#14

Health Insurance: Administrative Cost The following data are based on information from Domestic Affairs. 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 35 75

y 40 35 30 25 18

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

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

(c) Use a calculator to verify that =135, 2=7133, =148, 2=4674,=3040 Compute r. As x increases from 3 to 75, does the value r imply that y should tend to increase or decrease?? Explain.

#16

Geology: Earthquakes Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale) and let y be the depth (in kilometers) of the quake below the surface at the epicenter. The

following information was taken from the National Earthquake Information Service of the U.S. Geology Survey.

x 2.9 4.2 3.3 4.5 2.6 3.2 3.4

y 5.0 10.0 11.2 10.0 7.9 3.9 5.5

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

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

(c) Use a calculator to verify that =24.1, 2=85.75, =53.5, 2=458.31,=190.18. . Compute r, as x increases does the value r imply that y should tend to increase or decrease?? Explain.

Section 9.2

#10

Basketball: Fouls It is thought that basketball teams that make too many fouls in a game tend to lose the game even is they otherwise play well. Let x be the number of fouls that were more than (i.e., over and above) the number of fouls made by the opposing team. Let y be the percentage of times the team with the larger number of fouls won the game.

x 0 2 5 6

y 50 45 33 26

(a) Draw a scatter diagram displaying the data.

(b) Verify the given =13, =154, 2=65, 2=6290, =411, 0.988

(c) Find x, y, a, and b. Then find the equation of the least-squares line =a+bx.

(d) Graph the least-squares line on your scatter diagram. Be sure to use the point as (,) as one of the points on the line.

(e) Find the value of the coefficient of determination r2 . What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?

(f) If a team had x = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y?

#16

Research: Patents The following data are based on information from the Harvard Business Review. Let x be the number different research programs, and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their research programs:

x 10 12 14 16 18 20

y 1.8 1.7 1.5 1.4 1.0 0.7

(a) Draw a scatter diagram displaying the data.

(b) Verify the given =90, =8.1, 2=1420, y2=11.83, =113.8, 0.973

(c) Find x,y,a and b. Then find the equation of the least-squares line. y=a+bx.

(d) Graph the least-squares line on your scatter diagram. Be sure to use the point as (,) one of the points on the line.

(e) Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?

(f) Suppose a pharmaceutical company has 15 different research programs, what does the least-squares equation forecast for y = mean number of patents per program?