Question

Problem 4) Every 13 or 17 years, a brood of cicadas, sometimes in Biblical proportions, emerges from underground in the northeastern part of the United States., Although harmless to humans, cicadas cause damage to small trees and shrubs, and they make a piercing, irritating sound. Some research suggests that the density of cicadas is related to the density of moles, a natural predator of the cicada. Plots were randomly selected, and the density of moles (individuals per acre) and the density of cicadas (millions per acre) were carefully estimated. Entomologists want to predict the number of cicadas based on the density of moles. a) What is the explanatory variable? The response variable? Use the Rossman/Chance applet Analyzing Two Quantitative Variables to make a scatterplot and find the least squares regression line for the relationship. Copy and paste the data including top row of Cicada Mole exactly as in the excel file, tab cicada. Be careful assigning the explanatory and the response variable in the applet. Be careful assigning the explanatory and the response variable in the applet. You can toggle (Explanatory, Response) by clicking on it. Be sure that the applet designation is correct for your variables. You may need to toggle it. Print the screen with your scatterplot and analysis so we can refer to it in class.

Mole Cicada

4 1.5

6 0.8

3 1.2

0 1.4

2 1.5

4 1.5

0 1.7

5 1.2

4 1.1

b) Based on the scatterplot and correlation coefficient give the Direction of relationship: Form: Strength of relationship:

Table:

cicadas and moles

equation of least squares line in correct format

value for the correlation coefficient r

Interpretation of slope in the context of the problem

Interpretation of y-intercept in the context of the problem

Predict the cicada density if the mole density is 1 individual per acre

Predict the cicada density if the mole density is 12 individuals per acre

Answer 1