15.12 Beavers and beetles. Ecologlsts sometimes 11nd rather strange relatlonslnps 1n our envuonment. Une study seems to show that beavers benet beetles. The researchers laid out 23 circular plots, each 4 meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps 'om trees cut by beavers and the number of clusters of beetle larvae. Here are the data: Stumps: 2 2 l 3 3 4 3 l 2 5 1 3 Larvae clusters: 10 30 12 24 36 40 43 11 27 56 18 40 Stumps: 2 1 2 2 1 l 4 l 2 l 4 Larvaeclusbers: 25 8 21 14 16 6 54 9 13 14 50 Use your calculator to do the following: (a) Make a scatterplot that shows how the number of beaver-caused stumps inuences the number of beetle larvae clusters. What does your plot show? (Ecologists think that the new sprouts om stumps are more tender than other cottonwood growth, so that beetles prefer them.) (b) Find the least-squares regression line. Draw this line on your plot. (0) What is the correlation between these variables? What percentage of the observed variation in beetle larvae counts can be explained by straight-line dependence on stump counts? (d) Based on your work in (a), (b), and (0), do you think that counting stumps offers a quick and reliable way to predict beetle larvae clusters