y = −0.0431x + 129.84 where x = Year and y = Winning Time (in seconds)
The slope is -0.0431 and is negative since the winning times are generally decreasing. The slope indicates
that in general, the winning time decreases by 0.0431 second a year, and so the winning time decreases at
an average rate of 4(0.0431) = 0.1724 second each 4-year Olympic interval.
For the 2012 Summer Olympics, substitute x = 2012 to get y = −0.0431(2012) + 129.84 ≈ 43.1 seconds.
The regression line predicts a winning time of 43.1 seconds for the Men’s 400 Meter Dash in the 2012
Summer Olympics in London.
The data consisted of the winning times for the men’s 400m event in the Summer Olympics, for 1948
through 2008. The data exhibit a moderately strong downward linear trend, looking overall at the 60 year
period. The r2 and p-values indicate that a line is a reasonable model for this data, giving me confidence
in the prediction based on the regression line. The r2 value was not near 1.0, however, which means that
predictions are not expected to be extremely accurate.
The regression line predicts a winning time of 43.1 seconds for the 2012 Summer Olympics, which would be
nearly 0.4 second less than the existing Olympic record of 43.49 seconds, quite a feat! Will the regression
line’s prediction be accurate? In the last two decades, there appears to be more of a cyclical (up and
down) trend. Could winning times continue to drop at the same average rate? Extensive searches for
talented potential athletes and improved full-time training methods can lead to decreased winning times,
but ultimately, there will be a physical limit for humans.
Note that there were some unusual data points of 46.7 seconds in 1956 and 43.80 seconds in 1968, which
are far above and far below the regression line. I wondered if these values made the correlation less strong,
but when I investigated this, I found the coefficient of determination is r2 = 0.5351 which is not as strong as
when we considered the time period going back to 1948 (the p-value is 0.01 which is still below the 0.05
threshold). The lower coefficient of determination means that the prediction will not be as good. Also, the
most recent set of 10 winning times do not visually exhibit as strong a linear trend as the set of 16 winning
times dating back to 1948.
I have examined two linear models, using different subsets of the Olympic winning times for the men’s 400
meter dash. The prediction with the strongest coefficient of determination was 43.1 seconds for the 2012
Olympics. I checked on another website (olympic.org) and found that when the race was run in August,
2012, the winning time was 43.94 seconds. This means my estimate was off by 0.84 seconds from the
Does this mean the trend of the last 50 years is finally coming to an end? It will be interesting to compare
these results to the upcoming 2016 results to see what happens!