A visitor to Yellowstone National Park in Wyoming,U.S.A,sat down one day and observed Old Faithful,which faithfully erupts throughout the day,day in and day out.He surmised that the height of a given eruption was caused by the pressure buildup during the interval between eruptions and by the momentum buildup during the duration of the eruption.He wrote down the data to test his hypothesis,but he didn't know what to do with his data.
A)Height = 125.1 + 0.36 Interval - 0.89 Duration
B)Height = 24.8 + 0.53 Interval - 0.11 Duration
C)Height = 126.3 + 0.37 Interval - 0.079 Duration
D)Height = 126.3 + 0.73 Interval - 0.11 Duration
E)Height = 25.1 + 0.73 Interval - 0.62 Duration

Question

A visitor to Yellowstone National Park in Wyoming,U.S.A,sat down one day and observed Old Faithful,which faithfully erupts throughout the day,day in and day out.He surmised that the height of a given eruption was caused by the pressure buildup during the interval between eruptions and by the momentum buildup during the duration of the eruption.He wrote down the data to test his hypothesis,but he didn't know what to do with his data. 
A)Height = 125.1 + 0.36 Interval - 0.89 Duration 
B)Height = 24.8 + 0.53 Interval - 0.11 Duration 
C)Height = 126.3 + 0.37 Interval - 0.079 Duration 
D)Height = 126.3 + 0.73 Interval - 0.11 Duration 
E)Height = 25.1 + 0.73 Interval - 0.62 Duration

Quizplus · Accepted Answer

The equation that best fits the observations is: 
Height = 126.3 + 0.37 Interval - 0.079 Duration

This equation takes into account both the pressure buildup (Interval) and the momentum buildup (Duration) during the eruption. The coefficients for Interval and Duration are both positive, indicating that as these variables increase, the height of the eruption also increases. However, the coefficient for Duration is smaller in magnitude than the coefficient for Interval, suggesting that the momentum buildup has a slightly weaker effect on the height of the eruption than the pressure buildup.

This equation also fits well with the observation that Old Faithful reliably erupts throughout the day. Since the equation includes Interval (the time between eruptions), it can be used to predict the height of the next eruption based on the time elapsed since the last one.

A Visitor to Yellowstone National Park in Wyoming,U