BUAD 2070, Assignment on Simple Regression

It is well known that the famous geyser Old Faithful in Yellowstone National Park erupts quite regularly, and hence it has attracted millions of visitors. The data file OldFaith gives information about eruptions during October 1980*. Variables are the Duration in seconds of the current eruption, and the Interval, the time in minutes to the next eruption. The park service uses data like these to obtain a prediction equation for the time to the next eruption. Such time predictions are shown to the tourists who wait for the next eruption of Old Faithful.

*The data were collected by volunteers and made public by R. Hutchinson. Apart from missing data for the period from midnight to 6 am, this is a complete record of eruptions for that month.

1. Find a scatter diagram that summarizes a linear relation between Duration and Interval. Include in this diagram the “trendline” and the coefficient of determination. How would you interpret this coefficient?

2. What are the sample means and sample standard deviations of Duration and Interval?

3. Find a prediction equation for Interval from Duration. How would you interpret the slope of this linear equation? What is the 90% confidence interval for the population slope of Duration? Interpret this interval. What is the 95% confidence interval for the population slope of Duration? Compare the widths of the two intervals and make relevant comments about these widths.

4. Assuming the confidence level of 95%, conduct the t test for testing the significance of Duration. (Specify clearly your hypotheses, indicate the value of the test statistic and the distribution of the test statistic, find the test p-value, make your conclusion and interpret this conclusion.)

5. Suppose a tourist has just arrived at the end of an eruption that lasted 250 seconds. What is the predicted waiting time for the tourist?