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	33	72
y	40	35	30	26	16

(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?

moderate and positive

moderate and negative   

low and positive

strong and negative

low and negative

strong and positive

(c) Use a calculator to verify that Σx = 130, Σx² = 6556, Σy = 147, Σy² = 4657, and Σxy = 2825. 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

a) The scatterplot will be

b) Since the scatterplot suggest a downward trend and a approximately staraight lime hence the conclusion is

strong and negative

c) Using Σx = 130, Σx² = 6556, Σy = 147, Σy² = 4657, and Σxy = 2825.

X Values
∑ = 130
Mean = 26
∑(X - M_x)² = SS_x = 3176

Y Values
∑ = 147
Mean = 29.4
∑(Y - M_y)² = SS_y = 335.2

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = -997

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -997 / √((3176)(335.2)) = -0.966

Therefore,

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