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<title>2.6 - Exploring Data: Linear Models and Scatter Plots</title>
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<h1>2.6 - Exploring Data: Linear Models and Scatter Plots</h1>
<p>This section ties in heavily with the notes for a <a
href=".
./.
./m170/">statistics class</a>.
In particular, look at the
<a href=".
./.
./.
./ti82/ti-lists.html">Introduction to Statistics and Lists on the
TI82</a> and <a href=".
./.
./.
./ti82/ti-plot3.html">Scatter Plots and Regression
Lines on the
TI82</a>.
With that said, I will try to convey most of that information here,
also.</p>
<p>I have included notes for the TI82, TI83, and TI85 calculators.
I don't
normally do the TI85, but
the statistics mode on it is fairly difficult to grasp.
I do not have notes on how
to use any of the
other calculators, like the Casio or Sharp.
If you would rather see all of the
notes for your
calculator in one location, then see the lecture notes for either the <a
href="models82.html">TI82 / TI83</a> or the <a href="models85.html">TI85</a>.
Everything here is included there, so you only need to print one or the other.</p>
<h3>TI83 Users Only</h3>
<p>There is a correlation coefficient which is mentioned in the book.
By default,
the TI83 does not
give this to you.
You can enable it (you only need to do this once, and then it's
done forever
more until you lose power or reset your calculator) by going [Catalog]
(2<sup>nd</sup> zero).
Then, scroll
down to <strong>DiagnosticOn</strong> (hit D [the calculator is already in
alpha mode, so just press the inverse key] to get close quickly) and press enter
twice until
the calculator says Done.</p>
<h2>Correlation and Regression</h2>
<p>The Linear Correlation Coefficient (r) is a measure of the strength and
direction of a relationship
between two variables.
If the y gets larger when the x gets larger, the
coefficient is positive and
if the y gets smaller when the x gets larger, the coefficient is negative.
If
there is no linear
relationship between the two variables, then the coefficient is zero.
If all the
data exactly lies on
a line, then it is called perfect correlation and the value will either be 1 or -1.
The closer the
value is to 1 or -1, the closer the points are to the line and the stronger the
linear relationship.
The same concept applies for other types of regression (the TI82, TI83, and TI85
will do linear,
logarithmic, exponential, power, quadratic, cubic, and quartic regression).
</p>