Part Five

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Part Five

• Curve Fitting

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Motivation
In all practical engineering cases, the sampling
data are acquired at discrete points.
sampling points
interpolation points
That means the function values at points other
than these sampling points are undefined but
they are wanted in many applications.
Curve fitting tries to fit a continuous curve
through the sampling data that can then define
the function value at any point by interpolation.
x
In many cases, it is not required to find a
curve that fit exactly every sampling point
instead a curve (e.g. the blue line) that shows
the trend of the function is wanted. This is
called regression.
Example how to prove g 9.8 m/s2 ?
x
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Noncomputer Methods for Curve Fitting
Visually sketch a line that conforms to the
data (inaccurate)
Connect the data points consecutively by lines
segments (significant errors if the data are not
evenly spaced or the underlying relationship is
highly curvilinear)
Connect the data points consecutively by simple
curves (too tedious and difficult to do manually)
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Simple Statistics
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The Normal Distribution
normal distribution
histogram
In most engineering applications, the sampling
data set conforms to the normal distribution if
the size of the data set is sufficiently
large. For the normal distribution, the range
defined by and will
encompass approximately 68 percent of the total
measurement. Similarly, the range between
and will encompass approximately 95.
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Overall Structure