Ecologists classify the cause of forest fragmentation as either anthropogenic (i.e., due to human development activities such as road construction or logging) or natural in origin (e.g., due to wetlands or wildfire). Conservation Ecology (Dec. 2003) published an article on the causes of fragmentation for 54 South American forests. Using advanced high-resolution satellite imagery, the researchers developed two fragmentation indices for each forest—one index for anthropogenic fragmentation and one for fragmentation from natural causes. The values of these two indices (where higher values indicate more fragmentation) for 5 of the forests in the sample are shown in the accompanying table. The data for all 54 forests are saved in the FORFRAG file.

a. Ecologists theorize that an approximately linear (straight-line) relationship exists between the two fragmentation indices. Graph the data for all 54 forests. Does the graph support the theory?

b. Delete the data for the three forests with the largest anthropogenic
indices and reconstruct the graph, part a. Comment on the ecologists’ theory.    

c. Fit the straight-line model to the subset FORFRAG data file using the method of least-squares. Give the equation of the least-squares prediction equation.

d. Interpret the estimates of β_o and β₁ in the context of the problem.

e. Is there sufficient evidence to indicate that natural origin index (x) and anthropogenic index (y) are positively linearly related? Test using α = .05.

f. Find and interpret a 95% confidence interval for the change in the anthropogenic index (y) for every 1-point increase in the natural origin index (x).

Transcribed Image Text:

FORFRAG (First 5 observations listed) Anthropogenic index, y Natural origin Index, x Ecoregion (forest) Araucaria moist forests 34.09 30.08 Atlantic Coast restingas 40.87 27.60 Bahia coastal forests 44.75 28.16 Bahia interior forests 37.58 27.44 Bolivian Yungas 12.40 16.75