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	36	73
y	40	35	30	27	17

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

low and negative

strong and positive   

moderate and negative

low and positive

strong and negative

moderate and positive

(c) Use a calculator to verify that Σx = 134, Σx² = 6908, Σy = 149, Σy² = 4743, and Σxy = 3028. 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 increase as x increases.

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 remain constant as x increases.

Answer 1

X	Y	XY	X^2	Y^2
3	40	120	9	1600
7	35	245	49	1225
15	30	450	225	900
36	27	972	1296	729
73	17	1241	5329	289

n	5
sum(XY)	3028.00
sum(X)	134.00
sum(Y)	149.00
sum(X^2)	6908.00
sum(Y^2)	4743.00
Numerator	-4826.00
Denominator	5010.81
r	-0.9631
r square	0.9276
Xbar(mean)	26.8000
Ybar(mean)	29.8000
SD(X)	25.7558
SD(Y)	7.7820
b	-0.2910
a	37.5989

(b)

strong and negative

(c)

r = -0.963

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