Movies A mathematician exploring the relationship between

Chapter , Problem 66A

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Problem 66A

Movies A mathematician exploring the relationship between ratings of movies, their year of release, and their length discovered a paradox. Rather than list the data set of 100 movies in the original research, we have created a sample of size 10 that captures the properties of the original dataset. In the following table, the rating is a score from 1 to 10, and the length is in minutes. Source: Journal of Statistics Education.

Year	Rating	Length
2001	10	120
2003	5	85
2004	3	100
2004	6	105
2005	4	110
2005	8	115
2006	6	135
2007	2	105
2007	5	125
2008	6	130

a. Find the correlation coefficient between the years since 2000 and the length.

b. Find the correlation coefficient between the length and the rating.

c. Given that you found a positive correlation between the year and the length in part a, and a positive correlation between the length and the rating in part b, what would you expect about the correlation between the year and the rating? Calculate this correlation. Are you surprised?

d. Discuss the paradoxical result in part c. Write out in words what each correlation tells you. Try to explain what is happening. You may want to look at a scatterplot between the year and the rating, and consider which points on the scatterplot represent movies of length no more than 110 minutes, and which represent movies of length 115 minutes or more.