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\markright{{\bf Math 331, Spring 2006}}
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{\Large MAT 331, Spring 2006}\\[\baselineskip]
{\Large\bf Project 1: Fitting a line to data}\\[.25\baselineskip]

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In this project, you are to fit a line to some data in three different
ways.  First, by using the ``usual'' least squares method, which
minimizes the {\em sums of the squares of the vertical distances } between
the data and the line.  Then, find the line given by assuming that the
$x$ variable may contain the errors, and minimizing the sums of
squares of the {\em horizontal distances}.  Finally, you are to find the
line that minimizes the sum of the {\em absolute
distances } from the points to the line.
You should, of course,
also have Maple plot the three lines you find along with the data points.


Your project should be written as a paper which explains clearly each
step you take and why.  In particular, you {\em must} give a careful
derivation of the functions you minimize--- you cannot merely quote
the formula for the distance from a point to a line. You can use built-in Maple commands to check your
results, but you have to perform step by step calculations. You may, of
course, assume that the formula for the distance between two points in
the plane is known to the reader.  Your paper should be written so
that someone who has a good working knowledge of mathematics but has
never taken this class will understand what you are doing and why.

You should use Maple (or any another appropriate program of your preference) to do the actual computations.  
 {\em Do not} include false starts,
mistakes, or irrelevant calculations in your finished product.  Pay
attention to spelling, grammar, and sentence structure. \textbf{The expository
part of this project counts as much as the actual calculations}, and
should not be ignored.

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You will find a file containing the data points at

\centerline{{\tt http://www.math.sunysb.edu/~moira/sp06/projects/project1data/yourFirstName.txt},}

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where {\it yourFirstName} is the your first name (!).  Use
Maple's {\tt read} command to load this data.


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