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	30	74
y	40	35	30	28	20

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

Submission Data

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

strong and negativelow and positive     low and negativestrong and positivemoderate and negativemoderate and positive

(c) Use a calculator to verify that Σx = 129, Σx² = 6659, Σy = 153, Σy² = 4909, and Σxy = 3135. 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, we cannot draw any conclusions for the behavior of y as x increases.Given our value of r, y should tend to increase as x increases.

Answer 1

a) Take x on the horizontal axis and y on the vertical axis. Plotting the different combinations of(x,y) from the table we will get the scatterplot and the least square regression line(linear line of best fit) is the one that best fits the data here.

b) we can see that as x increases, y decreases, so we have a negative correlation here and it is strong.

c) Sxy = 3135 - 129*153/5 = -812.4

Sxx= 6659- 129^2/5 = 3330.8

Syy= 4909-153^2/5 = 227.2

So, r = -812.4/√3330.8*227.2 = -0.934 (rounded to 3 decimals)

From r we can see that as, x increases y should decrease since r is negative.