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	70
y	40	35	30	28	17

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

strong and negativestrong and positive     moderate and negativemoderate and positivelow and negativelow and positive

(c) Use a calculator to verify that Σx = 131, Σx² = 6479, Σy = 150, Σy² = 4798, and Σxy = 3013. 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, 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.     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.

Answer 1

Solution :

X	Y	XY	X^2	Y^2
3	40	120	9	1600
7	35	245	49	1225
15	30	450	225	900
36	28	1008	1296	784
70	17	1190	4900	289

n	5
sum(XY)	3013.00
sum(X)	131.00
sum(Y)	150.00
sum(X^2)	6479.00
sum(Y^2)	4798.00
Numerator	-4585.00
Denominator	4764.31
r	-0.9624
r square	0.9261
Xbar(mean)	26.2000
Ybar(mean)	30.0000
SD(X)	24.6852
SD(Y)	7.7201
b	-0.3010
a	37.8855

(b)

strong and negative

(c)

r = -0.962

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