Exotic Plants. In the article "Effects of Human Population, Area, and Time on Non-native Plant and Fish Diversity in the United States" (Biological Conservation, Vol. 100, No. 2, pp. 243-252), M. McKinney investigated the relationship of various factors on the number of exotic plants in each state. On the Weiss -Stats site, you will find the data on population (in millions), area (in thousands of square miles), and number of exotic plants for each state. Use the technology of your choice to determine the linear correlation coefficient between each of the following:

a. population and area

b. population and number of exotic plants

c. area and number of exotic plants

d. Interpret and explain the results you got in parts (a)-(C).

Short Answer

Expert verified

A) : r = 0.109

B) : r = 0.721

C) : r = -0.309

D) : For the linear relationship to remain true between the two variations x and that the data points need to be dispersed in the line.

Step by step solution

01

Step 1. Given 

The relationship of various factors on the number of exotic plants in each state. On the Weiss -Stats site, you will find the data on population (in millions), area (in thousands of square miles), and number of exotic plants for each state.

02

Step 2. Part ( a ) 

Follow the given steps mentioned below to obtain the linear correlation coefficient between population and area using Minitab.

Step 1. Store the data from the given table in columns named x and y respectively.

Step2 Choose Stats > Basic statistics > Correlation....

Step3. Specify C1 and C2 in the Variables text box.

Step4 Uncheck the Display p valuescheck box

Step5 Click OK

The screen shot is as follows:

Hence, the answer isr=0.109

03

Step 3. Part ( b ) 

Follow the given steps mentioned below to obtain the linear correlation coefficient r between population and number of plants using Minitab.

Step1 .Store the data from the given table in columns named x and y respectively

Step2 Choose Stats > Basic statistics > Correlation....

Step3. Specify C1 and C3 in the Variables text box

Step4. Uncheck the Display p values check box.

Step5. Click OK

The screen shot is as follows:

Hence, the answer isr=0.721

04

Step 4. Part ( c ) 

Follow the given steps mentioned below to obtain the linear correlation coefficient r between population and number of plants using Minitab.

Step1 .Store the data from the given table in columns named x and y respectively

Step2 ChooseStats > Basic statistics > Correlation....

Step3. Specify C1 and C3 in theVariables text box

Step4. Uncheck theDisplay p values check box.

Step5. Click OK

The screen shot is as follows:

Hence, the answer isr=-0.309

05

Step 5. Part ( d )

The coefficient of linearity between the two variations of the three sets does not indicate the correlation of the line between the variables x and that y For the linear relationship to remain true between the two variations x and that the data points need to be dispersed in the line.

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Most popular questions from this chapter

4.76 PCBs and Pelicans, Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979and by the Stockholm Convention on Persistent Organic Pollutants in 2001. One study, published in 1972 by R. Risebrough, is titled "Effects of Environmental Pollutants Upon Animals Other Than Man" (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, Vl, University of California Press, Pp. 443-463). In that study, 60Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBs, in parts per million (ppm). The data are on the Weiss Stats site.

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In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (Amer. icon Industrial Hyeiene Asseciution Journal, Vol. 63, Pp. 756-761), 1. Moa et al. reported on determining fiber density by two different methods. Twenty samples of varying fiber density were each counted by 10 viewers by means of an eyepiece method and a television screen method to determine the relationship between the counts done by each method. The results, in fibers per square millimeter, are presented on the Weiss Stats site.

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If y tends to decrease linearly as x increases. the variables are -------linearly correlated.

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