Refer to the Landscape Ecology Engineering (Jan. 2013) study of an ecological network, Exercise 10.37. Recall that the researchers used the data collected for 21 bird habitats to fit the model, E(y) = β_o + β₁x, where y =  bird density and x = vegetation coverage (percentage).

a. Use the least squares prediction equation to calculate the predicted values of bird density and associated residuals for the model.

b. Plot the residuals against ŷ. Do you detect a trend?

c. Based on the residual plot, which assumption appears to be violated?

d. What model modification do you recommend?

Data from Exercise 10.37

Refer to the Chemical Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, Exercise 10.10. You fit a straight-line model relating the mass y (in pounds) of the spill to elapsed time x (in minutes) using the data provided.

Data from Exercise 10.10

A contract engineer at DuPont Corp. studied the rate at which a spilled volatile liquid will spread across a surface (Chemical Engineering Progress, Jan. 2005). Assume 50 gallons of methanol spills onto a level surface outdoors. The engineer used derived empirical formulas (assuming a state of turbulent-free convection) to calculate the mass (in pounds) of the spill after a period of time ranging from 0 to 60 minutes. The calculated mass values are given in the accompanying table.

Transcribed Image Text:

LIQUIDSPILL Time Time Mass (pounds) Mass (minutes) (pounds) (minutes) 6.64 22 1.86 1 6.34 24 1.60 2 6.04 26 1.37 4 5.47 28 1.17 6 4.94 30 0.98 8 4.44 35 0.60 10 3.98 40 0.34 12 3.55 45 0.17 14 3.15 50 0.06 16 2.79 55 0.02 18 2.45 60 0.00 20 2.14