Forest fragmentation study. Refer to the Conservation Ecology (Dec. 2003) study on the cau...

Forest fragmentation study. Refer to the Conservation Ecology (Dec. 2003) study on the causes of fragmentation of 54 South American forests, presented in Exercise.

Forest fragmentation study. 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 indexes for each forest—one for anthropogenic fragmentation and one for fragmentation from natural causes. The values of these two indexes (where higher values indicate more fragmentation) for five of the forests in the sample are shown in the table below. The data for all 54 forests are saved in the FORFRAG file.

Based on Wade, T. G., et al. “Distribution and causes of global forest fragmentation.” Conservation Ecology, Vol. 72, No. 2, Dec. 2003.

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

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

Recall that researchers developed two fragmentation indexes for each forest—one index for anthropogenic (human development activities) fragmentation and one for fragmentation from natural causes. Data on 5 of the 54 forests saved in the FORFRAG file are listed in the Above table:

a. Ecologists theorize that a linear relationship exists between the two fragmentation indexes. Write the model relating y to x.

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b. Fit the model to the data in the FORFRAG file, using the method of least squares. Give the equation of the least squares prediction equation.

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c. Interpret the estimates of β0 and β1 in the context of the problem.

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

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e. 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 ).