The file Birdnest contains data for 99 species of North American passerine birds. Passerine are “ perching birds” and include many families of familiar small birds (e. g., sparrows and warblers), as well as some larger species like crows and ravens, but do not include hawks, owls, water fowl, wad-ing birds, and woodpeckers. One hypothesis of interest was about the relationship of body size to type of nest. Body size was measured as average length of the species. Although nests come in a variety of types (see the Nesttype variable), in this data set nest type was categorized into either closed or open. “Closed” refers to nests with only a small opening to the outside, such as the tree cavity nest of many woodpeckers or the pendant-style nest of an oriole. “Open” nests include the cup-shaped nest of the American robin.
a. Create a logistic regression model using bird length (Length) to estimate the probability that a bird species has a closed nest type. Interpret the model in terms of the odds ratio.
b. Use the Wald statistic to create a 95% confidence interval for the odds ratio.
c. Test H0: β1 = 0 versus Ha: β1 ≠ 0 using both Wald’s test and the likelihood ratio test. State your conclusion based on these tests.
d. Conduct the Hosmer-Lemeshow test to assess how well the model fits the data.
e. Explain why the Pearson chi-square test is not reliable for this example.
f. Report and interpret Somers’D, Goodman-Kruskal gamma, or Kendall’s tau-a for this logistic regression model.