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 72 y 40 35 30 26 17

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

(c) Use a calculator (show buttons on calculator) to verify that Σx = 127, Σx2 = 6367, Σy = 148, Σy2 = 4690, and Σxy = 2819. 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, 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. 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

Using the data:

x = 3 7 15 30 72

y = 40 35 30 26 17

The Scatter-plot is plotted as:

So, from the scatter-plot we can say that :

b) Correlation is strong and negative, because as we can see that the curve is downhill but very much in a linear line.

c) The table calculation is done to confirm the given details and to calculate the correlation coefficient as:

Now the correlation is calculated as:

So, based on the correlation coefficient which is negative but strong we can say that Given our value of r, y should tend to decrease as x increases.