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	27	16

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

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

strong and negativelow and positive    moderate and negativelow and negativemoderate and positivestrong and positive

(c) Use a calculator to verify that Σx = 132, Σx² = 6552, Σy = 148, Σy² = 4710, and Σxy = 2934. 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)

...........

correlation is :

strong and negative

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X	Y	XY	X²	Y²
3	40	120	9	1600
7	35	245	49	1225
15	30	450	225	900
37	27	999	1369	729
70	16	1120	4900	256

	X	Y	XY	X²	Y²
total sum	132.000	148.000	2934.00	6552.000	4710
mean	26.4000	29.6000

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correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.968

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

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