Being a Competitive Female Swimmer, You Wonder If Women Will $\widehat{\text { TFoverM }}$

question 57

Essay

Being a competitive female swimmer, you wonder if women will ever be able to beat the time of the male gold medal winner. To investigate this question, you collect data for the Olympic Games since 1910. At first you consider including various distances, a binary variable for Mark Spitz, and another binary variable for the arrival and presence of East German female swimmers, but in the end decide on a simple linear regression. Your dependent variable is the ratio of the fastest women's time to the fastest men's time in the 100 m backstroke, and the explanatory variable is the year of the Olympics. The regression result is as follows, $\widehat{\text { TFoverM }}$ = 4.42 - 0.0017 × Olympics,
where TFoverM is the relative time of the gold medal winner, and Olympics is the year of the Olympic Games. What is your prediction when females will catch up to men in this discipline? Does this sound plausible? What other functional form might you want to consider?

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