Refer to the Landscape Ecology Engineering (Jan. 2013) study of a new method of planning an ecological network, Exercise 10.37. Based on a sample of 21 bird habitats in China, the researchers modeled y = the bird density (number of birds per hectare) as a linear function of x = the percentage of the habitat covered by vegetation (i.e., a green area). Data similar to the data reported in the journal article are reproduced in the table. Suppose the researchers want to know if there is a curvilinear relationship between y and x. Specifically, is there evidence to indicate that the rate of increase of bird density with percent vegetation coverage is steeper for greener habitats (i.e., habitats with a greater percentage of vegetation). Conduct the appropriate analysis to answer the researchers’ question.

Data from Exercise 10.31

Refer to the IHS Journal of Hydraulic Engineering (September 2012) study of water pipes susceptible to breakage, Exercise 10.8. Recall that civil engineers used simple linear regression to model y = the ratio of repair to replacement cost of commercial pipe as a function of the x = diameter (in millimeters) of the pipe. Are the engineers able to conclude (at α = .05) that the cost ratio increases linearly with pipe diameter? If so, provide a 95% confidence interval for the increase in cost ratio for every 1 millimeter increase in pipe diameter.

Data from Exercise 10.8

Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe. A team of civil engineers used regression analysis to estimate y = the ratio of repair to replacement cost of commercial pipe in the IHS Journal of Hydraulic Engineering (September 2012). The independent variable in the regression analysis was x = the diameter (in millimeters) of the pipe. Data for a sample of 13 different pipe sizes are provided in the table.

Transcribed Image Text:

BIRDDEN HABITAT DENSITY COVER (birds/hectare) (%) 1 0.3 2 0.25 3 2 4 4 1 6. 0.5 9. 6. 10 7 3 12 8. 5 17 9 20 10 1 25 11 6. 30 12 37 13 40 14 2 45 15 7 50 16 16 58 17 5 60 18 20 71 19 5 80 20 37 90 21 100 2.