Lab 22

Old Faithful - Inference on Regression

The Old Faithful Geyser in Yellowstone National Park erupts every 35 to 120 minutes. The duration of each eruption lasts for 1½ to 5 minutes. Notice that Old Faithful is not as faithful as one might expect. The time between eruptions and the length of each eruption varies quite a bit. However, one can estimate the time of the next eruption quite accurately given the duration of the previous eruption.

In this part we will determine if there is a linear relationship between the duration of the eruption and the time between eruptions. The data set we will work with consists of the duration of eruption and time between eruptions for 222 different eruptions of Old Faithful taken over a number of days in August 1978 and August 1979. (From Applied Linear Regression, 2nd Edition, by Sanford Weisberg, pp. 231 and 234.) The times given are in minutes. We will use the length of the duration to predict the length of the amount of time until the next eruption again. The park rangers at Yellowstone do this and their predictions are posted near the geyser and at the web cam picture site located here.

Copy the Old Faithful data into a Minitab worksheet and answer the following questions.

We will first examine the data using descriptive methods.

Make a scatterplot with duration on the horizontal axis and time between eruptions on the vertical axis. Describe the relationship between the two variables. (Graph > Scatterplot > Simple.)
Find a regression equation where duration is the explanatory variable and the time between eruptions is the response variable. (Stat > Regression > Regression.)
Use your regression equation to estimate the length of the time between eruptions when the duration is 4.0 minutes.

We will now use the data set to do some inference.

Is there a positive relationship between the duration of an eruption and the time until the next erruption. Using the data test this hypotheses. Report the hypotheses, test statistic, P-value, and a conclusion. (You should have already obtained your test statistic and P-value in completing question 1b.)
Give both a 95% confidence interval and a 95% prediction interval for the length of time between eruptions for a 4.0 minute duration. (To do this go to Stat > Regression > Regression, click on Options then put 4.0 in the "Prediction intervals for new observations:" box.)
Explain the difference between a confidence interval and a prediction interval.
In the original data, there are 15 interval times given with a duration of 4.0 minutes. How many of these are in your prediction interval from part (b)? How many (or what proportion) would you expect to be in your prediction interval?

Cuckoo for ANOVA

Some bird species do not build nests and do not raise their own young. Instead, they lay their eggs in the nests of other "host" birds. In this country, the cowbird is the most common bird that will do this. In general, these types of birds are known as brood parasites. Due to the size differences and early hatching ability of the parasitic bird, the hosts raise only the young of the parasitic bird, thereby loosing their own clutch. It is somewhat comical to see a small bird such as a sparrow or a finch feeding its much larger "adopted" baby. To see a picture of a large cowbird egg in a nest of other smaller birds click here. To see a small host bird feeding a cowbird click here.

Cuckoos are another species of brood parasites. The data set that can be found here contains the length of cuckoo eggs that were found in nests of various other host birds. (Reference: L.H.C. Tippett, The Methods of Statistics, 4th Edition, John Wiley and Sons, Inc., 1952, p. 176.) The host birds represented are the Tree Pipit, Hedge Sparrow, Robin, Pied Wagtail, and Wren. All data are lengths in millimeters.

Baldness	None	Little	Some	Much	Extreme
Heart_disease	251	165	195	50	2
Control	331	221	185	34	1