From the graphs a number of conclusions can be made out, that are pretty evident from observation alone.
A Linear Regression even with a “complete dataset” is not a quite good fit, (and the sample data was reasonably “linear”) since most KDP values will lie above or below the Regression Line, as expected.
The Least Squares method will always produce a straight line, even if there is no relationship between the variables, or if the relationship is something other than linear.
An interpolating polynomial such as the “Natural Cubic Spline” provides a great fit, since every KDP is contained by the curve.
The “Delta Spline” also shows a perfect fit, with every KDP on it, as expected since it’s based on an interpolating polynomial.
It’s rather apparent that a “Linear” regression will be a “good enough” solution, but only for a limited range of the predefined air temperature values. Other than that, it’s not very recommended for forecasting purposes of this problem, since it can be appreciated that both the interpolated and extrapolated trends will yield improbable values.
Now, let’s take a look to the second scenario.
Most of the time, as confirmed before, a Linear Regression curve will not pass along the KDPs, and this case, with a limited dataset, is no exception. This of course, was expected.
What this limited dataset mostly shows are the limitation of both the Linear Regression and the “Natural Spline” (cubic) to extrapolate values.
As can be observed, the “Delta Spline” curve will always pass along all the KDPs, with no “overshooting” (as is common with other interpolating polynomials such as the “Natural Spline”) and will provide the best possible fit to the series data.
The method called “Delta Spline” was especially developed for this program, and as such was perfected to deal with this particular kind of data series.
Of the three exposed methods, the “Delta Spline” is the one with greatest potential as a valuable tool to match, interpolate and extrapolate the data series, having been demonstrated to be both reliable and robust.
The sole purpose of these methods is to help to take, as precisely as possible, that critical first shot from a cold bore. They are not meant for the occasional short, medium range shot. If not considering real long range situations (beyond the 800 yards mark) there is no major need to use them.
Gustavo F. Ruiz is long time fan of ballistics, reloading and above all hunting big game. He has contributed many articles for both local and foreign magazines (Spain). Professionally, he spent eight years at Microsoft. Holds a BS in Computer Science, a BS in Operations Research and an MBA.
He is also a LtCdr (res) in the Argentine Navy, and is involved with the LR shooting training program of their Special Forces operators. Currently he is developing ballistics/reloading software through Patagonia Ballistics (www.patagoniaballistics.com.), a small software development group located in Argentina.
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