Question

Can we predict the next eruption of the Old Faithful geyser by knowing the duration of the previous eruption? The observations and least squares regression line appear in the scatterplot. The scatterplot and the least-squares regression line for predicting the Interval (minutes) between eruptions and the Duration (minutes) of the previous eruption is given below. Which of the following is the correct interpretation of the slope of the least squares regression line for the data about Old Faithful?

Answer 1

The slope of the least-squares regression line for Old Faithful eruptions represents the estimated increase in the time interval between eruptions for each minute of increase in eruption duration.

Step-by-step explanation:

The slope of the least-squares regression line represents the rate of change between the two variables displayed on a scatter plot. In the context of Old Faithful's eruptions, the slope of the line would indicate how much the time interval between eruptions increases (or decreases) for each additional minute of eruption duration based on the sample data. By knowing the duration of the previous eruption and using the slope, we can predict the estimated interval before the next eruption.

For example, if the slope is 10, that would mean for each additional minute that an eruption lasts, the time interval until the next eruption increases by an estimated 10 minutes, according to the least-squares regression model. However, it is important to note that such predictions are only estimates and may not always be perfectly accurate because real-life data often have variability that cannot be perfectly captured by a simple linear relationship.

Answer 2

The correct answer is We can predict the time between eruptions will be 10.73 minutes and this can be stated with 0.901 probability.

Eruptions do not always produce symmetrical and imposing cones. Volcanic relief has varied shapes and we must analyze the properties of the lava and the conditions of spill occurrence to understand.