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 Restora- tion, 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-square line for predicting pop- ulation (y) from area (x ).
b. Use the least-squares line computed in part (a) to predict the population in an area of 5000 m2 .
c. Compute the least-square line for predicting ln y from ln x .
d. Use the least-squares line computed in part (c) to predict the population in an area of 5000 m2 .
e. Construct a scatterplot of population (y) versus area (x ).
f. Construct a scatterplot of ln y versus ln x .
|
Area
|
Population
|
Area
|
Population
|
|
3739
|
3015
|
2521
|
707
|
|
5277
|
1847
|
213
|
113
|
|
400
|
17
|
11958
|
1392
|
|
345
|
142
|
1200
|
157
|
|
392
|
40
|
12000
|
711
|
|
7000
|
2878
|
10880
|
74
|
|
2259
|
223
|
841
|
1720
|
|
81
|
15
|
1500
|
300
|
|
33
|
18
|
228
|
31
|
|
1254
|
229
|
228
|
17
|
|
1320
|
351
|
10
|
4
|
|
1000
|
92
|
g. Which of the two scatterplots appears to be more appropriately summarized by the least-squares line?
h. Which prediction is more reliable, the one in part (b) or the one in part (d)? Explain.