Endangered animal species often live in isolated patches of habitat. If the popu

Question

Endangered animal species often live in isolated patches of habitat. If the population in a patch varies a lot (due to weather, for example), the species is more likely to disappear from that patch in a bad year. Here is a general question: Is there less variation in population size when a patch of habitat has more diverse vegetation? If so, maintaining habitat diversity can help protect endangered species. A researcher measured the variation over time in the population of a cricket species in 45 habitat patches. He also measured the diversity of each patch. He reported his results by giving the least-squares equation along with the fact that r2 = 0.36.

Population Variation = 84.4 0.13 × diversity

1. Do these results support the idea that more diversity goes with less variation in population size?

Yes No   

2. Is the relationship very strong or not very strong?

not very strong or strong   

3. How much of the variation is explained by diversity?   

Explanation / Answer

1)
we see that the regression equation is

Population Variation = 84.4 0.13 × diversity

this means that

Variation and diversity are negatively related . for every unit increase in diversity , variation goes down by 0.13 units

2)
r2 = 0.36 , so r = sqrt(r2) = 0.6
byt as we know the beta1 is negative hence correlation is negative so the correlation is -0.6
hence it is not a very strong correlation

3)
r2 = 0.36
This means that the model is able to explain only 36% variability of population variation due to diversity

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