Same data, different models.
Which one is the best? And why?

Measuring and modeling by example

- How mathematical functions can be used (and misused) to describe the world

I finished this book 12 April 2024 and I had some preprints made (273 pages full color A4), but World Scientific published it in Jan. 2025, in a smaller format (380 pages, hardcover, ISBN: 978-981-12-9676-5, DOI: 10.1142/13948).

Final book cover:

I am an experimental physicist from Belgium, °1962, working as an independent tutor now, and I wrote this book about measuring, regression analysis and mathematical modeling because I want to share my experience from the last 40 years with anyone who needs it.

I know there are tons of books about this subject, but my focus is quite different. I try to teach the reader:

• The world cannot be described by linear models alone; absolutely not! There is a lot of beautiful other functions available!
• Measurement errors should not be neglected.
• Using common sense can make your measurements more precise.
• Finding a pattern in your data is an art; you shouldn't just crunch the numbers, but first of all try to understand what's behind them.
• The traditional least squares regression method (OLS) is flawed in many situations: it's asymmetrical in x and y. I propose a solution: multidirectional least squares (MDLS), which I implemented in a Windows software program, called FittingKVdm.
• Nonlinear data transformations to linearize models are not a good idea; iterative methods on the raw data are much more universally usable.
• Judging the "goodness-of-fit" or the usability of a model is really a lot more than just calculating r² and p values!
• I analyze many real world examples from all kinds of sciences, from physics to psychology, from biology to economy, from electronics to linguistics. Most of them can be replicated with simple home or classroom experiments or data from public sites. The data files are available.
• To keep it simple, I focus on models with 1 independent variable in this book. That can be difficult enough! I keep the abstract theory to a minimum; high school and college students who had the basics of calculus and statistics should be able to understand everything. But also teachers and researchers will have a benefit from it, I'm sure.

You can order it directly from the publisher: World Scientific, but I also have a few copies of the preprint (nicely printed, no errors that I know of, except a few colons and commas etc.) for 39€ + shipping (e.g.: B, NL, L, D: 10€; other countries 14-40€): mail me!

Author: Koen Van de moortel - info@lerenisplezant.be - +32 9 2277036 or +32 47 7368526

Keywords for the book: linear/nonlinear regression, multidirectional regression, orthogonal regression, least squares, curve fitting, mathematical modeling, weighted regression, data analysis, statistics, Monte Carlo methods, Pearson-r, Kendall-tau, chi squared, correlation, cross-correlation, pattern recognition, heteroskedasticity, simulation, iteration, goodness-of-fit, choosing a model, parameter estimation, parameterization, residuals, mathematical functions (linear, quadratic, cubic, polynomial, power, logistic, exponential, logarithmic, homographic, rational, Gompertz, Weibull, Gauss, Dagum, Lorentz, sine, cosine, tangent, cosh, tanh), distributions, calculus, applied mathematics, transformations, periodicity, growth, decay, calibration, prediction, interpolation, extrapolation, causality, theory testing, problem solving, research methodology, experiment design, error propagation, measurement precision, quantification.

Front cover, table of contents & Intro (12 April 2024, sent to the publisher!).

Back & index.

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BTW: "Leren is plezant" is Flemish for "Learning is pleasant".