Q.4.160 - Elementary Statistics

Question

PCBs and Pelicans. The data on shell thickness and concentration of PCBs for $60$ Anacapa pelican eggs from Exercise 4.76 are on the WeissStats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of r in terms of the linear relationship between the two variables in question.

Step-by-Step Solution

Answer

a). As a data descriptive metric, the linear correlation coefficient was ruled out.

b). The equation does not include the linear correlation coefficient.

c). We're stumped as to what the linear correlation coefficient actually signifies.

Part (a) Step 1: Given Information

The table of data of average high and low temperatures in January for a random sample of $50$ cities.

Part (a) Step 2: Explanation

For sixty Anacapa pelican eggs, draw a scatter plot of shell thickness and PCB content.

The scatter plot shows that the data points are distributed non-linearly.

As a result, we determined that the linear correlation coefficient is not a data descriptive metric. As a result, the remaining sections b and c have been omitted.

Part (b) Step 1: Given Information

The table of data of average high and low temperatures in January for a random sample of $50$ cities.

Part (b) Step 2: Explanation

Because the linear correlation coefficient is not a descriptive measure of the data, we opted to utilise it in part a. As a result, the linear correlation coefficient is omitted from the equation.

Part (c) Step 1: Given Information

The table of data of average high and low temperatures in January for a random sample of $50$ cities.

Part (c) Step 2: Explanation

Because the linear correlation coefficient is not a descriptive measure of the data, we chose to use it in part a.

As a result, the linear correlation coefficient is ignored, and the linear correlation coefficient is meaningless.