (в реальном тесте так сделать не получиться)
ts <- ts[ts$pred<3.368e+09,]
# сравниваем распределение ЗП и прогноза
summary(ts$pred) Min. 1st Qu. Median Mean 3rd Qu. Max.
7 554 582 701 615 29024200 summary(ts$trip_duration) Min. 1st Qu. Median Mean 3rd Qu. Max.
1.0 384.0 632.0 731.3 991.0 2092.0 7.2.1 Анализ эффективности модели
Анализиируем модель по результатом рапределения ошибки модели.
RMSE(ts$pred,ts$trip_duration)[1] 55157.72boxplot(ts$pred-ts$trip_duration)
qplot(ts$pred-ts$trip_duration)
summary(ts$pred-ts$trip_duration) Min. 1st Qu. Median Mean 3rd Qu. Max.
-1688 -394 -46 -31 196 29022795 7.3 Модель 3: XGBoost
Создаем sparse matrix, где будут значения наших предикторов, и отдельный вектор для зависимой прееменной. Далее сохраняем матрицу и вектор в объекте dtrain и ctest для тренировочной и тестовой выборки соответвенно.
ts$pred <- NULL
tr_matrix <- data.matrix(select(tr,-c(trip_duration)))
ts_matrix <- data.matrix(select(ts,-c(trip_duration)))
train_target <- tr$trip_duration
test_target <- ts$trip_duration
dtrain <- xgb.DMatrix(data=tr_matrix,label=train_target)
ctest <- xgb.DMatrix(data=ts_matrix,label=test_target)Создаем watchlist для просмотра промежуточных результатов.
watchlist = list(train=dtrain,test=ctest)Cтроим модель со следующими параметрами:
bst <- xgb.train(data=dtrain,
booster="gbtree",
watchlist = watchlist,
nrounds = 30000,
objective = "reg:linear",
eval_metric="rmse",
maximize = F,
early_stopping_rounds = 10,
max_depth=10,
subsample=0.7,
colsample_bytree=0.7,
lambda=0.01,
alpha=0.0001
)[1] train-rmse:648.846191 test-rmse:648.991577
Multiple eval metrics are present. Will use test_rmse for early stopping.
Will train until test_rmse hasn't improved in 10 rounds.
[2] train-rmse:510.795135 test-rmse:511.477814
[3] train-rmse:419.720764 test-rmse:421.043243
[4] train-rmse:368.974274 test-rmse:370.904144
[5] train-rmse:335.429901 test-rmse:337.635223
[6] train-rmse:315.083679 test-rmse:317.761658
[7] train-rmse:299.923187 test-rmse:303.028046
[8] train-rmse:290.015869 test-rmse:293.650391
[9] train-rmse:278.564789 test-rmse:282.470581
[10] train-rmse:273.517792 test-rmse:277.904388
[11] train-rmse:268.637421 test-rmse:273.369995
[12] train-rmse:262.466827 test-rmse:267.617920
[13] train-rmse:251.234955 test-rmse:256.794495
[14] train-rmse:248.161423 test-rmse:254.101349
[15] train-rmse:246.309052 test-rmse:252.572174
[16] train-rmse:240.802231 test-rmse:247.456406
[17] train-rmse:238.937027 test-rmse:246.033478
[18] train-rmse:237.901657 test-rmse:245.347702
[19] train-rmse:236.876312 test-rmse:244.565994
[20] train-rmse:235.539413 test-rmse:243.581528
[21] train-rmse:234.400269 test-rmse:242.763763
[22] train-rmse:232.871841 test-rmse:241.503098
[23] train-rmse:226.248779 test-rmse:235.161133
[24] train-rmse:225.527283 test-rmse:234.676910
[25] train-rmse:224.286819 test-rmse:233.755859
[26] train-rmse:223.803345 test-rmse:233.443604
[27] train-rmse:218.863251 test-rmse:228.860992
[28] train-rmse:218.538589 test-rmse:228.645599
[29] train-rmse:217.906219 test-rmse:228.249237
[30] train-rmse:216.568207 test-rmse:227.265076
[31] train-rmse:215.297516 test-rmse:226.160889
[32] train-rmse:214.545517 test-rmse:225.613251
[33] train-rmse:213.554153 test-rmse:224.887695
[34] train-rmse:212.275131 test-rmse:223.876526
[35] train-rmse:210.652161 test-rmse:222.581512
[36] train-rmse:209.994537 test-rmse:222.235413
[37] train-rmse:209.440536 test-rmse:221.954834
[38] train-rmse:208.934372 test-rmse:221.710892
[39] train-rmse:207.109543 test-rmse:220.239319
[40] train-rmse:206.294022 test-rmse:219.669128
[41] train-rmse:205.791931 test-rmse:219.386353
[42] train-rmse:204.528549 test-rmse:218.466415
[43] train-rmse:204.358536 test-rmse:218.423752
[44] train-rmse:203.836914 test-rmse:218.073959
[45] train-rmse:203.776245 test-rmse:218.062836
[46] train-rmse:203.200577 test-rmse:217.630157
[47] train-rmse:202.729477 test-rmse:217.405060
[48] train-rmse:202.415009 test-rmse:217.273468
[49] train-rmse:201.966400 test-rmse:217.070969
[50] train-rmse:201.780548 test-rmse:216.986160
[51] train-rmse:201.267746 test-rmse:216.632309
[52] train-rmse:200.880234 test-rmse:216.497711
[53] train-rmse:200.710785 test-rmse:216.443451
[54] train-rmse:199.607574 test-rmse:215.645554
[55] train-rmse:198.969040 test-rmse:215.178711
[56] train-rmse:198.708344 test-rmse:215.118958
[57] train-rmse:198.564697 test-rmse:215.086319
[58] train-rmse:198.472610 test-rmse:215.076416
[59] train-rmse:198.304596 test-rmse:215.063568
[60] train-rmse:198.227631 test-rmse:215.076416
[61] train-rmse:197.997971 test-rmse:215.041290
[62] train-rmse:197.770752 test-rmse:214.999756
[63] train-rmse:197.574585 test-rmse:214.964172
[64] train-rmse:197.189682 test-rmse:214.749619
[65] train-rmse:196.504532 test-rmse:214.304794
[66] train-rmse:196.218689 test-rmse:214.178986
[67] train-rmse:196.138138 test-rmse:214.166168
[68] train-rmse:196.046616 test-rmse:214.130096
[69] train-rmse:195.959412 test-rmse:214.122147
[70] train-rmse:195.649796 test-rmse:214.005066
[71] train-rmse:195.461136 test-rmse:213.989594
[72] train-rmse:195.027969 test-rmse:213.819534
[73] train-rmse:194.922897 test-rmse:213.828552
[74] train-rmse:194.658691 test-rmse:213.725479
[75] train-rmse:194.449829 test-rmse:213.670944
[76] train-rmse:194.128647 test-rmse:213.572525
[77] train-rmse:194.061523 test-rmse:213.566467
[78] train-rmse:193.774338 test-rmse:213.515778
[79] train-rmse:193.666306 test-rmse:213.515305
[80] train-rmse:193.239639 test-rmse:213.289642
[81] train-rmse:193.100266 test-rmse:213.258392
[82] train-rmse:192.562088 test-rmse:213.036301
[83] train-rmse:192.282623 test-rmse:212.884796
[84] train-rmse:192.193878 test-rmse:212.874939
[85] train-rmse:192.001740 test-rmse:212.836304
[86] train-rmse:191.804245 test-rmse:212.805344
[87] train-rmse:191.703735 test-rmse:212.794907
[88] train-rmse:191.584915 test-rmse:212.769516
[89] train-rmse:191.513000 test-rmse:212.766632
[90] train-rmse:191.428543 test-rmse:212.766266
[91] train-rmse:191.321106 test-rmse:212.753922
[92] train-rmse:191.226486 test-rmse:212.757034
[93] train-rmse:191.091644 test-rmse:212.755325
[94] train-rmse:191.009811 test-rmse:212.750381
[95] train-rmse:190.794464 test-rmse:212.721161
[96] train-rmse:190.698059 test-rmse:212.687027
[97] train-rmse:190.303650 test-rmse:212.516022
[98] train-rmse:190.217896 test-rmse:212.520050
[99] train-rmse:190.082001 test-rmse:212.506729
[100] train-rmse:189.867874 test-rmse:212.449020
[101] train-rmse:189.788574 test-rmse:212.435669
[102] train-rmse:189.777267 test-rmse:212.437973
[103] train-rmse:189.658661 test-rmse:212.425552
[104] train-rmse:189.165955 test-rmse:212.188904
[105] train-rmse:188.956879 test-rmse:212.133057
[106] train-rmse:188.754852 test-rmse:212.119583
[107] train-rmse:188.588058 test-rmse:212.112686
[108] train-rmse:188.394211 test-rmse:212.051544
[109] train-rmse:188.300430 test-rmse:212.030228
[110] train-rmse:188.241013 test-rmse:211.997345
[111] train-rmse:188.117020 test-rmse:211.964783
[112] train-rmse:188.053986 test-rmse:211.963715
[113] train-rmse:187.872864 test-rmse:211.934814
[114] train-rmse:187.802032 test-rmse:211.928970
[115] train-rmse:187.766785 test-rmse:211.925919
[116] train-rmse:187.631378 test-rmse:211.935730
[117] train-rmse:187.527481 test-rmse:211.946915
[118] train-rmse:187.462189 test-rmse:211.937546
[119] train-rmse:187.399841 test-rmse:211.937439
[120] train-rmse:187.155899 test-rmse:211.897537
[121] train-rmse:186.993393 test-rmse:211.874283
[122] train-rmse:186.831314 test-rmse:211.852509
[123] train-rmse:186.751572 test-rmse:211.838379
[124] train-rmse:186.704926 test-rmse:211.846573
[125] train-rmse:186.620865 test-rmse:211.839630
[126] train-rmse:186.582382 test-rmse:211.837723
[127] train-rmse:186.431427 test-rmse:211.831619
[128] train-rmse:186.108932 test-rmse:211.760727
[129] train-rmse:185.900757 test-rmse:211.696503
[130] train-rmse:185.781448 test-rmse:211.718796
[131] train-rmse:185.759018 test-rmse:211.722672
[132] train-rmse:185.693024 test-rmse:211.732452
[133] train-rmse:185.625931 test-rmse:211.732101
[134] train-rmse:185.393265 test-rmse:211.693909
[135] train-rmse:185.281357 test-rmse:211.677307
[136] train-rmse:185.125107 test-rmse:211.681335
[137] train-rmse:184.875061 test-rmse:211.558487
[138] train-rmse:184.800613 test-rmse:211.542831
[139] train-rmse:184.757370 test-rmse:211.553925
[140] train-rmse:184.707458 test-rmse:211.545334
[141] train-rmse:184.654068 test-rmse:211.552536
[142] train-rmse:184.415497 test-rmse:211.495163
[143] train-rmse:184.371582 test-rmse:211.497787
[144] train-rmse:184.294785 test-rmse:211.492081
[145] train-rmse:184.084885 test-rmse:211.475815
[146] train-rmse:184.052795 test-rmse:211.480988
[147] train-rmse:183.981293 test-rmse:211.495651
[148] train-rmse:183.842880 test-rmse:211.480301
[149] train-rmse:183.806656 test-rmse:211.480453
[150] train-rmse:183.645233 test-rmse:211.444977
[151] train-rmse:183.572006 test-rmse:211.447418
[152] train-rmse:183.509079 test-rmse:211.462723
[153] train-rmse:183.460831 test-rmse:211.461517
[154] train-rmse:183.424927 test-rmse:211.466415
[155] train-rmse:183.335312 test-rmse:211.484100
[156] train-rmse:183.261749 test-rmse:211.501465
[157] train-rmse:183.082642 test-rmse:211.465622
[158] train-rmse:182.969849 test-rmse:211.456848
[159] train-rmse:182.894669 test-rmse:211.429001
[160] train-rmse:182.752518 test-rmse:211.447342
[161] train-rmse:182.736801 test-rmse:211.444962
[162] train-rmse:182.670441 test-rmse:211.446930
[163] train-rmse:182.601288 test-rmse:211.436417
[164] train-rmse:182.537079 test-rmse:211.452744
[165] train-rmse:182.450256 test-rmse:211.454269
[166] train-rmse:181.948013 test-rmse:211.230042
[167] train-rmse:181.851334 test-rmse:211.228683
[168] train-rmse:181.714874 test-rmse:211.252380
[169] train-rmse:181.479080 test-rmse:211.199097
[170] train-rmse:181.436905 test-rmse:211.207413
[171] train-rmse:181.226089 test-rmse:211.150940
[172] train-rmse:181.177063 test-rmse:211.160278
[173] train-rmse:181.128250 test-rmse:211.170380
[174] train-rmse:181.004059 test-rmse:211.133286
[175] train-rmse:180.811462 test-rmse:211.102875
[176] train-rmse:180.690338 test-rmse:211.124939
[177] train-rmse:180.643524 test-rmse:211.124252
[178] train-rmse:180.589264 test-rmse:211.131668
[179] train-rmse:180.508606 test-rmse:211.145996
[180] train-rmse:180.263062 test-rmse:211.060791
[181] train-rmse:180.134293 test-rmse:211.067337
[182] train-rmse:180.092087 test-rmse:211.066727
[183] train-rmse:180.035538 test-rmse:211.079269
[184] train-rmse:179.971222 test-rmse:211.079071
[185] train-rmse:179.776581 test-rmse:211.026993
[186] train-rmse:179.743225 test-rmse:211.025681
[187] train-rmse:179.697968 test-rmse:211.023941
[188] train-rmse:179.640594 test-rmse:211.012466
[189] train-rmse:179.529770 test-rmse:211.024506
[190] train-rmse:179.466217 test-rmse:211.038116
[191] train-rmse:179.414932 test-rmse:211.049545
[192] train-rmse:179.316452 test-rmse:211.048798
[193] train-rmse:179.195618 test-rmse:211.051208
[194] train-rmse:179.136230 test-rmse:211.069626
[195] train-rmse:179.060211 test-rmse:211.076904
[196] train-rmse:178.910172 test-rmse:211.085419
[197] train-rmse:178.882126 test-rmse:211.096268
[198] train-rmse:178.845673 test-rmse:211.097794
Stopping. Best iteration:
[188] train-rmse:179.640594 test-rmse:211.0124667.3.1 Анализ эффективности модели
Анализиируем модель по результатом рапределения ошибки модели.
pred <- predict(bst,ctest)
RMSE(pred, ts$trip_duration)[1] 211.01258 Вывод
Мы видим, что модель линейной регрессии построенной на xgboost выдала нам сравнительно лучший результат.
A work by YOUR NAME
YOUREMAIL@gmail.com