Would you be surprised if the following data sets exhibited a regression to the mean? Would you expect them to exhibit this phenomenon? Explain your answers. (a) You go to 10 different restaurants...

Would you be surprised if the following data sets exhibited a regression to the mean? Would you expect them to exhibit this phenomenon? Explain your answers.

(a) You go to 10 different restaurants that you know nothing about in advance. You eat a meal in each one and give a numerical ranking—anywhere from 0 to 100—to the quality of the meal. You then return to each of these restaurants and again give a ranking to the meal. The data consist of the two scores of each of the 10 restaurants.

(b) At the beginning of an hour, 12 individuals check their pulse rates to determine the number of heartbeats per minute. Call these the x values. After 1 hour, they repeat this to obtain the y values.

(c) The set considers paired data concerning different mutual funds. For each mutual fund, the x variable is the 1995 ranking of the fund, and the corresponding y variable is the 1996 ranking.

(d) The data consist of the paired scores of 20 first-year preschoolers, with the first value in the pair being the student’s test score on an IQ examination given to all entering students and the second value being the same student’s score on an IQ test given at the end of the first month in school.