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<h1 class="title toc-ignore">Exploratory Data Analysis</h1>
</div>
<div id="visualization" class="section level2">
<h2>Visualization</h2>
<p>To provide an overall view of the distribution in arrival delay (in
minutes), we created a histogram for the arrival delay in 2013, a
barplot showing the arrival status categorized by three NYC departure
airports (<code>LGA</code>, <code>JFK</code>, <code>EWR</code>) and a
boxplot below displaying the top 6 average arrival delay grouped by
destinations. Additionally, we then visualized the correlation between
arrival delay and weather features (e.g.,<code>pressure</code>,
<code>wind</code>, <code>visibility</code>, etc.) and some other
external factors including <code>flight carriers</code>,
<code>month</code> and specific datetime features.</p>
<p>Note: All visualization parts were performed on data consisting of
flight and weather information in 2013. Data in 2017 was reserved for
testing purpose only.</p>
<pre class="r"><code>library(tidyr)
library(tidyverse)
library(rvest)
library(dplyr)
library(cowplot)
library(gridExtra)
library(RColorBrewer)
library(plotly)
library(corrplot)
library(ggpubr)
library(viridisLite)
library(patchwork)
knitr::opts_chunk$set(
echo = TRUE,
warning = FALSE,
fig.width = 8,
fig.height = 6,
out.width = "90%"
)
theme_set(theme_minimal() +
theme(legend.position = "bottom",
plot.title= element_text(hjust = 0.5))
)
options(
ggplot2.continuous.colour = "viridis",
ggplot2.continuous.fill = "viridis"
)
scale_colour_discrete = scale_colour_viridis_d
scale_fill_discrete = scale_fill_viridis_d
## Load dataset
df_2013 =
read_csv("data/merge_data_2013.csv", show_col_types = FALSE)
# Convert month to factor with levels in ascending order and labels as month abbreviations
df_2013$month <- factor(df_2013$month, levels = 1:12, labels = month.abb[1:12])
df_2013 <- df_2013 %>%
mutate(date = paste(month, day, sep = "_"))
average_delay_by_date <- df_2013 %>%
# group_by(date) %>%
group_by(month, date) %>%
summarise(
avg_arr_delay = mean(arr_delay, na.rm = TRUE),
avg_precip = mean(precip, na.rm = TRUE),
avg_wind_dir = mean(wind_dir, na.rm = TRUE),
avg_wind_speed = mean(wind_speed, na.rm = TRUE),
avg_wind_gust = mean(wind_gust, na.rm = TRUE),
avg_pressure = mean(pressure, na.rm = TRUE),
avg_visib = mean(visib, na.rm = TRUE)
)
# Aggregate the data by month and calculate averages
df_2013_avg <- df_2013 %>%
group_by(month) %>%
summarize(
avg_arr_delay = mean(arr_delay, na.rm = TRUE),
avg_precip = mean(precip, na.rm = TRUE),
avg_wind_dir = mean(wind_dir, na.rm = TRUE),
avg_wind_speed = mean(wind_speed, na.rm = TRUE),
avg_wind_gust = mean(wind_gust, na.rm = TRUE),
avg_pressure = mean(pressure, na.rm = TRUE),
avg_visib = mean(visib, na.rm = TRUE)
)</code></pre>
</div>
<div id="arrival-delay-summary" class="section level2">
<h2>Arrival Delay Summary</h2>
<pre class="r"><code>dd_hist =
ggplot(data = df_2013, aes(x = arr_delay)) +
geom_histogram(fill = 'skyblue', color = 'black')+
labs(title = "Distribution of Arrival Delay",
x = "Arrival Delay (minutes)",
y = "Frequency")
origin_delay = df_2013 |>
mutate(
arrival_type = ifelse(arr_delay <= 0, "on time", "delayed")) |>
ggplot(aes(x = origin, fill = arrival_type)) +
geom_bar()+
scale_fill_brewer(palette = "Set3") +
labs(title = "Arrival Status Depatured from NYC Airports",
x = "Origin",
y = "Counts")
# Calculate average arrival delay by destination
avg_arr_delay_by_dest <- df_2013 %>%
group_by(dest) %>%
summarize(avg_arr_delay_dest = mean(arr_delay, na.rm = TRUE)) %>%
arrange(desc(avg_arr_delay_dest)) %>%
head(6)
# Select only the top 6 destinations
top_destinations <- avg_arr_delay_by_dest$dest
# Filter the data for the top 6 destinations
filtered_data <- df_2013 %>% filter(dest %in% top_destinations)
# Create a boxplot for the top 6 destinations
top6_dest =
ggplot(filtered_data, aes(x = reorder(dest, -arr_delay), y = arr_delay, fill = dest)) +
geom_boxplot() +
scale_fill_brewer(palette = "Set3") +
labs(title = "Arrival Delay for Top 6 Destinations",
x = "Destination",
y = "Arrival Delay (minutes)")
dd_hist | origin_delay / top6_dest</code></pre>
<p><img src="EDA_files/figure-html/delay_summary-1.png" width="90%" /></p>
<pre class="r"><code>df_2013 |>
summarise(min_delay = min(arr_delay),
avg_delay = mean(arr_delay),
median_delay = median(arr_delay),
max_delay = max(arr_delay)
) |>
knitr::kable(
digits = 3,
col.names = c("Min Delay Time (Minutes)","Average Delay Time (Minutes)", "Median Delay Time (Minutes)",
"Max Delay Time (Minutes)")
)</code></pre>
<table style="width:100%;">
<colgroup>
<col width="23%" />
<col width="27%" />
<col width="26%" />
<col width="23%" />
</colgroup>
<thead>
<tr class="header">
<th align="right">Min Delay Time (Minutes)</th>
<th align="right">Average Delay Time (Minutes)</th>
<th align="right">Median Delay Time (Minutes)</th>
<th align="right">Max Delay Time (Minutes)</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">-74</td>
<td align="right">7.287</td>
<td align="right">-4</td>
<td align="right">783</td>
</tr>
</tbody>
</table>
<pre class="r"><code>df_2013 |>
mutate(
arrival_type = ifelse(arr_delay <= 0, "on time", "delayed")) |>
group_by(arrival_type) |>
summarise(count = n(),
average_delay_time = mean(arr_delay)) |>
knitr::kable(
digits = 3,
col.names = c("Arrival Type", "Count", "Average Delay Time (minutes)")
)</code></pre>
<table>
<thead>
<tr class="header">
<th align="left">Arrival Type</th>
<th align="right">Count</th>
<th align="right">Average Delay Time (minutes)</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">delayed</td>
<td align="right">30584</td>
<td align="right">38.163</td>
</tr>
<tr class="even">
<td align="left">on time</td>
<td align="right">42150</td>
<td align="right">-15.117</td>
</tr>
</tbody>
</table>
<p>The overall distribution of arrival delay was highly skewed to the
right, with the average delay time 7.28 minutes. Based on the barplot of
arrival delay grouped by origins, we found that EWR had the highest
portion of delays in respect to its total flights, and JFK had the the
lowest number of delays.Based on the boxplot displaying average time of
arrival delay, we did not perceive any major differences regarding
arrival delay time under the top 6 destinations.Approximately 58% of
records (n=42,150) in the dataset were reported as on-time, and among
them, the average time in earlier arrival was 15 minutes. On the
contrary, in the delay group, the delay time was calculated to be 38
minutes on average.</p>
</div>
<div id="correlation-plot" class="section level2">
<h2>Correlation Plot</h2>
<pre class="r"><code>df_2013 = read.csv("data/merge_data_2013.csv") |>
mutate(month = factor(month, levels = 1:12, labels = month.abb[1:12]))
df_corr = df_2013 |>
select(-year,-flight, -day, -minute, -hour) |>
select_if( is.numeric)
corrplot(cor(df_corr), type="upper", order="hclust",
col=brewer.pal(n=8, name="RdYlBu"))</code></pre>
<p><img src="EDA_files/figure-html/unnamed-chunk-2-1.png" width="90%" /></p>
<p>The correlation heatmap plot depicted some highly correlated pair of
features such as <code>wind_speed</code> and <code>precip</code>, and
<code>air_time</code> and <code>distance</code>. Thus, in the modeling
process, we will only keep one variable for each pair to avoid the
multicollinearity issue. In this case, we removed features
<code>wind speed</code> and <code>distance</code> when constructing the
model.</p>
</div>
<div id="arrival-delay-weather-factors" class="section level2">
<h2>Arrival Delay & Weather Factors</h2>
<p>To visualize the relationships between arrival delay and weather
features, we plot scatterplot of <code>arr_delay</code> against
<code>pressure</code>, <code>visibility</code>, <code>wind_gust</code>,
<code>wind_dir</code>, and <code>wind_speed</code> respectively.</p>
<div id="pressure" class="section level3">
<h3>Pressure</h3>
<pre class="r"><code># Average pressure against average arr_delay by month
pressure_delay_date =
ggplot(average_delay_by_date, aes(x = avg_pressure, y = avg_arr_delay)) +
geom_point(size = 3, aes(x = avg_pressure, y = avg_arr_delay, color = month)) +
geom_smooth(method = "lm", se = FALSE, color = "coral", size = 0.6) +
stat_cor(method = "pearson", label.x = 1020, label.y = -30, size = 5) +
labs(title = "Scatter Plot of Average Pressure against Arrival Delay by Date",
x = "Avg Pressure by Date",
y = "Avg Arrival Delay (minutes)")
pressure_delay_date</code></pre>
<p><img src="EDA_files/figure-html/pressure_date-1.png" width="90%" /></p>
<p>From the plot we could observe a trend that as pressure increased,
the arrival delay time decreased. Since the trend seemed not very clear,
we then calculated the correlation coefficient between the two
variables. The correlation coefficient was -0.26, suggesting a weak
negative correlation between pressure (mmhg) and arrival delay in
minutes. While the p-value was significantly small, it might be driven
by a large sample size (n=72,734).</p>
</div>
<div id="visibility" class="section level3">
<h3>Visibility</h3>
<pre class="r"><code>df_2013 |>
group_by(visib) |>
mutate(count_delay = if_else(arr_delay>0 , 1, 0)) |>
summarise(avg_delay = mean(arr_delay),
number_of_delays = sum(count_delay)
) |>
ggplot(aes(x=visib,
y=avg_delay, color=number_of_delays))+
geom_point() +
labs(title = "Arrival Delay Vs. Visibility",
x = "Visibility",
y = "Average of Arrival Delay Time (Minutes)") </code></pre>
<p><img src="EDA_files/figure-html/visib-1.png" width="90%" /></p>
<p>Based on the graph, it appeared that the incremental of visibility
did not linearly correlate with the reduction in the number of delays.
In the highest visibility 10, we perceived the highest number of delays.
There was no major difference in the number of delays in visibility
ranging from 0 to 9. However, we observed that visibility negatively
correlated with average delay time in minutes.</p>
</div>
<div id="wind" class="section level3">
<h3>Wind</h3>
<pre class="r"><code># Average Wind Direction against average arr_delay by date
wind_dir_delay_date =
ggplot(average_delay_by_date, aes(x = avg_wind_dir, y = avg_arr_delay)) +
geom_point(size = 3, aes(x = avg_wind_dir, y = avg_arr_delay, color = month)) +
geom_smooth(method = "lm", se = FALSE, color = "coral", size = 0.6) +
stat_cor(method = "pearson", size = 5) +
guides(color = 'none') +
labs(title = "Avg Wind Direction VS Arrival Delay",
x = "Avg Daily Wind Direction",
y = "Avg arr_delay")
# Average wind_gust against average arr_delay by date
wind_gust_delay_date =
ggplot(average_delay_by_date, aes(x = avg_wind_gust, y = avg_arr_delay)) +
geom_point(size = 3, aes(x = avg_wind_dir, y = avg_arr_delay, color = month)) +
geom_smooth(method = "lm", se = FALSE, color = "coral", size = 0.6) +
stat_cor(method = "pearson", size = 5) +
labs(title = "Avg Wind Gust VS Arrival Delay",
x = "Avg Daily Wind Gust",
y = "Avg arr_delay")
# Average wind_speed against average arr_delay by date
wind_speed_delay_date =
ggplot(average_delay_by_date, aes(x = avg_wind_speed, y = avg_arr_delay)) +
geom_point(size = 3, aes(x = avg_wind_speed, y = avg_arr_delay, color = month)) +
geom_smooth(method = "lm", se = FALSE, color = "coral", size = 0.6) +
stat_cor(method = "pearson", size = 5) +
guides(color = 'none') +
labs(title = "Avg Wind Speed VS Arrival Delay",
x = "Avg Daily Wind Speed",
y = "Avg arr_delay")
(wind_dir_delay_date | wind_speed_delay_date) / wind_gust_delay_date</code></pre>
<p><img src="EDA_files/figure-html/plot_weather_wind-1.png" width="90%" /></p>
<p>The three scatterplots with fitted lines here illustrated the
relationship between wind features and arrival delay. We also calculated
the correlation coefficients to confirm the trends we observed.
According to the first graph, arrival delay was negatively related to
wind direction. The correlation coefficient of -0.19 suggested that the
negative correlation between wind direction and arrival delay was weak.
In the second graph, generally arrival delay increased as wind speed
increased, and this positive correlation, though weak, was also shown by
its correlation coefficient of 0.1. Through the third graph and the
calculated correlation coefficient of 0.11, a weak positive correlation
between arrival delay and wind gust could be observed and derived. It
was worth noticing that the significantly small p-values calculated for
the three correlation coefficients might still be caused by the large
sample size (n=72,734) rather than a solid evidence of the
correlations.</p>
</div>
</div>
<div id="arrival-delay-carriers-temporal-factors"
class="section level2">
<h2>Arrival Delay & Carriers, Temporal Factors</h2>
<pre class="r"><code>carrier_plot = df_2013 |>
group_by(carrier) |>
mutate(delay_count = if_else(arr_delay >0 , 1, 0)) |>
summarise(delay_count = sum(delay_count)) |>
ggplot(aes(x = carrier,
y = delay_count)) +
geom_bar(stat = "identity", fill = viridis(16)) +
labs(title = "Number of Delays for Each Carrier",
x = "Carrier",
y = "Total Number of Delays")
month_plot = df_2013 |>
group_by(month) |>
mutate(delay_count = if_else(arr_delay >0 , 1, 0)) |>
summarise(delay_count = sum(delay_count)) |>
ggplot(aes(x = month,
y = delay_count, group=1)) +
geom_point(color="#0aa2fa") +
geom_line(color="#0aa2fa") +
labs(title = "Number of Delays for Each Month",
x = "Month",
y = "Total Number of Delays")
carrier_plot | month_plot</code></pre>
<p><img src="EDA_files/figure-html/unnamed-chunk-3-1.png" width="90%" /></p>
<p>The carrier <code>EV</code> was shown to have the highest number of
delays, followed by carrier <code>B6</code>. The number of delays for
carrier <code>HA</code> was found to be the lowest across all carriers.
Months such as March and April appeared to have the relatively high
number of delays, and the lowest total number of delays occurred in
September.</p>
<pre class="r"><code>df_2013_weekday = read_csv("data/merge_data_2013.csv") |>
mutate(delay_count = if_else(arr_delay >0 , 1, 0),
arrival_date = paste(year,"-",month,"-",day, sep = "")
) |>
mutate(week_date = weekdays(date(arrival_date)),
week_date = factor(week_date,
levels = c("Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday",
"Sunday"))
)
weekday_plot = df_2013_weekday |>
group_by(week_date) |>
summarise(delay_count = sum(delay_count)) |>
ggplot(aes(x = week_date,
y = delay_count, group=1)) +
geom_point(color="#6f98d1") +
geom_line(color="#6f98d1") +
labs(title = "Number of Delays Vs. Weekday",
x = "Weekday",
y = "Total Number of Delays")
weekday_plot_delay = df_2013_weekday |>
group_by(week_date) |>
summarise(avg_delay = mean(arr_delay)) |>
ggplot(aes(x = week_date,
y = avg_delay, group=1)) +
geom_point(color="#6f98d1") +
geom_line(color="#6f98d1") +
labs(title = "Average Time of Arrival Delays (minutes) Vs. Weekday",
x = "Weekday",
y = "Average Time of Arrival Delays (minutes)")
weekday_plot /weekday_plot_delay</code></pre>
<p><img src="EDA_files/figure-html/unnamed-chunk-4-1.png" width="90%" /></p>
<p>An increasing trend in the number of delays was perceived from Monday
to Thursday, followed by a decline on Friday and Saturday. Based on the
figures, Saturday had the lowest number of delays and average time of
arrival delays. It was also noted that Thursday was found to have the
highest number of delays and average time of arrival delays in
minutes.</p>
<pre class="r"><code>part_day_plot = df_2013 |>
mutate(hour = cut(hour,
breaks = c(-Inf, 5, 12, 17, 21, Inf),
labels = c("Late Night", "Morning", "Afternoon", "Evening", "Late Night"),
include.lowest = TRUE
)) |>
group_by(hour) |>
mutate(delay_count = if_else(arr_delay >0 , 1, 0)) |>
summarise(delay_count = sum(delay_count),
avg_delay = mean(arr_delay)) |>
ggplot(aes(x = hour,
y = delay_count, group=1)) +
geom_point(color="#eb8f2d") +
geom_line(color="#eb8f2d") +
labs(title = "Number of Delays Vs. Daytime",
x = "Daytime",
y = "Total Number of Delays")
part_day_plot_delay = df_2013 |>
mutate(hour = cut(hour,
breaks = c(-Inf, 5, 12, 17, 21, Inf),
labels = c("Late Night", "Morning", "Afternoon", "Evening", "Late Night"),
include.lowest = TRUE
)) |>
group_by(hour) |>
mutate(delay_count = if_else(arr_delay >0 , 1, 0)) |>
summarise(avg_delay = mean(arr_delay)) |>
ggplot(aes(x = hour,
y = avg_delay, group=1)) +
geom_point(color="#eb8f2d") +
geom_line(color="#eb8f2d") +
labs(title = "Average Time of Arrival Delay (minutes) Vs. Daytime",
x = "Daytime",
y = "Average Arrival Delays (minutes)")
part_day_plot / part_day_plot_delay</code></pre>
<p><img src="EDA_files/figure-html/unnamed-chunk-5-1.png" width="90%" /></p>
<p>Furthermore, we further visualized the changes of number of delays
and daytime divided into <code>Late Night</code>, <code>Morning</code>,
<code>Afternoon</code>, <code>Evening</code>. The number of arrival
delays was increased from time during laye night to afternoon, dropping
during the evening. We found a largest number of delays during
afternoon, with the average time delay of 9 minutes.</p>
</div>
<div id="insights-from-visualization" class="section level2">
<h2>Insights from Visualization</h2>
<p>Based on above visualizations, we anticipated weather factors such as
pressure,visibility and wind conditions can be beneficial in predicting
flight delay task. Additionally, other features such as information
about flight carrier and temporal characteristics are believed to
helpful in such prediction task as well. Thus, in the subsequent
sections, we would further quantity their correlations by leveraging
multiple linear regression.</p>
</div>
</div>
</div>
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