---
title: "Solution Session 1"
output: html_document
author: "Dr. Thomas Pollet, Northumbria University (thomas.pollet@northumbria.ac.uk)"
date: '`r format(Sys.Date())` | [disclaimer](http://tvpollet.github.io/disclaimer)'
---

## R Markdown for Lecture 1 exercise.

 Load the flights dataset.

 Calculate the mean delay in arrival for Delta Airlines (DL) (use **filter()**)

 Calculate the associated 95% confidence interval.

 Do the same for United Airlines (UA) and compare the two. Do their confidence intervals overlap?

 Calculate the mode for the delay in arrival for at JFK airport.

 save a dataset as .sav with only departing flights from JFK airport.


### Load the flights data.

```{r}
library(nycflights13)
flights<-nycflights13::flights
```

### Select just the delta flights

```{r}
require(dplyr)
delta<-filter(flights, carrier=="DL")
```

### Means 

```{r}
#remove the missings
# chose to work in same dataset. (for safety reasons you could make a new one!)
delta<-filter(delta, arr_delay!='NA')
mean(delta$arr_delay)
# store it
mean_delta<-mean(delta$arr_delay)
```

### 95% CI

First get the 'se'
```{r}
se_delta<-sd(delta$arr_delay)/sqrt(length(delta$arr_delay))
se_delta
```

Now calculate 95%CI.

```{r}
UL_delta<- (mean_delta + 1.96*se_delta)
LL_delta<- (mean_delta - 1.96*se_delta)
UL_delta
LL_delta
```

### United airlines.

All in one go

```{r}
require(dplyr)
united<-filter(flights, carrier=="UA")
united<-filter(united, arr_delay!='NA')
mean(united$arr_delay)
# store it
mean_united<-mean(united$arr_delay)
se_united<-sd(united$arr_delay)/sqrt(length(united$arr_delay))
se_united
UL_united<- (mean_united + 1.96*se_united)
LL_united<- (mean_united - 1.96*se_united)
UL_united
LL_united

```

### Conclusion: Delta vs. United.

The 95%CI's do not overlap. United [3.22 to 3.89] is significantly slower in terms of arrival time than Delta [1.25 to 2.04].

### JFK airport

#### Make a dataset.

```{r}
jfk<- filter(flights, origin=="JFK")
# remove the missings.
jfk<- filter(jfk, arr_delay!='NA')
```

#### Calculate the mode.

```{r}
library(modeest)
mlv(jfk$arr_delay,  method='mfv')
```

The mode is  -13. The most common value in the dataset is thus 13 minutes early!

#### Write away the data.

```{r}
require(haven)
write_sav(jfk, 'jfk.sav')
```

The end.

```{r, out.width = "400px", echo=FALSE}
knitr::include_graphics("https://i.imgur.com/60CsJQf.gif")
```