Question

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	37	72
y	40	35	30	28	17

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

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

low and positivemoderate and negative    strong and positivestrong and negativelow and negativemoderate and positive

(c) Use a calculator to verify that Σx = 134, Σx² = 6836, Σy = 150, Σy² = 4798, and Σxy = 3075. Compute r. (Round your answer to three decimal places.)
r =

As x increases, does the value of r imply that y should tend to increase or decrease? Explain.

Given our value of r, y should tend to decrease as x increases.Given our value of r, we cannot draw any conclusions for the behavior of y as x increases.    Given our value of r, y should tend to increase as x increases.Given our value of r, y should tend to remain constant as x increases.

Answer 1

Correlation

We solve the problem in Excel.

a. We go to Insert option and select the Scatter plot to get the following output:

b. From the scatter plot we can say that the Correlation is strong and negative.

c. We calculate the values in Excel and get the following table:

Using CORREL function we get the value of Correlation coefficient, r as -0.961.

Since the Correlation is strongly negative here, there is a reverse relationship between X and Y. In fact Correlation coefficient lies between -1 to +1 where -1 indicates perfect negative linear relationship. So given the value of r, y should tend to decrease as x increases.