Mathematical Modeling for the Macintosh

Examples Equations Kepler -- Mars Daytime Quantum Defects Hale-Bopp CN Spectral Peak Distributions Batting Averages Hyphens Dice Rolls Salaries 10,000 Gammas

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?

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

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

• Primary download site (causaScientia.org)

Note: You will 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

16. 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
17. Special Simulated Annealing mode to help find initial parameter estimates
18. Optimization criteria:
    -- Least-squares
    -- Minimum average deviation
19. [Optional] Weights (for the dependent variable, y)
20. [Optional] Listing of fitted data and residuals

Stochastic Modeling

21. 56 Built-in distributions:
    -- 30 Continuous
    -- 17 Continuous binary mixtures
    -- 5 Discrete
    -- 4 Discrete binary mixtures
22. Optimization criteria:
    -- Maximum-likelihood (all)
    -- Minimum Kolmogorov-Smirnov statistic (continuous variates)
    -- Minimum Chi-square (discrete variates)
23. [Optional] Discrete input may be grouped
24. [Optional] Creation of samples of random variates (textfiles, see Example #10)

Platform Requirements

1. Regress+ runs on any recent Macintosh (G3 or later), PPC or Intel, under either
   OS X
   or
   OS 9 plus CarbonLib (1.4 or greater)
   
2. For older platforms, Regress+ 2.3.1 (1.5 Meg download) is still available.

Coming Attractions

• Regress+ 3.0 is already under development. Check out some of the new features.
• It will be accompanied by a new, improved Compendium.

Who Uses Regress+ ?