Old Faithful Chris Parrish

Transcription

1 Old Faithful Chris Parrish Contents Old Faithful eruptions 1 data duration waiting time short and long eruptions predicting waiting times Old Faithful eruptions references: - Old Faithful, Wikipedia - Geyser Observation and Study Association data?faithful # in package datasets data <- faithful colnames(data) <- c("duration", "waiting") head(data) ## duration waiting ## ## ## ## ## ## str(data) ## 'data.frame': 272 obs. of 2 variables: ## $ duration: num ## $ waiting : num duration Histogram. Summarize the shape, center, spread, and range of the distribution of durations of Old Faithful eruptions. 1

2 ggplot(data, aes(duration)) + geom_histogram(color = "saddlebrown", fill = "wheat") + labs(x = "Duration (min)", title = "Old Faithful Duration") Old Faithful Duration count Duration (min) data %>% summarize(mean = mean(duration), median = median(duration), sd = sd(duration), n = n()) ## mean median sd n ## Boxplot. What do you see in this boxplot that is not evident in the histogram? ggplot(data, aes(x = 1, y = duration)) + geom_boxplot(color = "saddlebrown", fill = "wheat") + labs(x = "", y = "Duration (min)", title = "Old Faithful Duration") + coord_flip() 2

3 1.4 Old Faithful Duration Duration (min) Do the mean and median coincide? Why? summary(data$duration) ## waiting time Summarize the shape, center, spread, and range of the distribution of waiting times of Old Faithful eruptions. ggplot(data, aes(waiting)) + geom_histogram(color = "saddlebrown", fill = "wheat") + labs(x = "Waiting time (min)", title = "Old Faithful Waiting Time") 3

4 Old Faithful Waiting Time count 1 data %>% summarize(mean = mean(waiting), sd = sd(waiting), n = n()) ## mean sd n ## Waiting time (min) What do you see in this boxplot that is not evident in the histogram? ggplot(data, aes(x = 1, y = waiting)) + geom_boxplot(color = "saddlebrown", fill = "wheat") + labs(x = "", y = "Waiting time (min)", title = "Old Faithful Waiting Time") + coord_flip() 4

5 1.4 Old Faithful Waiting Time Waiting time (min) summary(data$waiting) ## short and long eruptions Both distributions are bimodal. Are short eruptions followed by short waiting times? Tag the observations with short durations. data <- mutate(data, short.duration = duration <= 3) str(data) ## 'data.frame': 272 obs. of 3 variables: ## $ duration : num ## $ waiting : num ## $ short.duration: logi FALSE TRUE FALSE TRUE FALSE TRUE... data %>% group_by(short.duration) %>% summarize(mean = mean(duration), sd = sd(duration), n = n()) ## # A tibble: 2 4 ## short.duration mean sd n ## <lgl> <dbl> <dbl> <int> ## 1 FALSE ## 2 TRUE Did we successfully separate the eruptions with short and long durations? ggplot(data, aes(duration)) + geom_histogram(color = "saddlebrown", fill = "wheat") + facet_grid(short.duration ~.) + labs(x = "Duration (min)", title = "Old Faithful") 5

6 Old Faithful count 1 1 FALSE TRUE Duration (min) Are short duration eruptions followed by short waiting times? Are there many exceptions? ggplot(data, aes(waiting)) + geom_histogram(color = "saddlebrown", fill = "wheat") + facet_grid(short.duration ~.) + labs(x = "Waiting time (min)", title = "Old Faithful") 6

7 Old Faithful count 1 1 FALSE TRUE Waiting time (min) Summarize the overlap in waiting times after eruptions with short and long durations. Create a way to quantify the overlap. How many observations fall into the overlap zone? How many observations were there altogether in the original dataset? waiting.after.short <- data[data$short == TRUE, "waiting"] waiting.after.long <- data[data$short == FALSE, "waiting"] # longest waiting times after short tail(sort(waiting.after.short), ) ## [1] # shortest waiting times after long head(sort(waiting.after.long), ) ## [1] predicting waiting times Prepare some advice for park rangers who answer visitors questions at Yosemite National Park. How long will a visitor have to wait for the next eruption after a short eruption? How much error should we expect in this estimate? summary(waiting.after.short) 7

8 ## sd(waiting.after.short) ## [1] How long will a visitor have to wait for the next eruption after a long eruption? How much error should we expect in this estimate? summary(waiting.after.long) ## sd(waiting.after.long) ## [1] How long will a visitor have to wait for the next eruption if we don t know the length of the last eruption? How much error should we expect in this estimate? summary(data$waiting) ## sd(data$waiting) ## [1]