# Mathematical Modeling for the Macintosh

Kepler -- Mars

Batting Averages

## Did you ever

• have to fit your data to a function that was not necessarily a straight line?
• believe that you already knew some/all of the model parameters?
• discover that the residuals were Laplacian, not Gaussian :-(
• wonder if the optimum fit were statistically acceptable?
• want the minimum average deviation instead of least-squares?
• desire robust confidence intervals for the fitted parameters?
• wish that you could make a picture of the result (see Example above) with one keystroke?
• need to find the distribution that best described a set of random variates?
•    or prove that they were truly Gaussian? Uniform? Poisson? ...
• think that a combination of two distributions might be the real answer?
• try to find the formula for the mean, variance, mode, etc., of some density function?
• require millions of variates from a specified distribution?
• give up on any of these and settle for second-best?
Well, now you don't have to.

Regress+ ("Regress_plus") can do all of that and more!
It sets a new standard -- unmatched in power, flexibility, and user-friendliness.

View an introductory Tutorial (271 K), on modeling in general, or download (1.4 MB) the complete, free package (stuffed and binhexed):

Note: You might need the latest Stuffit Expander® freeware to extract Regress+.

## Regress+ (2.5.3) Features

### General

1. Simple (univariate) mathematical modeling
2. Data:
-- deterministic (regression)
-- stochastic (random variates)
3. Up to 2,147,483,647 points (minimum 7)
4. Robust goodness-of-fit testing
5. Bootstrap confidence intervals (90, 95, and 99 percent) for
-- parameters
-- stochastic-model goodness-of-fit metrics
6. Bootstrap methodology (where appropriate):
-- BCa technique (state-of-the-art)
-- percentile technique
-- tunable precision
7. Optional "freezing" of initial estimate(s) for any parameter(s)
8. Choice of optimization criterion
9. No hidden assumptions anywhere:
-- no approximations, apart from those common to sampling and bootstrapping generally
-- no data transformations of any kind
10. "Smart" dialogs to run unattended and/or in the background
11. Textfile input (may contain unlimited comments)
12. Both text and graphical output
13. One keystroke makes a plot (may be saved as a PICT)
14. Extensive documentation (in PDF):
-- Tutorial (50 pp.)
-- Users' Guide (36 pp.)
-- Technical Details and References (8 pp.)
-- Appendix A: A Compendium of Common Probability Distributions (120 pp., separate volume)
-- Appendix B: Error Messages (4 pp.)
15. Lots of sample datafiles

### Deterministic Modeling

1. Models: y = f(x), with 1 to 10 parameters
-- 22 Built-in families of models
-- Gaussian-Lorentzian model for spectral peaks (see Example #5)
-- "User-defined" model
2. Special Simulated Annealing mode to help find initial parameter estimates
3. Optimization criteria:
-- Least-squares
-- Minimum average deviation
4. [Optional] Weights (for the dependent variable, y)
5. [Optional] Listing of fitted data and residuals

### Stochastic Modeling

1. 56 Built-in distributions:
-- 30 Continuous
-- 17 Continuous binary mixtures
-- 5 Discrete
-- 4 Discrete binary mixtures
2. Optimization criteria:
-- Maximum-likelihood (all)
-- Minimum Kolmogorov-Smirnov statistic (continuous variates)
-- Minimum Chi-square (discrete variates)
3. [Optional] Discrete input may be grouped
4. [Optional] Creation of samples of random variates (textfiles, see Example #10)

### Platform Requirements

1. Regress+ 2.5 runs on any PPC Macintosh under either
OS X
or
OS 9 plus CarbonLib (1.4 or greater)
2. It will also run on any Intel Mac provided that Rosetta is installed. Starting with OS 10.6 (Snow Leopard), this is an Optional install that must be done manually. [See Coming Attractions, below.]
3. For older platforms, Regress+ 2.3.1 (1.5 Meg download) is still available.

### Coming Attractions

• Regress+ 2.7 is under development for Snow Leopard and above. It has some new features and is much, much faster.
• It will also be accompanied by a new, improved Compendium.