Do beavers benefit beetles? Researchers laid out 2323 circular plots, each 44 meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so that beetles prefer them. If so, more stumps should produce more beetle larvae. The table contains the data.
Stumps
Beetle larvae
22
1010
22
3030
11
1212
33
2424
33
3636
44
4040
33
4343
11
1111
22
2727
55
5656
11
1818
33
4040
22
2525
11
88
22
2121
22
1414
11
1616
11
66
44
5454
11
99
22
1313
11
1414
44
5050
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Analyze these data to see if they support the "beavers benefit beetles" idea. Follow the four‑step process in reporting your work.
SOLVE: Calculate the correlation for the data. Also calculate the slope and intercept of the regression line. Drag
the correct answers to the appropriate bins.
Calculate the fraction of the variation in the values of the number of beetle larvae that is explained by the least‑squares regression with the number of tree stumps as the explanatory variable. Give your answer to three decimal places.
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Does the association supports the idea that beavers benefit beetles?
Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
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