STA 242/ENV 255
Homework 5 (optional; for extra credit)

Your answers should be typed, formatted, and concise. Do not paste in SPlus output.

  1. Data was collected along the trail surrounding the Duke Golf Course to study the habitat of the campus squirrel. A student walked the length of the trail and recorded sightings of squirrels. The trail was then divided into 10 meter intervals. The student defined a variable, "Y", as a binary variable which took a value of "1" if a squirrel was seen in a 10 meter interval or a "0" if a squirrel was not seen in that interval. His results are detailed in the table below. For each interval, there is a variable "X" which is defined as the distance in meters to the nearest garbage can. We are interested in comparing the odds that a squirrel is seen within 20 meters of a garbage can with the odds that a squirrel is seen beyond 20 m of a garbage can.


    Distance to Nearest Garbage Can

    Less than 20 meters

    Greater than 20 meters

    Squirrel Sighting

    Yes

    35

    15

    No

    100

    350

    1. Compute and interpret the odds ratio in a sentence.
    2. How can the student use a logistic regression model to test the hypothesis that the odds of seeing a squirrel are equally likely within 20 meters and beyond 20 meters of the garbage can? Write out the model he might consider. Give null and alternative hypotheses and the rejection region for such a test.

  2. The data in birdskel.txt were sampled at random from a larger study by Prange et al. (1979) They reinvestigated the question of whether birds have proportionately lighter skeletons than mammals because of their adaptation for flight. All weights are in kilograms. Of interest to researchers is whether skeletal mass can be predicted from body mass, and whether this relationship is different for birds and mammals.

    1. Choose and report the model that best addresses the research question. Report your model selection steps, including test statistics, etc, as you would in a writing assignment.
    2. Give confidence intervals for the slopes for birds and for mammals.
    3. For a mammal with body mass equal to 0.5 kg, what is the predicted value of skeletal mass assuming the model is true? Give a confidence interval for the mean of skeletal mass at this value of body mass. Is this the same interval you would provide if you were asked for a confidence interval for a future value of skeletal mass at body mass equal to 0.5 kg?
    4. Answer the researcher's question in one or two sentences.

  3. Exercise 11 on p. 603, based on the space shuttle data. For part e) include 95% CI's for your estimates.

Splus instructions:

To fit a logistic regression with failure as the response and temp as the explanatory variable: