1.3 Olympic records The following data give the best foot race running times recorded in the modern Olympic Games up to 1984, taken from the 1985 World Almanac. Men Women Distance(m) Time(s) Year Time(s) Year 100 9.9 1968 11.0 1984 200 19.8 1984 21.8 1984 400 43.8 1968 48.8 1984 800 103.0 1984 113.5 1980 1500 212.5 1984 236.6 1980 3000 516.0 1984 5000 785.6 1984 10000 1658.4 1972 42195 7761.0 1984 8692.0 1984 A computer is not required for this problem. 1.3.1 Draw a scatter plot of time versus distance for all the data, using a different symbol for men's times and for women's times. Given such disparate values for both time and distance, you will quickly discover that this display is both hard to draw and to interpret. As an alternative, try plotting transformations of time and distance, perhaps log(time) versus log(distance), or speed = distance/time versus distance or log(distance). 1.3.2 Perform relevant calculations that will help to summarize the relationship apparent in these data. You will probably want to do separate analyses for men and for women. 1.3.3 Are F-tests and t-tests relevant in this problem? Why or why not? (Hint: What is random in these data?) If you prefer to use a computer.... Format of data in computer file: Gender 0 = Men 1 = Women Distance In Meters Time In Seconds Year Year record established Source: Weisberg, S. Applied Linear Regression, 2nd Edn. Wiley, New York, 1985.