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Interpreting the Intercept and Slope of Regression Lines

Old Faithful

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 you collect data on 21 eruptions. For each observed eruption, you write down its duration (call it DUR) and the waiting time to the next eruption (call it TIME).

That is, your variables are:

DUR Duration of the previous eruption (in minutes)
TIME Time until the next eruption (in minutes)
You obtain the following regression output (abbreviated).

------------------------------------------------------------------------------
TIME | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
DUR | 9.790068 1.299906 7.531 0.000 7.0690687 12.510931
_cons | 31.013115 4.416584 7.022 0.000 21.769098 40.257132
------------------------------------------------------------------------------
(a) Write down the estimated regression equation, and verbally interpret the intercept and the slope coefficients (in terms of geysers and eruption times).
(b) At a 5% significance level, is the intercept significant? Is DUR significant? Give a full sentence interpreting significance at the 5% level.
(c) The most recent eruption lasted 3 minutes. What is your best estimate for the time till the next eruption?

Solution Preview

(a) Write down the estimated regression equation, and verbally interpret the intercept and the slope coefficients (in terms of geysers and eruption times).
Answer: the estimated regression equation: Time=31.013115+9.790068(DUR)
Interpretation of slope: if duration of the previous eruption of the Old Faithful geyser increases for 1 minute, ...

Solution Summary

The solution gives detailed steps on interpreting the intercept and slope of regression lines, the significance of coefficients and predicting the dependent variable when the value of a independent variable is given.

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