In brbatv/lab7: RC class for ridge regression

In this file we try to predict the delay of each flight using the ridgereg() function from the package lab7ab.

library(devtools)
library(caret)
library(nycflights13)
library(dplyr)
#install_github("brbatv/lab7",force=TRUE)
library(lab7ab)

Cleaning "weather" and "flights" datasets:

Exploring the dataset from nycflights13 library.

The dataset weather has the following variables:

colnames(weather)

The dataset flights has the following variables:

colnames(flights)

The two datasets have some common variable such as: year,month, day, origin, hour, time_hour so a new dataset is created by adding extra informations to the flights dataset.

flights_weather <- left_join(flights, weather,by = c("year", "month", "day", "origin", "hour", "time_hour"))

The weather variables are interesting to be selected for the prediction so the database has been created with the added columns:

database <- select(flights_weather,month,day, sched_dep_time,sched_arr_time, dep_delay, arr_delay,temp,dewp,wind_dir, wind_speed,wind_gust,precip,pressure,visib)

Data partition: test, train and validation

To use the caret package all the missing values need to be taked off from the database. The data, at this point, have been splitted into three new dataset:

\itemize{

\item train 80% of the observations \item test 5% of the observations \item validation 15% of the observations

}

library(caret)
set.seed(3456)
database<-na.omit(database)

trainIndex = createDataPartition(database$arr_delay, 
                       p=0.8, list=FALSE,times=1)
train = database[trainIndex,]
notrain = database[-trainIndex,]
validationIndex = createDataPartition(notrain$arr_delay, 
                       p=0.75, list=FALSE,times=1)
validation=database[validationIndex,]

test = notrain[-validationIndex,]

Training Ridge Regression

Training on the train dataset the best value obtained for lambda is $10^{8}$.

#root mean squared arror
rmse <- function(error){
    sqrt(mean(error^2))
}

#formula for ridge regression
formula=arr_delay~month+day+sched_dep_time+sched_arr_time+dep_delay+temp+dewp+wind_dir+ wind_speed+wind_gust+precip+pressure+visib 

#training ridge regression for different values of lambda
mod<-ridgereg$new(formula=formula, data=train,lambda=10^8)

Y_validation<-validation$arr_delay
Y_predicted <- mod$predict(newdata=validation)

#calculating the error
error= Y_predicted - Y_validation


RMSE_check<-rmse(error)

Best Lambda found for the predicted model

The best lambda has been found, with it the test set has been predicted and the RMSE of the predicted model is:

best_lambda=10^8

mod<-ridgereg$new(formula=formula, data=train,lambda=best_lambda)  

Y_test<-test$arr_delay
Y_predicted2 <- mod$predict(newdata=test)

error2= Y_predicted2 - Y_test

RMSE_best_lambda<-rmse(error2)
RMSE_best_lambda