players in any sport who are having great seasons, turning in performances that are much better than anyone might haveanticipated, often are pictured on the cover of sports illustrated. frequently, their performances then faltersomewhat, leading some athletes to believe in a "sports illustrated jinx." similarly, it is common for phenomenal rookies to have less stellar second seasons, the so-called "sophomore slump." while fans, athletes, and analysts have proposed many theories about what leads to such declines, a statistician might offer a simpler(statistical) explanation. explain.

what would be a better explanation for the decrease in performance of the sports illustrated cover athlete?

a. people on the cover are usually there for outstanding performances. because they are so far from the mean, the performance in the next year is likely to be closer to the mean.
b. the slope of the linear regression, predicting performance from years in the sport, must be negative because an athlete's performance always decreases over time. no matter how well an athlete performed one year, they must perform worse the next year.
c. people on the cover are usually considered the best of theyear, so naturally they reached the maximum level of athletic performance that year and it is impossible to improve upon that.
d. once an athlete has made the cover of sports illustrated, they have reached their ultimate goal as an athlete and lack motivation to try the following year.

I pick the reasoning of option A

Step-by-step explanation:

I like the reasoning given in B, however, there are many cases of Athletes that, after reaching the top, maintain supremacy and improve over the years, adapting to their old age. Usually speed and physical resistance are replaced by technique and experience in the case of the top athletes.

I dont like C and D argument too much because being the best in a sport doesnt mean either that you reach the maximum level possible (in many cases you can keep growing) or that you dont have more motivations. Many athletes are super competitive people and they try to improve themselves all the time to reach, and stay, in the top.

I choose option A as answer because people on the cover doesnt neccesarily mean that they are the absolute best. Their performance was way better than their usual performance, and that may be due to either real skill growth, heavy training or a lucky streak. If it is a lucky streak, it is natural for that player's performance to go down into more terrenal levels for him. On the other hand, If he trained heavily, then he might have big injuries on later seasons and his performance wont be able to keep up for long. Thats why 'surprises' (that also sell better due to be a novelty) tend to go downhill after they reach the cover of sports illustrated.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above