The time between eruptions of the Old Faithful geyser in Yellowstone National Park is random, but is related to the duration of the previous eruption. In order to investigate this relationship data on 21 eruptions was gathered. For each observed eruption, its duration (call it DUR) and the waiting time to the next eruption (call it TIME) were recorded. That is, the variables are: DUR Duration of the eruption (in minutes) TIME Time until the next eruption (in minutes)

See data attached.

(a) Write down the estimated regression equation, and verbally interpret the intercept and the slope coefficients (in terms of geysers and eruption times). (b) (Optional) At a 5% significance level, is the intercept significant? Is DUR significant? (c) The most recent eruption lasted 3 minutes. What is your best estimate for the time until the next eruption.