2. A few years ago some Exercise Physiologists at UCLA published a paper in NATURE wherein they predicted that by the year 2004, the women's world record in the marathon would be faster than the men's record. The mechanism for the improvement in performance is thought to be the improvement of training methods and the expansion of the talent pool. But the data was examined only to describe the trend, not to explain it.

This problem examines the winning Olympic times for the 100 m races for both Men and Women. As the years have gone by, the times have improved for both Men and Women. Below we present a table with the data for the winning times (in seconds)


Year

Men's 100

time

Women's 100

time

1896

Burke

12.0

1900

Jarvis

11.0

1904

Hahn

11.0

1906

Hahn

11.2

1908

Walker

10.8

1912

Craig

10.8

1920

Paddock

10.8

1924

Abrahams

10.6

1928

Williams

10.8

Robinson

12.2

1932

Tolan

10.3

Walasiewicz

11.9

1936

Owens

10.3

Stephens

11.5

1948

Dillard

10.3

Blankers-Koen

11.9

1952

Remigino

10.4

Jackson

11.5

1956

Morrow

10.5

Cuthbert

11.5

1960

Har

10.2

Rudolph

11.0

1964

Hayes

10.0

Tyus

11.4

1968

Hines

9.95

Tyus

11.0

1972

Borsov

10.14

Stecher

11.07

1976

Crawford

10.06

Richter

11.08

1980

Wells

10.25

Kondratyeva

11.06

1984

Lewis

9.99

Ashford

10.97

1988

Lewis

9.92

Joyner

10.54

1992

Christie

9.96

Devers

10.82

1996

Bailey

9.84

Devers

10.94

2000

Greene

9.87

Jones

10.75

 

a. Use EXCEL's trendline feature to find the best straight lines (one for Men and one for Women) through the data, where

T = mY + b

is the straight line for the best time (T) as a function of the Olympic year (Y) with EXCEL determining the slope (m) and intercept (b). Write the equations for the best linear models and show (on a single graph) the graphs of the data and linear model for both Men and Women. Be sure to label which lines correspond to the data for the Men and Women.

b. Use the model to determine the predicted year when the best time is 10.0 sec for Men and 11.0 sec for Women, then compare your prediction to the actual data.

c. Use the model to predict the time for the 2000 and 2004 Olympics for both Men and Women in this event. Give the percent error between the actual and predicted value in 2000.

d. According to the model, which Olympics will first see Women outrunning the Men? Give a short discussion on the validity of this prediction and why you think it is true or false. What fundamental premise do you consider to be critical? Can you formulate another model that might be more valid?