Use these data on world records for the 1-mile run to answer the questions below. Times are in minutes and seconds.
Year ....................................Runner Time
1915 .................. Norman Taber, U.S. 4:12.6
1923 ................ Paavo Nurmi, Finland 4:10.4
1937 ............ Sydney Wooderson, U.K. 4:06.4
1942 .............. Gunder Haegg, Sweden 4:06.2
1945 .............. Gunder Haegg, Sweden 4:01.4
1958 ................ Herb Elliott, Australia 3:54.5
1967 ........................ Jim Ryun, U.S. 3:51.1
1979 .................. Sebastian Coe, U.K. 3:49.0
1985 .................... Steve Cram, U.K. 3:46.31
1993 ................ Noureddine Morceli, Algeria
a. Let x represent the year, and let y represent the time in seconds. What is the equation of the median-median line?
b. What is the real-world meaning of the slope?
c. Use the equation to interpolate and predict what new record might have been set in 1954. How does this compare with Roger Bannister's actual 1954 record of 3:59.4?
d. Use the equation to extrapolate and predict what new record might have been set in 1875. How does this compare with Walter Slade's 1875 world record of 4:24.5?
e. Describe some problems you might have with the meaning of 997.12 as a y-intercept.
f. Has a new world record been set since 1993? Find more recent information on this subject and compare it with the predictions of your model.