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 22 22 11 33 33 44 33 11 22 55 11 33
Beetle larvae 1010 3030 1212 2424 3636 4040 4343 1111 2727 5656 1818 4040
Stumps 22 11 22 22 11 11 44 11 22 11 44
Beetle larvae 2525 88 2121 1414 1616 66 5454 99 1313 1414 5050
Analyze these data to see if they support the "beavers benefit beetles" idea. Follow the four‑step process in reporting your work.
STATE: Choose the statement that best describes the goal of the research.
Beetle larvae are the explanatory variable, and we expect an increase in beetle larvae to induce an increase in the response variable, the number of tree stumps.
The number of tree stumps is the explanatory variable, and we expect an increase in the number of tree stumps to induce a decrease in the response variable, the number of beetle larvae.
The number of tree stumps is the explanatory variable, and we expect an increase in the number of tree stumps to induce an increase in the response variable, the number of beetle larvae.
Beetle larvae are the explanatory variable, and we expect an increase in beetle larvae to induce a decrease in the response variable, the number of tree stumps.
PLAN: Make a scatterplot of the data and examine the pattern. Choose the statement that best describes your findings:
The relationship doesn't seem to be linear.
There is a strong negative linear relationship.
There is a positive linear relationship.
There is a weak negative linear relationship.
CONCLUDE: 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. Enter your answer as a decimal rounded to three decimal places.
2=
Which of the choices correctly describes whether the association supports the idea that beavers benefit beetles?
a. Yes, the weak negative association supports the idea that beavers benefit beetles.
b. Yes, the strong positive association supports the idea that beavers benefit beetles.
c. No, the strong positive association does not support the idea that beavers benefit beetles.
d. No, the strong negative association does not support the idea that beavers benefit beetles.
e. There is not enough information to tell.
Stumps Larvae
2 10
2 30
1 12
3 24
3 36
4 40
3 43
1 11
2 27
5 56
1 18
3 40
2 25
1 8
2 21
2 14
1 16
1 6
4 54
1 9
2 13
1 14
4 50