a) The residual is 2.07 minutes.
b) The positive residual of 2.07 minutes indicates that the actual wait time was 2.07 minutes longer than the predicted wait time.
(a) In one cycle, it took 62 minutes between eruptions, and the duration of the previous eruption was 2 minutes.
Calculate the residual for this cycle.
The residual is the difference between the actual wait time and the predicted wait time. The predicted wait time for a previous eruption of 2 minutes is ŷ = 33.35 + 13.29 * 2 = 59.93 minutes. Therefore, the residual is 62 - 59.93 = 2.07 minutes.
(b) Interpret the residual for this cycle.
The positive residual of 2.07 minutes indicates that the actual wait time was 2.07 minutes longer than the predicted wait time. In other words, the geyser took 2.07 minutes longer to erupt than expected, given the duration of the previous eruption.
Overall, the image shows that there is a positive relationship between the duration of the previous eruption and the wait time until the next eruption. This means that longer eruptions tend to be followed by longer wait times.
However, there is also some variability in the data, as indicated by the fact that the actual wait times can deviate from the predicted wait times.
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