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	28	16

(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 positivestrong and negativemoderate and negative

(c) Use a calculator to verify that Σx = 134, Σx² = 6908, Σy = 149, Σy² = 4765, and Σxy = 2991. 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, we cannot draw any conclusions for the behavior of y 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 remain constant as x increases.

Answer 1

(a)

From above scatter plot, we see that x and y are linearly related.

Option: Line.

b. We observed from scatter plot that as x increases y decreases. Hence x and y are strong negatively correlated.

Option: strong negative.

c.

R code:

x=c(3,7,15,36,73)
y=c(40,35,30,28,16)
plot(x,y)#(a)
#(c)
sum(x)
sum(x^2)
sum(y)
sum(y^2)
sum(x*y)
Sxx=sum(x^2)-(sum(x))^2/5
Syy=sum(y^2)-(sum(y))^2/5
Sxy=sum(x*y)-(sum(x)*sum(y))/5
Sxx
Syy
Sxy
r=Sxy/sqrt(Sxx*Syy)
round(r,3)

Value of r=-0.966 which indicates strong negative correlation hence

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