Old Faithful Duration Prediction

how long will this eruption last?

Stephen D. Wells
data castaway

Old Faithful

  1. Located in Yellowstone National Park (United States), Old Faithful was the first named cone geyser in the park.
  2. A legend for it's predictability, it was known to erupt every 91 minutes.
  3. The length of the interval has increased possibly due to earthquakes affecting subterranean water levels.

Dataset

  • directly from R datasets package
  • 272 observations with 2 columns eruptions and waiting

Observations

  • The times are in seconds and are heavily rounded to the nearest 5
  • there are better versions but this was chosen for it's accessibility and simplicity

Prediction Algorithm

  • Created a simple prediction routine after fitting eruptions to wait times
  • Input: waiting time and confidence level

Core Code

data(faithful)
fit <- lm(eruptions ~ waiting, data=faithful)

duration <- function (waiting=91, level=.95) {
  predict(fit, data.frame(waiting), interval="predict", level=level)
}

duration()

##     fit   lwr   upr
## 1 5.008 4.025 5.991

UI Design Decisions

  • Slider Bar and Numeric Input
    • visually broke up the display
    • allowed testing of two different forms of input
  • Horizontal Stem-and-Leaf Plot
    • fixed width to incorporate the range of values
    • width of the box visually displays the confidence interval
    • changes to the wait time show how the volume moves up and down
  • Submit Button
    • without it the display had movement and you could see the reaction
    • the delay due to processing became unwieldly so automated updates were scraped.

Summary

Two-thousand meters under the earth, water collects on rocks superheated by magma. Eventually it boils, causing the water to expand rapidly. Under this intense pressure, a violent spray of boiling water and steam erupt from the earth. This intermittent explosion is known as a geyser. One of the most famous is Old Faithful in Yellowstone National Park, US.

Taking 272 observations of the duration the eruptions and the length of time between them we were able to build a prediction algorithm that would identify how long the eruption would take place given the amount of time between the last eruption. We were able to conclude that the more time between eruptions, the more water would build up and the longer the geyser would discharge.

See Also