# Curve Fitting and Regression
Curve fitting is finding a curve which matches
a series of data points and possibly other
constraints. It is most often used by scientists
and engineers to visualize and plot the curve
that best describes the shape and behavior
of their data.
Regression
procedures find an association between independent
and dependent variables that, when graphed,
produces a straight line, plane or curve.
The
independent variables are the known, or predictor,
variables. These are most often your X-axis
values. The dependent variables are also
called as response variables and are most
often your Y-axis values.
Regression
finds the equation that most closely describes,
or fits, the actual data, using the values
of one or more independent variables to predict
the value of a dependent variable. The resulting
equation can then be plotted over the original
data to produce a curve that fits the data.
Dynamic Curve Fitting
Nonlinear curve fitting is an iterative process
that may converge to find a best possible
solution. It begins with a guess at the parameters,
checks to see how well the equation fits,
the continues to make better guesses until
the differences between the residual sum
of squares no longer decreases significantly.
For complicated curve fitting problems, use
SigmaPlot?s Dynamic Fit Wizard to find the
best solution.
The
Dynamic Fit Wizard automates the search for
initial parameter values that lead to convergence
to the best possible solution.
Like
the Regression Wizard, the Dynamic Fit Wizard
is a step-by-step guide through the curve
fitting procedures, but with an additional
panel in which you set the search options
(in the figure below).
Please note that
the Dynamic Fit Wizard is especially useful
for more difficult curve fitting problems
with three or more parameters and possibly
a large amount of variability in the data
points. For linear regressions or less difficult
problems, such as simple exponential two
parameter fits, the Dynamic Fit Wizard is
overkill and you should be using the Regression
Wizard.
Remove
measurement noise
Fill
in missing data points, such as when one
or more measurements are missing or improperly
recorded
Interpolate,
which is estimating data between data points,
such as if the time between measurements
is not small enough
Extrapolate,
which is estimating data beyond data points,
such as looking for data values before or
after a measurement
Differentiate
digital data, such as finding the derivative
of the data points by modeling the discrete
data with a polynomial and differentiating
the resulting polynomial equation
Integrate
digital data, such as finding the area under
a curve when you have only the discrete points
of the curve
Obtain
the trajectory of an object based on discrete
measurements of its velocity, which is the
first derivative, or acceleration, which
is the second derivative
**Visit the links
below for more technical information and
examples of how curve fitting is easy using
SigmaPlot. **
Case
Study: Curve Fitting using SigmaPlot
Global
Curve Fit of Enzyme Kinetics
Global
Analysis of Concentration-Response Curves
Using
Global Curve Fitting to Determine Dose
Response Parallelism
Global
Curve Fitting for Ka and Kd from Sedimentation |