Untitled
Md Asaduzzaman
2024-09-22
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.
When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:
summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00Including Plots
You can also embed plots, for example:
Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.
Load packages
In this lab, we will explore and visualize the data using the tidyverse suite of packages. The data can be found in the companion package for OpenIntro labs, openintro.
Let’s load the packages.
library(tidyverse)
library(openintro)The data
The Bureau of Transportation Statistics (BTS) is a statistical agency that is a part of the Research and Innovative Technology Administration (RITA). As its name implies, BTS collects and makes transportation data available, such as the flights data we will be working with in this lab.
First, we’ll view the nycflights data frame. Type the
following in your console to load the data:
data(nycflights)
nycflights## # A tibble: 32,735 × 16
## year month day dep_time dep_delay arr_time arr_delay carrier tailnum
## <int> <int> <int> <int> <dbl> <int> <dbl> <chr> <chr>
## 1 2013 6 30 940 15 1216 -4 VX N626VA
## 2 2013 5 7 1657 -3 2104 10 DL N3760C
## 3 2013 12 8 859 -1 1238 11 DL N712TW
## 4 2013 5 14 1841 -4 2122 -34 DL N914DL
## 5 2013 7 21 1102 -3 1230 -8 9E N823AY
## 6 2013 1 1 1817 -3 2008 3 AA N3AXAA
## 7 2013 12 9 1259 14 1617 22 WN N218WN
## 8 2013 8 13 1920 85 2032 71 B6 N284JB
## 9 2013 9 26 725 -10 1027 -8 AA N3FSAA
## 10 2013 4 30 1323 62 1549 60 EV N12163
## # ℹ 32,725 more rows
## # ℹ 7 more variables: flight <int>, origin <chr>, dest <chr>, air_time <dbl>,
## # distance <dbl>, hour <dbl>, minute <dbl>The data set nycflights that shows up in your workspace
is a data matrix, with each row representing an
observation and each column representing a variable. R
calls this data format a data frame, which is a term
that will be used throughout the labs. For this data set, each
observation is a single flight.
To view the names of the variables, type the command
names(nycflights)## [1] "year" "month" "day" "dep_time" "dep_delay" "arr_time"
## [7] "arr_delay" "carrier" "tailnum" "flight" "origin" "dest"
## [13] "air_time" "distance" "hour" "minute"This returns the names of the variables in this data frame. The codebook (description of the variables) can be accessed by pulling up the help file:
?nycflightsOne of the variables refers to the carrier (i.e. airline) of the flight, which is coded according to the following system.
carrier: Two letter carrier abbreviation.9E: Endeavor Air Inc.AA: American Airlines Inc.AS: Alaska Airlines Inc.B6: JetBlue AirwaysDL: Delta Air Lines Inc.EV: ExpressJet Airlines Inc.F9: Frontier Airlines Inc.FL: AirTran Airways CorporationHA: Hawaiian Airlines Inc.MQ: Envoy AirOO: SkyWest Airlines Inc.UA: United Air Lines Inc.US: US Airways Inc.VX: Virgin AmericaWN: Southwest Airlines Co.YV: Mesa Airlines Inc.
Remember that you can use glimpse to take a quick peek
at your data to understand its contents better.
glimpse(nycflights)## Rows: 32,735
## Columns: 16
## $ year <int> 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, …
## $ month <int> 6, 5, 12, 5, 7, 1, 12, 8, 9, 4, 6, 11, 4, 3, 10, 1, 2, 8, 10…
## $ day <int> 30, 7, 8, 14, 21, 1, 9, 13, 26, 30, 17, 22, 26, 25, 21, 23, …
## $ dep_time <int> 940, 1657, 859, 1841, 1102, 1817, 1259, 1920, 725, 1323, 940…
## $ dep_delay <dbl> 15, -3, -1, -4, -3, -3, 14, 85, -10, 62, 5, 5, -2, 115, -4, …
## $ arr_time <int> 1216, 2104, 1238, 2122, 1230, 2008, 1617, 2032, 1027, 1549, …
## $ arr_delay <dbl> -4, 10, 11, -34, -8, 3, 22, 71, -8, 60, -4, -2, 22, 91, -6, …
## $ carrier <chr> "VX", "DL", "DL", "DL", "9E", "AA", "WN", "B6", "AA", "EV", …
## $ tailnum <chr> "N626VA", "N3760C", "N712TW", "N914DL", "N823AY", "N3AXAA", …
## $ flight <int> 407, 329, 422, 2391, 3652, 353, 1428, 1407, 2279, 4162, 20, …
## $ origin <chr> "JFK", "JFK", "JFK", "JFK", "LGA", "LGA", "EWR", "JFK", "LGA…
## $ dest <chr> "LAX", "SJU", "LAX", "TPA", "ORF", "ORD", "HOU", "IAD", "MIA…
## $ air_time <dbl> 313, 216, 376, 135, 50, 138, 240, 48, 148, 110, 50, 161, 87,…
## $ distance <dbl> 2475, 1598, 2475, 1005, 296, 733, 1411, 228, 1096, 820, 264,…
## $ hour <dbl> 9, 16, 8, 18, 11, 18, 12, 19, 7, 13, 9, 13, 8, 20, 12, 20, 6…
## $ minute <dbl> 40, 57, 59, 41, 2, 17, 59, 20, 25, 23, 40, 20, 9, 54, 17, 24…The nycflights data frame is a massive trove of
information. Let’s think about some questions we might want to answer
with these data:
- How delayed were flights that were headed to Los Angeles?
- How do departure delays vary by month?
- Which of the three major NYC airports has the best on time percentage for departing flights?
Analysis
nycflights %>%
group_by(month)%>%
summarise(dep_delay, month,flight)## Warning: Returning more (or less) than 1 row per `summarise()` group was deprecated in
## dplyr 1.1.0.
## ℹ Please use `reframe()` instead.
## ℹ When switching from `summarise()` to `reframe()`, remember that `reframe()`
## always returns an ungrouped data frame and adjust accordingly.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `summarise()` has grouped output by 'month'. You can override using the
## `.groups` argument.## # A tibble: 32,735 × 3
## # Groups: month [12]
## month dep_delay flight
## <int> <dbl> <int>
## 1 1 -3 353
## 2 1 37 4412
## 3 1 -3 369
## 4 1 -4 1433
## 5 1 -3 56
## 6 1 167 575
## 7 1 -4 4390
## 8 1 -9 4120
## 9 1 -3 645
## 10 1 -6 21
## # ℹ 32,725 more rowslax_flights <-nycflights %>% filter(dest == "LAX")
lax_flights %>% group_by(month)%>%
summarise(mean_dep_delay = mean(dep_delay), median_dep_delay=median(dep_delay),n=n())## # A tibble: 12 × 4
## month mean_dep_delay median_dep_delay n
## <int> <dbl> <dbl> <int>
## 1 1 3.06 -2 115
## 2 2 4.52 -1 95
## 3 3 6.01 -1 128
## 4 4 12.2 -1 148
## 5 5 13.0 0 122
## 6 6 17.9 1 141
## 7 7 17.8 1 131
## 8 8 7.18 -1 136
## 9 9 11.1 -1 159
## 10 10 7.71 -2 126
## 11 11 3.35 -2 144
## 12 12 10.7 1 138nycflights %>%
group_by(origin)%>%
summarise(mean_dt=mean(dep_time), max(dep_time))## # A tibble: 3 × 3
## origin mean_dt `max(dep_time)`
## <chr> <dbl> <int>
## 1 EWR 1335. 2357
## 2 JFK 1393. 2400
## 3 LGA 1318. 2358nrow() function in R Language is used to return the number of rows of the specified matrix.
JFK_airport <- nycflights %>%
summarise (flight, origin, dep_time, dep_delay, air_time) %>%
filter(origin =="JFK") ## Warning: Returning more (or less) than 1 row per `summarise()` group was deprecated in
## dplyr 1.1.0.
## ℹ Please use `reframe()` instead.
## ℹ When switching from `summarise()` to `reframe()`, remember that `reframe()`
## always returns an ungrouped data frame and adjust accordingly.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.JFK_airport## # A tibble: 10,897 × 5
## flight origin dep_time dep_delay air_time
## <int> <chr> <int> <dbl> <dbl>
## 1 407 JFK 940 15 313
## 2 329 JFK 1657 -3 216
## 3 422 JFK 859 -1 376
## 4 2391 JFK 1841 -4 135
## 5 1407 JFK 1920 85 48
## 6 20 JFK 940 5 50
## 7 34 JFK 1217 -4 46
## 8 1271 JFK 757 -3 131
## 9 27 JFK 1638 8 334
## 10 97 JFK 2310 105 223
## # ℹ 10,887 more rowsJFK_percentage_delay <- (nrow(subset(JFK_airport, dep_delay > 0))/
nrow(JFK_airport))*100
JFK_percentage_delay## [1] 38.15729LGA_airport <- nycflights %>%
summarise(flight, origin, dep_time, dep_delay, air_time) %>%
filter(origin =="LGA")## Warning: Returning more (or less) than 1 row per `summarise()` group was deprecated in
## dplyr 1.1.0.
## ℹ Please use `reframe()` instead.
## ℹ When switching from `summarise()` to `reframe()`, remember that `reframe()`
## always returns an ungrouped data frame and adjust accordingly.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.LGA_airport## # A tibble: 10,067 × 5
## flight origin dep_time dep_delay air_time
## <int> <chr> <int> <dbl> <dbl>
## 1 3652 LGA 1102 -3 50
## 2 353 LGA 1817 -3 138
## 3 2279 LGA 725 -10 148
## 4 1639 LGA 1320 5 161
## 5 645 LGA 2054 115 104
## 6 5273 LGA 1126 11 58
## 7 369 LGA 1626 -3 150
## 8 1433 LGA 626 -4 105
## 9 3388 LGA 1251 -4 83
## 10 3478 LGA 821 -8 77
## # ℹ 10,057 more rowsLGA_percentage_delay <- (nrow(subset(LGA_airport, dep_delay > 0))/
nrow(LGA_airport))*100
LGA_percentage_delay## [1] 33.07837EWR_airport <- nycflights %>%
summarise (flight, origin, dep_time, dep_delay, air_time) %>%
filter(origin =="EWR")## Warning: Returning more (or less) than 1 row per `summarise()` group was deprecated in
## dplyr 1.1.0.
## ℹ Please use `reframe()` instead.
## ℹ When switching from `summarise()` to `reframe()`, remember that `reframe()`
## always returns an ungrouped data frame and adjust accordingly.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.EWR_airport## # A tibble: 11,771 × 5
## flight origin dep_time dep_delay air_time
## <int> <chr> <int> <dbl> <dbl>
## 1 1428 EWR 1259 14 240
## 2 4162 EWR 1323 62 110
## 3 5790 EWR 809 -2 87
## 4 4412 EWR 2024 37 53
## 5 4241 EWR 644 -1 45
## 6 1030 EWR 859 -1 121
## 7 1724 EWR 729 9 154
## 8 3852 EWR 2253 123 53
## 9 3709 EWR 752 -3 103
## 10 4224 EWR 1944 15 117
## # ℹ 11,761 more rowsEWR_percentage_delay <- (nrow(subset(EWR_airport, dep_delay > 0))/
nrow(EWR_airport))*100
EWR_percentage_delay## [1] 45.11936Departure delays
Let’s start by examing the distribution of departure delays of all flights with a histogram.
ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
This function says to plot the dep_delay variable from
the nycflights data frame on the x-axis. It also defines a
geom (short for geometric object), which describes the type
of plot you will produce.
Histograms are generally a very good way to see the shape of a single distribution of numerical data, but that shape can change depending on how the data is split between the different bins. You can easily define the binwidth you want to use:
ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram(binwidth = 15)
ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram(binwidth = 150)
- Look carefully at these three histograms. How do they compare? Are features revealed in one that are obscured in another?
Insert your answer here: Small bin width shows more bar in the graph than the larger bin width. There are many bar is not visible in the larger bin width.
If you want to visualize only on delays of flights headed to Los
Angeles, you need to first filter the data for flights with
that destination (dest == "LAX") and then make a histogram
of the departure delays of only those flights.
lax_flights <- nycflights %>%
filter(dest == "LAX")
ggplot(data = lax_flights, aes(x = dep_delay)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Let’s decipher these two commands (OK, so it might look like four
lines, but the first two physical lines of code are actually part of the
same command. It’s common to add a break to a new line after
%>% to help readability).
- Command 1: Take the
nycflightsdata frame,filterfor flights headed to LAX, and save the result as a new data frame calledlax_flights.==means “if it’s equal to”.LAXis in quotation marks since it is a character string.
- Command 2: Basically the same
ggplotcall from earlier for making a histogram, except that it uses the smaller data frame for flights headed to LAX instead of all flights.
Logical operators: Filtering for certain
observations (e.g. flights from a particular airport) is often of
interest in data frames where we might want to examine observations with
certain characteristics separately from the rest of the data. To do so,
you can use the filter function and a series of
logical operators. The most commonly used logical
operators for data analysis are as follows:
==means “equal to”!=means “not equal to”>or<means “greater than” or “less than”>=or<=means “greater than or equal to” or “less than or equal to”
You can also obtain numerical summaries for these flights:
lax_flights %>%
summarise(mean_dd = mean(dep_delay),
median_dd = median(dep_delay),
n = n())## # A tibble: 1 × 3
## mean_dd median_dd n
## <dbl> <dbl> <int>
## 1 9.78 -1 1583Note that in the summarise function you created a list
of three different numerical summaries that you were interested in. The
names of these elements are user defined, like mean_dd,
median_dd, n, and you can customize these
names as you like (just don’t use spaces in your names). Calculating
these summary statistics also requires that you know the function calls.
Note that n() reports the sample size.
Summary statistics: Some useful function calls for summary statistics for a single numerical variable are as follows:
meanmediansdvarIQRminmax
Note that each of these functions takes a single vector as an argument and returns a single value.
You can also filter based on multiple criteria. Suppose you are interested in flights headed to San Francisco (SFO) in February:
sfo_feb_flights <- nycflights %>%
filter(dest == "SFO", month == 2)Note that you can separate the conditions using commas if you want
flights that are both headed to SFO and in February. If
you are interested in either flights headed to SFO or
in February, you can use the | instead of the comma.
- Create a new data frame that includes flights headed to SFO in
February, and save this data frame as
sfo_feb_flights. How many flights meet these criteria?
Insert your answer here There are 68 flights in the dataframe.
sfo_feb_flights <- nycflights %>%
filter(dest == "SFO", month == 2)
dim(sfo_feb_flights)## [1] 68 16- Describe the distribution of the arrival delays of these flights using a histogram and appropriate summary statistics. Hint: The summary statistics you use should depend on the shape of the distribution.
Insert your answer here
ggplot(data=sfo_feb_flights, aes(x=arr_delay))+
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# obtain numerical summaries for SFO flights
sfo_feb_flights %>%
summarise(mean_SFO = mean(arr_delay),
median_SFO = median(arr_delay),
count = n(),
stdev = sd(arr_delay),
Inter_quart_range = IQR(arr_delay),
min_valve = min(arr_delay),
max_value = max(arr_delay))## # A tibble: 1 × 7
## mean_SFO median_SFO count stdev Inter_quart_range min_valve max_value
## <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
## 1 -4.5 -11 68 36.3 23.2 -66 196Another useful technique is quickly calculating summary statistics
for various groups in your data frame. For example, we can modify the
above command using the group_by function to get the same
summary stats for each origin airport:
sfo_feb_flights %>%
group_by(origin) %>%
summarise(median_dd = median(dep_delay), iqr_dd = IQR(dep_delay), n_flights = n())## # A tibble: 2 × 4
## origin median_dd iqr_dd n_flights
## <chr> <dbl> <dbl> <int>
## 1 EWR 0.5 5.75 8
## 2 JFK -2.5 15.2 60Here, we first grouped the data by origin and then
calculated the summary statistics.
- Calculate the median and interquartile range for
arr_delays of flights in in thesfo_feb_flightsdata frame, grouped by carrier. Which carrier has the most variable arrival delays?
Insert your answer here UA has most arrival delays.
sfo_feb_flights %>%
group_by(carrier)%>%
summarise(median_sfo_feb_flights = median(arr_delay),
interquartil_range = IQR(arr_delay),
count = n()) %>%
arrange(desc(count))## # A tibble: 5 × 4
## carrier median_sfo_feb_flights interquartil_range count
## <chr> <dbl> <dbl> <int>
## 1 UA -10 22 21
## 2 DL -15 22 19
## 3 VX -22.5 21.2 12
## 4 AA 5 17.5 10
## 5 B6 -10.5 12.2 6Departure delays by month
Which month would you expect to have the highest average delay departing from an NYC airport?
Let’s think about how you could answer this question:
- First, calculate monthly averages for departure delays. With the new
language you are learning, you could
group_bymonths, thensummarisemean departure delays.
- Then, you could to
arrangethese average delays indescending order
nycflights %>%
group_by(month) %>%
summarise(mean_dd = mean(dep_delay),median_dd=median(dep_delay)) %>%
arrange(desc(mean_dd))## # A tibble: 12 × 3
## month mean_dd median_dd
## <int> <dbl> <dbl>
## 1 7 20.8 0
## 2 6 20.4 0
## 3 12 17.4 1
## 4 4 14.6 -2
## 5 3 13.5 -1
## 6 5 13.3 -1
## 7 8 12.6 -1
## 8 2 10.7 -2
## 9 1 10.2 -2
## 10 9 6.87 -3
## 11 11 6.10 -2
## 12 10 5.88 -3- Suppose you really dislike departure delays and you want to schedule your travel in a month that minimizes your potential departure delay leaving NYC. One option is to choose the month with the lowest mean departure delay. Another option is to choose the month with the lowest median departure delay. What are the pros and cons of these two choices?
Insert your answer here
Mean is the average value of set of given data. It shows the average departure delay. A con of this choice is that the data can suddenly change direction or positio due to outiers.
A median is the middle value when the data set is arranged in an order either ascending or descending. It set up all the data in the line and picked the middle value so it won’t be direction or position becuase of the outliers. A con is that it doesn’t perfectly represent all of data distributed.
On time departure rate for NYC airports
Suppose you will be flying out of NYC and want to know which of the three major NYC airports has the best on time departure rate of departing flights. Also supposed that for you, a flight that is delayed for less than 5 minutes is basically “on time.”” You consider any flight delayed for 5 minutes of more to be “delayed”.
In order to determine which airport has the best on time departure rate, you can
- first classify each flight as “on time” or “delayed”,
- then group flights by origin airport,
- then calculate on time departure rates for each origin airport,
- and finally arrange the airports in descending order for on time departure percentage.
Let’s start with classifying each flight as “on time” or “delayed” by
creating a new variable with the mutate function.
nycflights <- nycflights %>%
mutate(dep_type = ifelse(dep_delay < 5, "on time", "delayed"))The first argument in the mutate function is the name of
the new variable we want to create, in this case dep_type.
Then if dep_delay < 5, we classify the flight as
"on time" and "delayed" if not, i.e. if the
flight is delayed for 5 or more minutes.
Note that we are also overwriting the nycflights data
frame with the new version of this data frame that includes the new
dep_type variable.
We can handle all of the remaining steps in one code chunk:
nycflights %>%
group_by(origin) %>%
summarise(ot_dep_rate = sum(dep_type == "on time") / n()) %>%
arrange(desc(ot_dep_rate))## # A tibble: 3 × 2
## origin ot_dep_rate
## <chr> <dbl>
## 1 LGA 0.728
## 2 JFK 0.694
## 3 EWR 0.637- If you were selecting an airport simply based on on time departure percentage, which NYC airport would you choose to fly out of?
You can also visualize the distribution of on on time departure rate across the three airports using a segmented bar plot.
ggplot(data = nycflights, aes(x = origin, fill = dep_type)) +
geom_bar()
Insert your answer here
LGA has the best departure percentage
# We can now find best on time rate NYC airport
nycflights %>%
group_by(origin) %>%
summarise(dep_rate = sum(dep_type == "on time") / n()) %>%
arrange(desc(dep_rate))## # A tibble: 3 × 2
## origin dep_rate
## <chr> <dbl>
## 1 LGA 0.728
## 2 JFK 0.694
## 3 EWR 0.637# We can now visualize the results above and conclude that LGA has the best departure percentage
ggplot(data = nycflights, aes(x = origin, fill = dep_type)) +
geom_bar()
More Practice
- Mutate the data frame so that it includes a new variable that
contains the average speed,
avg_speedtraveled by the plane for each flight (in mph). Hint: Average speed can be calculated as distance divided by number of hours of travel, and note thatair_timeis given in minutes.
Insert your answer here
nycflights <- nycflights %>%
mutate(avg_speed = distance / (air_time / 60))
nycflights## # A tibble: 32,735 × 18
## year month day dep_time dep_delay arr_time arr_delay carrier tailnum
## <int> <int> <int> <int> <dbl> <int> <dbl> <chr> <chr>
## 1 2013 6 30 940 15 1216 -4 VX N626VA
## 2 2013 5 7 1657 -3 2104 10 DL N3760C
## 3 2013 12 8 859 -1 1238 11 DL N712TW
## 4 2013 5 14 1841 -4 2122 -34 DL N914DL
## 5 2013 7 21 1102 -3 1230 -8 9E N823AY
## 6 2013 1 1 1817 -3 2008 3 AA N3AXAA
## 7 2013 12 9 1259 14 1617 22 WN N218WN
## 8 2013 8 13 1920 85 2032 71 B6 N284JB
## 9 2013 9 26 725 -10 1027 -8 AA N3FSAA
## 10 2013 4 30 1323 62 1549 60 EV N12163
## # ℹ 32,725 more rows
## # ℹ 9 more variables: flight <int>, origin <chr>, dest <chr>, air_time <dbl>,
## # distance <dbl>, hour <dbl>, minute <dbl>, dep_type <chr>, avg_speed <dbl>- Make a scatterplot of
avg_speedvs.distance. Describe the relationship between average speed and distance. Hint: Usegeom_point().
Insert your answer here
ggplot(data = nycflights, aes(x = distance, y = avg_speed, color= carrier)) +
geom_point() +
geom_smooth(method=lm) ## `geom_smooth()` using formula = 'y ~ x'
- Replicate the following plot. Hint: The data frame
plotted only contains flights from American Airlines, Delta Airlines,
and United Airlines, and the points are
colored bycarrier. Once you replicate the plot, determine (roughly) what the cutoff point is for departure delays where you can still expect to get to your destination on time.
Insert your answer here
filtered_carrier <- nycflights %>%
filter(carrier == "AA" | carrier == "DL" | carrier == "UA")
ggplot(data = filtered_carrier, aes(x = dep_delay, y = arr_delay, color= carrier)) + geom_point()