Justify log spirals

[tingard]

• Convenient property of constant pitch angle
• Fewer parameters than comparable models
• $R^2$ values range ... therefore
  • define $R^2$

[tingard]

𝑅2(𝑠𝑎𝑚𝑝𝑙𝑒𝑠)=0.8621±0.0000 𝑅2(expectation)=0.8624

[tingard]

Wikipedia:

In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.[1][2][3]

[tingard]

I do need to double-check this is all appropriate, as we're fitting a nonlinear model using Bayesian regression.

[tingard]

Decided on

"As we wish to utilize the logarithmic spiral's desirable properties of a constant pitch angle and small number of fittable parameters, we make use of it here without an explicit comparison to other models. This comparison of a logarithmic spiral profile to other spiral forms (i.e. Archimedian or polynomial) is another important piece of work, outside of the scope of this research."