Chapter 4.1, Problem 14P

Health Insurance:Administrative Cost The following data are based on information from Domestic Affairs. Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.

x	3	7	15	35	75
y	40	35	30	25	18

(a) Make a scatter diagram and draw the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong? positive or negative?

(c) Use a calculator to verify that $\sum x=135,\sum x^2=7133,\sum y=148,\sum y^2=4674,\text{and }\sum xy=3040.$ Compute r. As x increases from 3 to 75, does the value of r imply that y should tend to increase or decrease? Explain.