pca for regression part 1, cases in modeling

A straightforward OLS doesn't seem to produce sensible results, so we use so called orthogonal regression to the problem and obtain a much better result. However, neither OLS nor MA regression applied without regard to the data generation process (DGP) produce unsatisfactory results. I suggest that the regression model works best only when the model specification matches the studied phenomenon. So, I show you how to build a very simple model that produces an amazing fit to a rather complex movement of a paraglider in the air. I still used basic OLS with PCA but with a model that mimics the equations of motion.

I also give an example of a problem in Finance that may be suited well for the technique.

All examples are in Excel. Excel sheet is available to my students.

Pre-requisites: OLS, PCA.
Deired: polar and spherical coordinates, basic trigonometry.

Part 1: Background to Type II (major axis) regression with PCA, learn about the paraglider problem and why straightforward OLS didn't work but orthogonal regression may
Part 2: How to apply Type II regression to a paraglider data in straighforward manner, and get much better results than OLS. The reason is because latitude and longitude are equal not in dependent/independent relation. Study the Excel example in detail. Learn about the "rules" of application of Type II regression developed in Ecology.
Part 3: Discuss why it is important to develop models that match DGP. Learn about complec motion of a paraglider soaring in air moved by a thermal and wind. Discuss a possible model structure that would reflect DGP. Discuss an example in Finance that may ask for PCA for regression.
Part 4, 5: Build a simple but realistic model of paraglider's motion, that produces excellent fit to the data. Step by step Excel solution with equations explained too.