Q. 4.76 - Elementary Statistics

Question

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 $1979$ and 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, $60$ Anacapa 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.

a. Obtain a scatterplot for the data.

b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f).

Step-by-Step Solution

Answer

a. The scatter plot is,

b. Finding the regression line for the provided data is not feasible.

Part (a) Step 1: Given Information

The scatterplot for the given data must be determined. 

Part (a) Step 2: Explanation

The MINITAB can be used to create a scatterplot like follows:

• Save the data in the $x$ and $y$ columns, correspondingly.
• Select Scatter plot from the graph menu.
• Select the Scatter Plot With Connect Lines option.
• In the $Y$ variables text box, specify the thickness column.
• In the $X$ variables text box, type PVB's column and click OK.

The scatterplot can be made as follows:

Part (b) Step 1: Given Information

Determine whether or not the regression line's evaluation is reasonable.

Part (b) Step 2: Explanation

No, finding a regression line for the supplied data is not reasonable because there is no linear pattern. As a result, the data does not appear to represent a linear pattern.

As a result, portions (c) through (f) are omitted.