Curve-Fitting Q&A

How can I view the built-in equations?

The Help menu has a List Equations option that lists every built-in equation within the product. These are numbered and grouped by type.

There are help items associated with the various linear equation types and for each non-linear equation.

The product ships with Adobe Acrobat PDF files. Included is lineareq.pdf, a document listing all linear equations, and nonlineq.pdf, a document detailing each non-linear equation.

The Edit Custom Equation Set option offers the means to customize an equation set from the full set of built-in equations.

How do I decide which equations to fit?

TableCurve 2D assumes that it is not often easy to know which equations may be appropriate to a given data set. In the beginning, until you gain certain experience with the product, it is a simple matter to fit All Equations to the data.

All of the other fitting options for built-in equations represent conveniences to save fitting time. Since the Review’s equation list can be filtered and sorted in a number of ways after the fact, it is not necessary to limit the list of candidate equations by restricting the set being fitted.

Where can I find an overview of the built-in fitting options?

All Equations: fits all 3667 built-in equations. This is the recommended option until you become more familiar with the equations.

Linear Equations: all 3491 linear equations; omits the 176 built-in non-linear equations. This is often a good option when searching for an approximating function.

Simple Equations: fits all 2-parameter linear equations as well as non-linear power and exponential functions.

Robust Straight Line: fits a simple straight line equation by least-squares and three robust non-linear procedures. This is generally used when outliers are present or suspected and only a straight line fit is desired.

Poly/Ratl Equations: All polynomials and rationals, including high-precision, Chebyshev, and Fourier series.

Peak Functions: All built-in non-linear peak functions (up to 74 depending on intercept options).

Transition Functions: All built-in non-linear transition functions (up to 29 depending on intercept options).

Kinetic Equations: All built-in non-linear kinetic models (up to 58 depending on intercept options).

Waveform Functions: sine and sine-squared equations.

What is a ‘high-precision’ polynomial or rational equation?

For Intel coprocessor precision, it is wise to limit polynomials to order 10 and rationals to orders 5/5. TableCurve 2D offers a special class of polynomials through 20th order, and rationals through 10/10th order. In order to produce effective fits of these higher order models, TableCurve 2D performs all fit computations as well as the confidence/prediction intervals evaluation using an entirely separate 38-digit high-precision 32-bit assembly language math emulator. Function evaluation is with the Intel FPU.

If you are fitting full precision generated data, these equations have the potential for producing fractional residuals near the 1E-18 limit. While the high-precision software floating point is exceptionally fast, it is still a matter of software emulation, therefore, the fitting of these equations may appear to be considerably slower than those fitted using the Intel floating point unit. This may be particularly evident when confidence or prediction intervals are being graphed.

What is a ‘Chebyshev converted’ polynomial or rational equation?

A Chebyshev series polynomial can be reduced to a standard polynomial, one that can be evaluated in about half the time. TableCurve 2D includes this option for those instances where the precision losses certain to be a part of this conversion can be tolerated. The Precision Summary is used to ascertain the extent of these losses.

How do I set the curve-fitting preferences?

The Curve-Fit Preferences option in the Process menu is used for setting the preferences for all fitting options except the Peak Functions, Transition Functions, and Kinetic Equations which have their own separate configuration.

Why are there different matrix methods for linear fitting?

All linear fits produce an exact least-squares solution only with unlimited precision. In the finite precision world of digital computing, each procedure has its own strengths and weaknesses. In general, there are two major types of algorithms: SVD and the more conventional procedures. Unless you have specific experience with matrix methods, the default Fast Std is recommended.

When should I use robust fitting?

There are three robust procedures available for non-linear fitting. Robust fitting is of value when there is a large dynamic range on the Y-variable (spanning several orders of magnitude or more), and the lowest Y value points are not being sufficiently fitted. It is also of use in managing outliers which adversely affect the fit. The Lorentzian minimization is highly effective and the fastest converging of the robust algorithms. Unless one of these factors is present, least-squares should generally be used.

How do I create a custom equation set?

For a set containing only the equations you want to have fitted, use the Process menu’s Edit Custom Equation Set option to configure the desired equations.

You can use the Curve-Fit Custom Equation Set option to fit this set at anytime.

As soon as I load a data set, some kind of fitting seems to be taking place. What is going on?

On a multithreading operating system, it is possible for TableCurve 2D to perform two quite independent operations at the same time.

The Background Thread Fitting option is used to set up a certain intelligence whereby TableCurve 2D can begin fitting the data the moment it has been imported. This can be used to eliminate a good deal of waiting if you generally fit a specific equation set option.

The light bulb icon is lit when background thread fitting is underway.

Is this the same thing as the ‘Fit in Background’ option that appears in the curve-fit progress dialog?

No. The Fit in Background button merely minimizes TableCurve 2D while a fit is in progress so that you can work in another application.