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Discussion: All Topics in Algebra II
Topic: Curve of Best Fit for Car's Skidding Distance


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Subject:   RE: Curve of Best Fit for Car's Skidding Distance
Author: Jesdisciple
Date: Jan 9 2008
On Jan  9 2008, Craig wrote:
> I have read some of the posts for this message--some give power
> function regressions, one mentioned an exponential regression,
> another says "the solutions is" and gives a quadratic function.
Yes, that was my post.  I'm a programmer in college, so I have no authority to
speak of, but "I'm very confident that [Y=X^2/21 is] the original function."
This is the first function I found that satisfies all the data (after rounding
to the nearest whole number), and the first that uses only integers as
constants.

> I believe, from a physics standpoint, that Newton would agree with a
> quadratic function.  However, what is the source of the data?  Is it
> actual measurements, or was it generated by some formula?  (my
> guess: it was generated by a formula based on regressing on real
> data, but I have no way of knowing).  
I have no idea how the original data was generated; the Texas Department of
Public Safety published it in the Texas Drivers Handbook.  This is why I
consider Y=X^2/21 more reliable for its exclusive use of whole constants,
because I think a government agency would prefer them for the simple purpose of
giving drivers an idea of how far inertia will carry them despite brakes.

> From a statistical standpoint, the small number of data points given
> would not rule out any of the options presented, and indeed, a few
> others might work, as well.  A glance at the residual plot for y =
> x^2 / 21 is less than ideal, even though the maximum absolute error
> is less than 0.5. From a technology standpoint, I saw mention of a
> graphing calculator (TI-89, but most have regression capability
> these days) and a Shodor applet.  Many spreadsheets also have
> regression capabilities; Excel, for instance, allows a power
> regression but also allows a forced intercept of 0 for some (such as
> polynomial).
Yes, the Shodor applet at
http://www.shodor.org/interactivate/activities/flydata/index.html was the tool I
used to find the function.  I supplied the regression (if it's correctly called
so) by changing the function until it fit.

> I like this data set, and it can engender good conversation in my
> Statistics class (next year, when we do the regressions unit, or
> later this year as we review for the AP exam).  So whether your
> posting to Math Tools was intentional or mistaken, I appreciate it!
Then I guess I'll give you the rest of the data given in the same table.  (The
decimals shown here are rounded in the book.)  I hope the tab characters
maintain their width as shown in this text area.

APPROXIMATE STOPPING DISTANCES
It takes the average person 1-1/2 seconds to think, react and apply the
brakes.  The following table shows how far you travel in that 1-1/2 seconds,
plus how many feet you travel while skidding to a stop.

MPH Time (Seconds) to Stop
Thinking Skidding Total
20 44 19.05 63.05
30 66 42.86 108.86
40 88 76.19 164.19
50 110 119.05 229.05
60 132 171.43 303.43
70 154 233.33 387.33

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