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	31	75
y	40	35	30	26	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 positive strong and negative     strong and positive low and negative moderate and negative moderate and positive

(c) Use a calculator to verify that Σx = 131, Σx² = 6869, Σy = 148, Σy² = 4690, and Σxy = 2896. 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 remain constant as x increases. Given our value of r, y should tend to decrease as x increases.     Given our value of r, y should tend to increase as x increases. Given our value of r, we cannot draw any conclusions for the behavior of y as x increases.

Answer 1

a) Scatter plot:

b) Correlation is strong and negative.

c) table:

X	Y	XY	X²	Y²
3	40	120	9	1600
7	35	245	49	1225
15	30	450	225	900
31	26	806	961	676
75	17	1275	5625	289

Sample size, n =	5
Ʃ x =	131
Ʃ y =	148
Ʃ xy =	2896
Ʃ x² =	6869
Ʃ y² =	4690

SSxx = Ʃx² - (Ʃx)²/n =	3436.8
SSyy = Ʃy² - (Ʃy)²/n =	309.2
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	-981.6

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = -0.952

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