The article "Estimating Population Abundance in Plant Species with Dormant Life-Stages: Fire and the Endangered Plant Grevillea caleye R. Br." (T. Auld and J. Scott, Ecological Management and Restoration, 2004:125-129) presents estimates of population sizes of a certain rare shrub in areas burnt by fire. The following table presents population counts and areas (in m2) for several patches containing the plant.

a. Compute the least-squares line for predicting population (y) from area (x).
b. Plot the residuals versus the fitted values. Does the model seem appropriate?
c. Compute the least-squares line for predicting ln y from ln x.
d. Plot the residuals versus the fitted values. Does the model seem appropriate?
e. Using the more appropriate model, construct a 95% prediction interval for the population in a patch whose area is 3000m2.

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Area Population Area Population Ar PopulationArea Population 3739 5277 400 345 392 7000 707 113 1392 157 223 15 18 841 1500 228 228 10 3015 1847 17 2521 213 11958 1200 12000 10880 2259 81 1720 300 31 17 40 2878 1254 1320 1000 351 92 74