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	71
y	40	35	30	26	17

(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?

low and positivelow and negative    moderate and positivestrong and negativemoderate and negativestrong and positive

(c) Use a calculator to verify that Σx = 132, Σx² = 6620, Σy = 148, Σy² = 4690, and Σxy = 2958. 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, 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, we cannot draw any conclusions for the behavior of y as x increases.

Answer 1

ans a ) using minitab>Graph>scatterplot

we have

b ) the correlation is strong and positive.

c )

x	y	x2	y2	xy
3	40	9	1600	120
7	35	49	1225	245
15	30	225	900	450
36	26	1296	676	936
71	17	5041	289	1207
132	148	6620	4690	2958

Σx = 132, Σx² = 6620, Σy = 148, Σy² = 4690, and Σxy = 2958.

using minitab>stat>bbasic stat>correlation

Correlation: x, y

Pearson correlation of x and y = -0.964
P-Value = 0.008

r = -0.964

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