Elementary Statistics Module 9 Correlation and Regression

Task: Solve the following

1. How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

x	3	6	12	14	23
y	60	95	140	152	175

Use a calculator to verify that x =58, x² =914, y = 622, y² = 85,954 and xy = 8,583. Computer. (Round your answer to four decimal places.)

2. 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.

x	3.0	3.8	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

Use a calculator to verify that x = 23.8, x² = 83.14, y = 53.5, y² = 458.31 and xy = 186.68. Compute r. (Round your answer to four decimal places.)

3. In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.

x	0.241	0.251	0.286	0.263	0.268	0.339	0.299
y	1.4	3.5	5.5	3.8	3.5	7.3	5.0

Use a calculator to verify that x = 1.947, x² = 0.548, y = 30.0, y² = 149.44 and xy = 8.696.Compute r. (Round your answer to four decimal places.)

4. 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	32	72
y	40	35	30	28	20

Use a calculator to verify that x = 129, x² = 6491, y = 153, y² = 4909, and xy = 3151. Compute r. (Round your answer to four decimal places.) r =

5. Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.

x	12.3	28.2	24.5	14.3	7.5	27.7	16.2	20.1
y	24	72	39	23	15	30	15	25

Use a calculator to verify that x = 150.8, x² = 3241.26, y = 243, y² = 9785 and xy = 5299.0.Compute r. (Round your answer to four decimal places.)