FlightDelaysAnalysis_Team3.Rmd

---
title: "FlightDelays"
author: "[redacted]"
date: "[redacted]"
output: html_document
---

## R Markdown
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see <http://rmarkdown.rstudio.com>.

**This exercise is under construction. Please report any errors at https://forms.gle/2W4tffs4YJA1jeBv9**

Goal: Experience the Fraud Analytics Process Model

Background:
The Fraud Analytics Process Model:
1. ID Problem
2. ID Data Sources
3. Select Data
4. Clean Data
5. Transform Data
6. Analyze Data
7. Interpret Model
8. Refine Model

**The first ten questions are for the individual assignment and the remaining questions are for the team assignment. Specifically:**
**For the individual assignment submissions: Delete everything below Q10. Then, knit and submit your html and Rmd files.**
**For the team assignment submissions: Pick any individual team member's answers for the first ten questions. Then complete the remaining questions to submit for the team assignment.**

1. Delete everything below Q10 and submit for individual assignment.
2. Pick any individual team member's answers for the first ten questions and then knit the remaining questions to submit for the team assignment.

Individual assignment: 25 total points
Team assignment: 135 total points


## [1 point] Q1.
*Start by entering your name and today's date in Lines 3 and 4, respectively.* 
*Then, run the chunk of code below by clicking on the green arrow (that points to the right) on the top right of the chunk.*
*Tip: This line of code (knitr...) is generated by RStudio. It allows you to format (knit) your output so you can share in a readable format. We will use an html format for output as specified in Line 5. You will be instructed to "knit" after completing the assignment without any errors.*
*Tip: I numbered code chunks corresponding to their numbers. Chunk 1 specified the knitting parameters.*

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


# 1. ID Problem: 
*This assignment is inspired by https://www.nbcnews.com/business/business-news/united-airlines-fined-1-9-million-long-tarmac-delays-largest-n1280051 and similar events.*
*Flight cancellations and delays due to weather are not the airlines' responsibility. Our goal is to detect and report any delays that are not due to weather for further investigation.*

# 2. ID Data Sources
*We will analyze data in nycflights13 because it contains information about all flights originating from NYC airports in 2013. Please take a moment to skim https://cran.r-project.org/web/packages/nycflights13/nycflights13.pdf with a focus on finding information about cancellations/delays as well as weather.*

## [2 points] Q2. 
*Install and load packages tidyverse and nycflights13.*
*Tip: tidyverse package gives you a tidy way of manipulating data.*
*Tip: install.packages("packageName") command installs package packageName. library(packageName) will load package packageName.*
*Tip: You only need to install packages once and you are free to load them afterwards. In fact, you will need to remove the install command to knit and submit your solutions.*

```{r}
#install.packages("tidyverse")
library(tidyverse)
#install.packages("nycflights13")
library(nycflights13)
```

## [1 point] Q3. 
*Confirm that the package you loaded in the previous chunk by using the search() function. There is nothing enclosed in parentheses because search doesn't need any information (parameters).*
```{r}
# Confirmed what packages have been loaded
search()

```

## [1 point] Q4. 
*Now, take a peek inside nycflights13 by using the command ls("package:nycflights13")*
*Tip: ls("package:packageName") gives the names of the objects in packageName.*
```{r}
ls("package:nycflights13")

```

## [1 point] Q5. 
*Now, see what is in your environment by using the command ls() without anything inside the parentheses.*
*Tip: ls() provides information about data sets and functions defined by the user. This will give character(0) if there is nothing in the environment. It is a good idea to start every R script with a clean environment so previous data doesn't corrupt your script.* 
*Tip: You may clean your environment at any time by using the broom in the environment tab (likely near top right of RStudio) or using the command rm(list = ls()).*
```{r}
#rm(list = ls())
ls()

```

## [2 points] Q6.
*Find the tibbles that contain information about flight delays and weather using the information from nycflights13 documentation, and assign them to variables names tFlights and tWeather, respectively.*
*Tip: Tibbles are a more robust and refined version of data frames. You may Google tibble to learn more about tibbles (but it is not necessary at this time).*
*Tip: You may start variable names with 1+ letters abbreviating the data type, followed by a descriptive word (or words) for the variable. For example, "tFlights" can be used for the tibble containing flights data. By just reading the variable name, you can deduce that it is a tibble because it starts with "t", and that it contains flights data because of the word "flights". You need not worry about long variable names because you can copy-paste or use autocomplete. You may learn more about naming conventions at https://en.wikipedia.org/wiki/Naming_convention_(programming).*

```{r}
tFlights = flights
view(tFlights)

tWeather = weather
view(tWeather)

```

## [1 point] Q7.
*Now, use ls() to see how your environment have changed.*
*Tip: Also, checkout the new variables in the environment tab.*

```{r}
ls()
```

## [2 points] Q8. 
*Now, use head function to print and check out the first 10 lines of the tibbles containing the flights and weather data.*
*Tip: Use https://cran.r-project.org/web/packages/nycflights13/nycflights13.pdf to understand the details of each data set.*
*Tip: Always check what you read into your program.*
*Tip: Get accustomed vertical and horizontal scrolling.*
*T1ip: Get accustomed to clicking on different tabs when they are printed by one code chunk.*

```{r}
head(tFlights, 10)
head(tWeather, 10)
```

## [4 points] Q9. 
*Now, print the structure and summary statistics of the tibbles containing the flights and weather data.*
*Tip: Get accustomed to working with datasets that can't fit on a spreadsheet (and your head).*

```{r}
str(tFlights)
summary(tFlights)

str(tWeather)
summary(tWeather)

```


# 3. Select Data

## [10 points] Q10.
*Using the information above, identify columns of each tibble that you will need for your analysis.*
*Tip: Copy-paste from https://cran.r-project.org/web/packages/nycflights13/nycflights13.pdf and then delete what you don't need after completing your analysis. This will serve as your data dictionary.*
*Tip: You may update this list as you progress through the rest of the assignment. Don't worry about getting it perfect right now.*
```{r}
### This section doesn't require code. Just list all the columns of each dataset you'll need for your analysis.### 
#year, month, day, hour Time of recording.
#origin Weather station. Named origin to facilitate merging with flights data.

# flight dataset

#  year, month, day         flight date information.         
#  dep_delay                flight delay time in minutes, positive number means there is a delay.     
#  carrier                  airline abbreviation  
#  flight                   flight number
#  origin                   flight departure airport   
#  dest                     flight arrival airport
#  hour                     flight departure hour
#  minute                   flighty departure minute
  
# weather dataset

#  origin                   weather station in the flight departure airport     
#  year, month, day, hour   time when the weather information is recorded           
#  temp, dewp, humid        temperature information       
#  wind_dir, wind_speed, 
#  wind_gust                wind information       
#  time_hour                time when weather was recorded  
#  precip                   precipitation in inches
#  pressure                 sea level pressure in millibars
#  visib                    weather visibility
```

**For the individual assignment submissions: Delete the everything below this line. Then, knit and submit your html and Rmd files.**
**For the team assignment submissions: Pick any individual team member's answers for the first ten questions. Then complete the remaining questions to submit for the team assignment.**

# 4. Clean Data
# 5. Transform Data
*Cleaning and transforming usually goes hand in hand. (This usually includes merging and sometimes includes sampling and other techniques.)*

## [6 points] Q11.

*Merge your the flights and weather tibbles to form one dataset called tFlightWeather with all the information you need from both tibbles in one dataframe.*

*Then, print the structure of the merged dataset.*

*Tip: The function merge(x1, x2, by = c("col1", "col2")) will merge x1 and x2 wherever columns col1 and col2 are identical. Google "merge function in R" for more details.*

*Tip: To identify the column(s) for merging the weather and flight data, consider what you need to connect the flight data to the weather data. Hint: there are 2 columns containing information about the originating airport and time.*

*Tip: Read the nycflights.pdf documentation at the link shared earlier.*
*Rubric: Merging = 5; structure = 1*

```{r}
tFlightWeather= merge(tFlights, tWeather, by=c("origin","time_hour"))
str(tFlightWeather)
```

## [3 points] Q12. 
*Does the merged dataset have fewer rows than the flights dataset? If so, which rows are omitted, and why? Does any data type change?*
*Tip: Merge is an inner join. Look for rows with missing information on join.*
```{r}
### This section requires code and descriptive answers

# Yes, the merged data set have fewer rows than the flights data set.The flights data set have 336776 rows while the merged data set have 335220 rows.

# There are many hours in the weather data set that don't have any flights.

# There is no weather information from 19:00PM on November 2 to 1AM on November 3

print("The number of row in flights dataset is:")
nrow(tFlights)

print("The number of row in flights and weather merged dataset is:")
nrow(tFlightWeather)

# Check how many rows are omitted
anti_join(tFlights, tWeather,
          by = c("time_hour", "origin")) %>%
  nrow()


```

## [4 points] Q13. 
*Answer the following questions based on the merged dataset:*

*1. What are the columns with .x and .y appended to their names?*
 # year, month, day and hour columns have .x and .y appended to their column names

*2. Are they redundant?*
 #  Yes
  
*3. Why isn't there a .x and .y appended to origin and time_hour.*
 #  .x and .y did not append to origin and time_hour because they are shared columns being used to join both data sets.   

*Rubric: 1 points for each part; 1 point for overall logic.*

```{r}
### This section doesn't require code. Just list all the columns of each dataset you'll need for your analysis.### 

```

## [7 points] Q14. 
*Now, remove any duplicate columns from merged data and store the result in dfMyFlightsWeather.*
*Then, rename the columns so that there is no ".x" and ".y" in the column names.*
*Finally, print the structure of dfMyFlightsWeather to validate your code.*
*Tip: x = y %>% select(!c("col1", "col2", ...)) will remove columns named col1, col2, ...*
*Tip: x = rename(x, c("oldcol1" = "newcol1", "oldcol2" = "newcol2", ...)) will rename oldcol1, oldcol2, ... *
*Tip: Googling for help is a learning objective for this chunk.*
*Rubric: Remove columns = 3; rename = 3, structure = 1*

```{r}
dfMyFlightsWeather = tFlightWeather %>% select(!c("year.y", "month.y", "day.y", "hour.y"))

#install.packages("plyr")
library("plyr")
dfMyFlightsWeather = rename(dfMyFlightsWeather, c("year.x" = "year", "month.x"="month", "day.x"="day", "hour.x"="hour"))
str(dfMyFlightsWeather)


```

# 6. Analyze Data
# 7. Interpret Model
# 8. Refine Model

## [5 points] Q15.
*Now, plot a simple histogram of all values in the dep_delay column. Just use the default values for any optional parameters. Assign your the output from ggplot to a descriptive variable name so you can reuse it later.*
*Then, print pMyFlightsWeather.*
*Tip: I used pMyFlightsWeather = ggplot(dfMyFlightsWeather, aes(x = dep_delay)) + geom_histogram().*
*Tip: Always remember to visualize the data before analyzing it.*
*Tip: ggplot is your friend.*
*Rubric: Plotting = 4, naming plot = 1*

```{r}
# You may copy, paste, and modify this chunk to answer later questions.
  pMyFlightsWeather = ggplot(dfMyFlightsWeather, aes(x = dep_delay)) + geom_histogram()
  pMyFlightsWeather

```

## [2 points] Q16.
*Now, print the summary statistics of dep_delay column in the merged dataframe.*

```{r}
summary(dfMyFlightsWeather$dep_delay)
```

## [3 points] Q17.
*Describe what you have learned about the distribution of dep_delay?*
*Rubric: Minimum of 3 items for 1 point each (max of 3 points).*

```{r}
### This section doesn't require code. Just answer the question.### 
# Majority flights are on time
# 8227 flights have NA information, probably they were cancelled flights

```

## [6 points] Q18.
*The previous histogram plot included canceled flights. Now, create a new dataframe called dfCanceled that contains just the flights that were canceled (dep_delay is NA).*
*Then, plot a simple histogram of all values in dfCanceled's dep_delay column.*
*Tip: You may copy, paste, and modify a previous chunk to answer part(s) of this question.*
*Tip: filter(!is.na(dep_delay)) will filter out all rows with "na" for dep_delay.*
*Tip: Don't forget to assign the output from ggplot to a descriptive variable name so you can reuse it later.*
*Rubric: Filtering = 3; plotting = 2, naming plot = 1*

```{r}
dfCanceled = dfMyFlightsWeather %>%  filter(is.na(dep_delay))
cancelledFlight = ggplot(dfCanceled, aes(x = dep_delay)) + geom_histogram()
cancelledFlight
#str(cancelledFlight)
```

## [3 points] Q19.
*Review and explain the previous histogram. Is that what you expected?*

```{r}
### This section doesn't require code. Just answer the question.### 
# The plot histogram is empty because it is for all flights which were cancelled, not delayed. Thus nothing is displayed.

```

## [2 points] Q20. 
*Now, set a variable called delayCutoff in the chunk below with a cutoff of the maximum delay that you do not want to investigate?*
*Tip: We declare it as a variable because we are likely to change it if it is too low or too high.*
*Tip: There's no right answer for this question. 0 is obviously not a good choice because it will distract us with flights that are just a few minutes late. 24 hours (1440 minutes) is not a good choice because they are going to ignore too many flights that are several hours late. Feel free to return to this line, refine your choice, and restart from here.*

```{r}
# Find out flights that are delayed for 2 hours
delayCutoff = 120

```

## [6 points] Q21. 
*Now, create a new dataframe dfDelayedCutoff that contains all flights that are defined as delayed based on your delayCutoff.*
*Then, plot a simple histogram of all values in dfDelayedCutoff's dep_delay column.*
*Tip: This dataframe should not include canceled flights.*
*EXA Tip: filter(delayCutoff < dep_delay) will filter out all rows with "na" dep_delay.*
*Rubric: Filtering = 3; plotting = 2, naming plot = 1*

```{r}
# Find out all those flights that are delayed for at least two hours
dfDelayedCutoff = dfMyFlightsWeather %>%  filter(delayCutoff < dep_delay)
delayedCutoffFlights = ggplot(dfDelayedCutoff, aes(x = dep_delay)) + geom_histogram()
delayedCutoffFlights
```

## [2 points] Q22. 
*Now, print the summary statistics of dfDelayedCutoff's dep_delay column.*
```{r}
print(summary(dfDelayedCutoff$dep_delay))
```

## [6 points] Q23.
*Let's focus on dfDelayedCutoff now and visualize the dependency on weather components, starting with temp, by plotting it.*
*Also, also a trendline to visualize any patterns.*
*Tip: Use ggplot(DATA, aes(x = VAR_X, y = VAR_Y, color = COLOR_CODING)) + geom_point() + geom_smooth(method = "lm") + labs(x = "VAR_X's name (units)", y = "VAR_Y's name(units)", title = "VAR_Y's name vs. VAR_X's name")*
*Tip: color doesn't need to be set for this chunk.*
*Rubric: ggplot call = 5, storing the result = 1*

```{r}
# You can copy, paste, and modify this chunk to answer later questions.
pTemperature = ggplot(dfDelayedCutoff, aes(x = temp, y = dep_delay, color = "#FFCC00")) + 
  geom_point() + geom_smooth(method = "lm") + 
  labs(x = "Temperature (F)", y = "Departure Delay (minutes)", title = "Departure Delay vs. Temperature")
pTemperature
```

## [2 points] Q24. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
# We don't see any trend, it seems there were a tiny bit more departure delays when the temperature was more than 75°F.

```

## [4 points] Q25. 
*Repeat the directions of the previous plot with color coding based on the origin.* 
*Rubric: ggplot call = 2, color coding = 1, storing the result = 1*
```{r}
# You can copy, paste, and modify this chunk to answer later questions.
pTemperatureColor = ggplot(dfDelayedCutoff, aes(x = temp, y = dep_delay, color = origin)) + 
  geom_point() + geom_smooth(method = "lm") + 
  labs(x = "Temperature (F)", y = "Departure Delay (minutes)", title = "Departure Delay vs. Temperature")
pTemperatureColor
```

## [2 points] Q26. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
# There was no correlation between departure delay and temperature
# Most flights delayed less than 500 minutes
# Flights from airport LGA delayed less minutes
# All three airports (LGA, JFK and EWR) had similar delay pattern. Most departure flights delayed for less than 500 minutes, quite a few departure flights delayed between 500 to 1000 minutes, very few departure flights delayed for more than 1000 minutes.

```

## [3 points] Q27.
*Repeat the previous plot with dew point as the independent variable (x-axis).*
*Tip: Don't forget to check the units.*
*Rubric: ggplot call = 2, storing the result = 1*

```{r}
pDewpoint = ggplot(dfDelayedCutoff, aes(x = dewp, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Dewpoint (F)", y="Departure Delay (minutes)", title = "Departure Delay vs. Dewpoint")
pDewpoint
```

## [1 point] Q28. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was no obviously correlation between dewpoint and departure delay, but there were a little more departure flight delayed when the dewpoint was around 70°F.
#
```


## [3 points] Q29.
*Repeat the previous plot with relative humidity as the independent variable (x-axis).*
*Tip: Don't forget to check the units.*

```{r}
pHumidity = ggplot(dfDelayedCutoff, aes(x = humid, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Humidity (relative humidity based on the scale of 100)", y="Departure Delay (minutes)", title = "Departure Delay vs. Humidity")
pHumidity

```

## [1 point] Q30. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was no clear correlation between humidity and departure delay.  
# 
```

## [3 points] Q31.
*Repeat the previous plot with wind direction as the independent variable (x-axis).*
```{r}
pWindDirection = ggplot(dfDelayedCutoff, aes(x = wind_dir, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Wind Direction (in degrees)", y="Departure Delay (minutes)", title = "Departure Delay vs Wind Direction")
pWindDirection

```

## [1 point] Q32. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was no correlation between wind direction and departure delay.
```

## [3 points] Q33.
*Repeat the previous plot with wind speed as the independent variable (x-axis).*
```{r}
pWindSpeed = ggplot(dfDelayedCutoff, aes(x = wind_speed, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Wind Speed (in degrees)", y="Departure Delay (minutes)", title = "Departure Delay vs Wind Direction")
pWindSpeed

```

## [1 point] Q34. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was no clear correlation between wind speed and departure delay.
#
```

## [3 points] Q35.
*Repeat the previous plot with wind gust as the independent variable (x-axis).*
```{r}
pWindGust = ggplot(dfDelayedCutoff, aes(x = wind_gust, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Wind Gust (in degrees)", y="Departure Delay (minutes)", title = "Departure Delay vs Wind Gust")
pWindGust

```

## [1 point] Q36. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was some correlation between wind gust and departure delay. It seems there were more departure delays when then Wind Gust was around 20 degrees.
# 
```

## [3 points] Q37.
*Repeat the previous plot with precipitation as the independent variable (x-axis).*
```{r}
pPrecip = ggplot(dfDelayedCutoff, aes(x = precip, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Precipitation (in inches)", y="Departure Delay (minutes)", title = "Departure Delay vs Preciptation")
pPrecip

```

## [1 point] Q38. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was some correlation between Precipitation and departure delay. There were more departure delays when the precipitation was less than 0.25 inches. Maybe when the weather was bad travelers would be late for checking in and that could cause the issue.
#
# Overall, airport LGA had more departure delays, followed by JFK, and then followed by EWR.
# 
```

## [3 points] Q39.
*Repeat the previous plot with sea level pressure as the independent variable (x-axis).*
```{r}
pSeaLevel = ggplot(dfDelayedCutoff, aes(x = pressure, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Pressure (in millibars)", y="Departure Delay (minutes)", title = "Departure Delay vs Pressure")
pSeaLevel


```

## [1 point] Q40. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
#  It didn't seem there was a clear correlation between sea level pressure and departure delay.
#
```

## [3 points] Q41.
*Repeat the previous plot with visibility as the independent variable (x-axis).*
```{r}
pVisibility = ggplot(dfDelayedCutoff, aes(x = visib, y = dep_delay, color = origin)) + geom_point() + geom_smooth(method = "lm") + labs(x = "Visibility (in miles)", y="Departure Delay (minutes)", title = "Departure Delay vs Visibility")
pVisibility

```

## [1 point] Q42. 
*What trends do you see, if any?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# There was a correlation between visibility and departure delay. When the visibility number was higher, there were more flights departure delay.
#
```

## [19 points] Q43. 
*Now plot the histograms of all weather related aspects for the flights that were canceled.*
*Tip: This chunk plots 9 histograms.*
*Tip: You may google how to display multiple plots in a grid. I used cowplot library is one of those items. After installing cowplot, plot_grid(X1, x2, ...) can display x1, x2, ... in one grid.*
*Rubric: 2 points for each histogram. 10 points for displaying them in one grid.*
```{r}
# Do not delete these line of code. This will help you get started with temp. 
# You may copy, paste, and modify this chunk to complete this question.
# 
# Note:
# Check the PDF file from URL https://cran.r-project.org/web/packages/nycflights13/nycflights13.pdf to get the column format from the weather data frame

pCTemp = ggplot(dfCanceled, aes(x = temp)) + geom_histogram() + labs(x = "Temperature (F)")
pCTemp


pCDewp = ggplot(dfCanceled, aes(x = dewp)) + geom_histogram() + labs(x = "Dewpoint (F)")
pCDewp


pCHumidity = ggplot(dfCanceled, aes(x = humid)) + geom_histogram() + labs(x = "Humidity (relative humidity based on the scale of 100)")
pCHumidity


pCWindDirection = ggplot(dfCanceled, aes(x = wind_dir)) + geom_histogram() + labs(x = "Wind Direction (in degrees)")
pCWindDirection

pCWindSpeed = ggplot(dfCanceled, aes(x = wind_speed)) + geom_histogram() + labs(x = "Wind Speed (in degrees)")
pCWindSpeed

pCWindGust = ggplot(dfCanceled, aes(x = wind_gust)) + geom_histogram() + labs(x = "Wind Gust (in degrees)")
pCWindGust

pCPrecipitation = ggplot(dfCanceled, aes(x = precip)) + geom_histogram() + labs(x = "Precipitation (in inches.)")
pCPrecipitation

pCPressure = ggplot(dfCanceled, aes(x = pressure)) + geom_histogram() + labs(x = "Pressure (in millibars)")
pCPressure

pCVisib = ggplot(dfCanceled, aes(x = visib)) + geom_histogram() + labs(x = "Visibility (in miles)")
pCVisib

# Install the cowplot library and plot all 9 histograms
#install.packages("cowplot")
library("cowplot")
 plot_grid(pCTemp, pCDewp, pCHumidity, pCWindDirection, pCWindSpeed, pCWindGust, pCPrecipitation, pCPressure, pCVisib)

```

## [20 points] Q44. 
*Reflect on your analysis and summarize what you have learned about the dependence of delayed and canceled flights on the weather. What does this tell you about the likely causes of delayed and canceled flights?*
```{r}
### This section doesn't require code. Just answer the question.### 
#
# In general, there was not so much correlation between departure delay and weather.
# Maybe there was a correlation between cancelled flights and weather. There were more cancelled flights when the weather conditions got worst. And when those flights were cancelled due to weather, they were not counted as departure delay. Thus we didn't see much correlation between departure delay and weather.

```

## [5 points] Q45. 
*Knit to html after eliminating all the errors. Submit both the Rmd and html files.* 
*Tip: Do not worry about minor formatting issues.*
*Tip: This will take some time as you are processing medium size data sets.*
```{r}
### This section doesn't require code. Just knit and submit the Rmd and html files.### 
```