NYCFlightsDataModel
Kaiyan Wei_ANLY 505
06/3/2019
Summarize Data
daily <- flights %>%
mutate(date = make_date(year, month, day)) %>%
group_by(date) %>%
summarize(n = n())
ggplot(daily, aes(date, n)) +
geom_line()
Investigate Daily-Weekly Pattern
daily <- daily %>%
mutate(wday = wday(date, label = TRUE))
ggplot(daily, aes(wday,n)) +
geom_boxplot()
mod = lm(n ~ wday, data = daily)
grid <- daily %>%
data_grid(wday) %>%
add_predictions(mod, "n")
ggplot(daily, aes(wday, n)) +
geom_boxplot() +
geom_point(data = grid, color = "orange", size = 4)
Investigate residuals
daily <- daily %>%
add_residuals(mod)
daily %>%
ggplot(aes(date, resid)) +
geom_ref_line(h = 0) +
geom_line()
ggplot(daily, aes(date, resid, color = wday)) +
geom_ref_line(h = 0, colour = "red") +
geom_line()
daily %>%
filter(resid < -100)## # A tibble: 11 x 4
## date n wday resid
## <date> <int> <ord> <dbl>
## 1 2013-01-01 842 Tue -109.
## 2 2013-01-20 786 Sun -105.
## 3 2013-05-26 729 Sun -162.
## 4 2013-07-04 737 Thu -229.
## 5 2013-07-05 822 Fri -145.
## 6 2013-09-01 718 Sun -173.
## 7 2013-11-28 634 Thu -332.
## 8 2013-11-29 661 Fri -306.
## 9 2013-12-24 761 Tue -190.
## 10 2013-12-25 719 Wed -244.
## 11 2013-12-31 776 Tue -175.daily %>%
ggplot(aes(date, resid)) +
geom_ref_line(h = 0, colour = "red", size = 1) +
geom_line(color = "grey50") +
geom_smooth(se = FALSE, span = 0.20)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Seasonal Saturday effect
daily %>%
filter(wday == "Sat") %>%
ggplot(aes(date, n)) +
geom_point()+
geom_line() +
scale_x_date(
NULL,
date_breaks = "1 month",
date_labels = "%b"
)
Add Seasonal Variable
term <- function(date) {
cut(date,
breaks = ymd(20130101, 20130605, 20130825, 20140101),
labels = c("spring", "summer", "fall")
)
}
daily <- daily %>%
mutate(term = term(date))
daily %>%
filter(wday == "Sat") %>%
ggplot(aes(date, n, color = term)) +
geom_point(alpha = 1/3)+
geom_line() +
scale_x_date(
NULL,
date_breaks = "1 month",
date_labels = "%b"
)
daily %>%
ggplot(aes(wday, n, color = term)) +
geom_boxplot()
mod1 <- lm(n ~ wday, data = daily)
mod2 <- lm(n ~ wday * term, data = daily)
daily %>%
gather_residuals(without_term = mod1, with_term = mod2) %>%
ggplot(aes(date, resid, color = model)) +
geom_line(alpha = 0.75)
grid <- daily %>%
data_grid(wday, term) %>%
add_predictions(mod2, "n")
ggplot(daily, aes(wday, n)) +
geom_boxplot() +
geom_point(data = grid, color = "red") +
facet_wrap(~ term)
Better model for outliers (Robust regression)
mod3 <- MASS::rlm(n ~ wday * term, data = daily)
daily %>%
add_residuals(mod3, "resid") %>%
ggplot(aes(date, resid)) +
geom_hline(yintercept = 0, size = 2, color = "red") +
geom_line()
Computed Variables
# If you are creating variables it might be a good idea to bundle the creation of the variables up into a function
compute_vars <- function(data) {
data %>%
mutate(term = term(date),
wday = wday(date, label = TRUE)
)
}
# Another option would be to put the transformations directly in the model formula:
wday2 <- function(x) wday(x, label = TRUE)
mod3 <- lm(n ~ wday2(date) * term(date), data = daily)Time of Year: An Alternative Approach
# We could use a more flexible model to capture the pattern of school term in the data
library(splines)
mod <- MASS::rlm(n ~ wday * ns(date, 5), data = daily)
daily %>%
data_grid(wday, date = seq_range(date, n = 13)) %>%
add_predictions(mod) %>%
ggplot(aes(date, pred, color = wday)) +
geom_line() +
geom_point()
# We see a strong pattern in the numbers of Sat flights. This is reassuring, because we also saw that pattern in the raw data. It's a good sign when you get the same signal from different approaches.Question #1
Why are there fewer than expected flights on January 20, May 26 and September 1? (Hint: they all have the same explanation.) How would these days generalize into another year?
holiday <- c("0121", "0526", "0902")
years <- 2013:2019
map(years, ~ wday(ymd(paste0(.x, holiday, sep = "")), label = TRUE))## [[1]]
## [1] Mon Sun Mon
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[2]]
## [1] Tue Mon Tue
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[3]]
## [1] Wed Tue Wed
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[4]]
## [1] Thu Thu Fri
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[5]]
## [1] Sat Fri Sat
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[6]]
## [1] Sun Sat Sun
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[7]]
## [1] Mon Sun Mon
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < SatAnswer: Because the dates conincide with public holidays, including Martin Luther King day, Trinity Sunday and Labor day. There was a spike during the long weekend compared with previous year.
Question #2
What do the three days with high positive residuals represent? How would these days generalize to another year?
daily %>%
top_n(3, resid)## # A tibble: 3 x 5
## date n wday resid term
## <date> <int> <ord> <dbl> <fct>
## 1 2013-11-30 857 Sat 112. fall
## 2 2013-12-01 987 Sun 95.5 fall
## 3 2013-12-28 814 Sat 69.4 fallAnswer: THe weekend seems unpredicted if we assumed the residuals are not absolute figures.
Question #3
Create a new variable that splits the “wday” variable into terms, but only for Saturdays, i.e., it should have Thurs, Fri, but Sat-summer, Sat-spring, Sat-fall. How does this model compare with the model with every combination of “wday” and “term”?
daily <-
flights %>%
mutate(date = make_date(year, month, day)) %>%
group_by(date) %>%
summarize(n = n()) %>%
mutate(wday = wday(date, label = TRUE))
mod <- lm(n ~ wday, data = daily)
daily <- add_residuals(daily, mod)
term <- function(date) {
cut(date,
breaks = ymd(20130101, 20130605, 20130825, 20140101),
labels = c("spring", "summer", "fall")
)
}
daily <-
daily %>%
mutate(term = term(date))
###
new_daily <-
daily %>%
mutate(wday = as.character(wday),
term_sat = ifelse(wday == "Sat", paste0(wday, "-", term), wday))
mod1 <- MASS::rlm(n ~ term_sat, data = new_daily)
new_daily %>%
add_residuals(mod1) %>%
ggplot(aes(date, resid)) +
geom_line()
Answer: By observing the graph, the prediction result is exactly the same since both the Jan-March under prediction and the outliers are present from summer to winter.
Question #4
Create a new “wday” variable that combines the day of week, term(for Saturdays), and public holidays. What do the residuals of the model look like?
daily_holidays <-
new_daily %>%
mutate(holidays = case_when(date %in% ymd(c(20130101, # new years
20130121, # mlk
20130218, # presidents
20130527, # memorial
20130704, # independence
20130902, # labor
20131028, # columbus
20131111, # veterans
20131128, # thanksgiving
20131225)) ~ "holiday",
TRUE ~ "None")) %>%
unite(new_term, term_sat, holidays)
mod2 <- lm(n ~ new_term, data = daily_holidays)
daily_holidays %>%
add_residuals(mod2) %>%
ggplot(aes(date, resid)) +
geom_line()
Answer:The residual and the model doen’t change too much on the unexplained variation.
Question #5
What happens if you fit a day-of-week effect that varies by month (i.e.m n ~ wday*month)? Why is this not very helpful?
mod2 <- lm(n ~ wday * month(date), data = daily_holidays)
daily_holidays %>%
add_residuals(mod2) %>%
ggplot(aes(date, resid)) +
geom_line()
Answer: By oberserving the graph, there are more outlier shown in the result. And the prediction becomes more uncertainty since less observations is found.
Question #6
What would you expect the model n ~ wday + ns(date,5) to look like? Knowing what you know about the data, why would you expect it not to be particularly effective?
mod5 <- lm(n ~ wday * month(date), data = daily_holidays)
daily_holidays %>%
add_residuals(mod2) %>%
ggplot(aes(date, resid)) +
geom_line()
Answer: The expect model should work for the specific year(this year). However, since we know the days various by each year, so we would know that it would not be particularly effective into generalize to another year.
Question #7
We hypothesized that people leaving on Sundays are more likely to be business travelers who need to be somewhere on Monday. Explore the hypothesis by seeing how if breaks down based on distance and time: if it’s true, you’d expect to see more Sunday evening flights to places that are far away.