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Sample submitted solutions:
(No submitted solutions
got credit for this problem. Here are the
expected solutions.)
1. Based on the graph what do you think
the women's winning time should have been
this year at the Sidney 2000 Olympic Games?
Fitting a line, the answer should be somewhere
in the range of 115 to 130 minutes. If the
students use a linear regression, they will
come up with y = -1.6x +3236.5, and get
a time of about 37 minutes! If students
look at the graph and notice that the times
have flattened out considerably in the past
few races, they may answer somewhere slightly
under 140 minutes.... It seems that we have
hit a "wall" in terms of our ability
to continue to get faster.
2. Predict when women will run the marathon
as fast as men.
Using the fitted line, this would happen
somewhere between 2005 and 2020. If you
look at the flattening-out theory, though,
it seems as if it would be further out in
the future. I'm not even sure we can predict
that, because when I flatten out the women's
line, the two lines look close to parallel.
3. What do you think the women's world
record marathon time was in 1926?
In 1926, the women's record time was 3 hours,
40 minutes, 22 seconds, which is 220.36
minutes. Using a fitted line, an estimate
of 280 minutes is not unreasonable.
4. Using lines to model data can be
a powerful tool, but we have to be careful
to be aware of their limitations. What real-world
limitations do you think a line has in modeling
the data?
There are many. The most glaring is that
data can look linear in a small window.
But when you look at the big picture, other
considerations creep in. People have physical
limitations, and at some point, they won't
be able to run much faster than the previous
records, and a line won't fit the data.
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