In the first post, we looked at the pattern of bronze medal times in the men’s 200 meter run. By plotting the log time against year, we figured out the general pattern of decrease over years. That’s the first part of the story.
By exploring the residuals from the loess fit, we can learn more. Below I’ve pasted the residual graph — remember that the residuals are expressed in a log (base e) scale.
What do we see in this residual graph?
- Most of the residuals fall between -.01 and +.01. Remember that .01 on the log e scale corresponds to a change of 1%. So most of the times fall within 1% of the fitted curve.
- I see three outliers — there are three residuals smaller than -0.01 — they appear to correspond to the years 1912, 1968, and 1996.
Are there any special circumstances in the years 1912, 1968, and 1996 that would explain these unusually low bronze medal running times? Actually, 1968 was a special year in that the Olympics were held in Mexico City which has a high altitude. A venue at a high altitude means perhaps less air resistance that could contribute to faster running times. One of the most remarkable Olympics records is Bob Beamon’s amazing long jump which occurred during these same Olympics.