Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For Part II see ibid. vol.3 no.6 (2001). In previous parts  used linear least squares to fit polynomials of various degree to the annual global temperature anomalies for 1856 to 1999. Polynomials are much beloved by mathematicians but are of limited value for modeling measured data. Natural processes often display linear trends, and occasionally a constant acceleration process exhibits quadratic variation. Hover, higher-order polynomial behavior is rare in nature, which is more likely to produce exponentials, sinusoids, logistics, Gaussians, or other special functions. Modeling such behaviors with high-order polynomials usually gives spurious wiggles beten the data points, and low-order polynomial fits give nonrandom residuals.  saw an example of this syndrome in Figure 4 of Part 1 (ibid. vol.3 no.5 (2001)), where  attempted to model a quasicyclic variation with a fifth-degree polynomial. That example also illustrated that polynomial fits usually give unrealistic extrapolations of the data.
['Bert W. Rust']
I am writing a research paper on a idea Fitting nature's basic functions. I am writing a research paper on a idea Part III: exponentials, sinusoids, and nonlinear least squares
[{"from": "human", "value": "I am writing a research paper on a idea Fitting nature's basic functions. I am writing a research paper on a idea Part III: exponentials, sinusoids, and nonlinear least squares"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For Part II see ibid. vol.3 no.6 (2001). In previous parts  used linear least squares to fit polynomials of various degree to the annual global temperature anomalies for 1856 to 1999. Polynomials are much beloved by mathematicians but are of limited value for modeling measured data. Natural processes often display linear trends, and occasionally a constant acceleration process exhibits quadratic variation. Hover, higher-order polynomial behavior is rare in nature, which is more likely to produce exponentials, sinusoids, logistics, Gaussians, or other special functions. Modeling such behaviors with high-order polynomials usually gives spurious wiggles beten the data points, and low-order polynomial fits give nonrandom residuals.  saw an example of this syndrome in Figure 4 of Part 1 (ibid. vol.3 no.5 (2001)), where  attempted to model a quasicyclic variation with a fifth-degree polynomial. That example also illustrated that polynomial fits usually give unrealistic extrapolations of the data."}]