STATE: Choose the statement that best describes the goal of the research. A) 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. B) 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. C) 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. D) 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. PLAN: Make a scatterplot of the data and examine the pattern. Choose the statement that best describes your findings: A) There is a weak negative linear relationship. B) The relationship doesn't seem to be linear. C) There is a positive linear relationship. D)There is a strong negative linear relationship. 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. Correlation: Slope: Intercept: 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. r^2 = Which of the choices correctly describes whether the association supports the idea that beavers benefit beetles? A) There is not enough information to tell. B) No, the strong positive association does not support the idea that beavers benefit beetles. C) Yes, the weak negative association supports the idea that beavers benefit beetles. D) No, the strong negative association does not support the idea that beavers benefit beetles. E) Yes, the strong positive association supports the idea that beavers benefit beetles.

STATE: Choose the statement that best describes the goal of the research. A) 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. B) 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. C) 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. D) 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. PLAN: Make a scatterplot of the data and examine the pattern. Choose the statement that best describes your findings: A) There is a weak negative linear relationship. B) The relationship doesn't seem to be linear. C) There is a positive linear relationship. D)There is a strong negative linear relationship. 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. Correlation: Slope: Intercept: 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. r^2 = Which of the choices correctly describes whether the association supports the idea that beavers benefit beetles? A) There is not enough information to tell. B) No, the strong positive association does not support the idea that beavers benefit beetles. C) Yes, the weak negative association supports the idea that beavers benefit beetles. D) No, the strong negative association does not support the idea that beavers benefit beetles. E) Yes, the strong positive association supports the idea that beavers benefit beetles.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Do beavers benefit beetles? 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 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
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

STATE: Choose the statement that best describes the goal of the research.

A) 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.

B) 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.

C) 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.

D) 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.

PLAN: Make a scatterplot of the data and examine the pattern. Choose the statement that best describes your findings:

A) There is a weak negative linear relationship.

B) The relationship doesn't seem to be linear.

C) There is a positive linear relationship.

D)There is a strong negative linear relationship.

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.

Correlation:

Slope:

Intercept:

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.

r^2 =

Which of the choices correctly describes whether the association supports the idea that beavers benefit beetles?

A) There is not enough information to tell.

B) No, the strong positive association does not support the idea that beavers benefit beetles.

C) Yes, the weak negative association supports the idea that beavers benefit beetles.

D) No, the strong negative association does not support the idea that beavers benefit beetles.

E) Yes, the strong positive association supports the idea that beavers benefit beetles.

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Stumps	Beetle 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

Stumps	Beetle 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

Stumps	Beetle 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