Final answer:
To calculate the residual for a cycle, information from a regression model or trend line is needed to determine the expected time. The residual is the difference between the observed time between eruptions and the predicted time. Without the model, we cannot compute the exact residual.
Step-by-step explanation:
To calculate the residual for a cycle in a scatter plot showing the relationship between eruption durations and the time between eruptions, we need to know the actual observed time between eruptions and what the expected time would be based on a fitted line or curve that represents the average trend in the data. However, with the information provided, we can't determine what the expected time between eruptions should be, because we would need a regression equation or a trend line from the scatter plot.
In the case of the Old Faithful geyser represented in Figure 0.5, we see a general increasing trend that suggests longer eruption durations tend to follow longer intervals between eruptions. But without knowing the exact trend line or expected time for a 2-minute eruption, we can't calculate the residual. The residual is the difference between the observed value and the value predicted by our regression model.
Therefore, to compute the exact residual, additional information is required from the scatter plot or a predictive model that provides expected wait times based on eruption durations.