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				<p style="Sous-titre" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Limitations of Linear Correlation and Extrapolation</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">by Paul Lorczak</p>
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					</f> has the potential to be misinterpreted. This example shows the potential for misunderstanding, and the dangers of extrapolation from fitted parameters. Consider the following example. Let z and y be related by the following formula:</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">This is not a linear relationship. However, if we have only data from a small interval, we might compute the correlation coefficient based on an insufficient sampling to see the relationship: </p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">When we plot the points and the line, we get this graph:</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">It seems conclusive that z and fz are linearly correlated over this small range. Once we move to larger values of z, however, the difference between the true functional value and the assumed linear one becomes apparent.</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Here is another set of data with what looks like a linear functional relationship. </p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Again, we compute the intercept and slope of the best-fitting line.</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">When we graph the points, we see that they might be drawn from any number of functions that pass through them. Adequate sampling frequency and range of measurement is critical to draw meaningful conclusions about your data.</p>
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