A statistician is curious if the gold medal time for the women's 100 - meter freestyle depends upon the year that the Summer Olympics took place. A sample of every other Summer Olympics for the...

 A statistician is curious if the gold medal time for the women's 100 - meter freestyle depends upon the year that the Summer Olympics took place.  A sample of every other Summer Olympics for the women's 100-meter freestyle produced the following data:

Year

1912

1924

1932

1952

1960

1968

1976

1984

1992

2000

2008

Time (in seconds)

82.2

72.4

66.8

66.8

61.2

60.0

55.65

55.92

54.64

53.8

53.1

a)   Identify a lurking variable for this situation.

b)  Find the equation of the least-squares line. Identify and interpret the slope and the y - intercept.

c) Find the correlation coefficient and interpret and Determine if there is a significant correlation between the gold medal time and the year of the Summer Olympics. Explain your reasoning.