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	70
y	40	35	30	26	16

(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?

moderate and negative

low and positive    

low and negative

moderate and positive

strong and positive

strong and negative

(c) Use a calculator to verify that Σx = 132, Σx² = 6552, Σy = 147, Σy² = 4657, and Σxy = 2897. 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

(a)

(b)

(c)

The provided data are shown in the table below

X	Y
3	40
7	35
15	30
37	26
70	16

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	3	40	120	9	1600
	7	35	245	49	1225
	15	30	450	225	900
	37	26	962	1369	676
	70	16	1120	4900	256
Sum =	132	147	2897	6552	4657

The correlation coefficient r is computed using the following expression:

Therefore, based on this information, the sample correlation coefficient is computed as follows

Given our value of r, y should tend to decrease as x increases.

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