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Abstract:
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Our company conducted a study on satiety, where subjects self-rated their 'fullness' at time intervals before and after drinking a nutritional product. The objective was to estimate how long it took for subjects to return to baseline fullness. The resulting raw data was quite irregular. Our in-house clients requested we mimic a method cited in a publication, which was to fit a Weibull curve to the data. Note that we are not implying a Weibull distribution, but that we wanted to fit a curve to the shape of our "fullness*time" graph. The graph was obviously not any recognizable common 'shape', but with some flips and shifts, it started to look like a Weibull curve. To fit the data using the NLIN procedure on SAS® required good starting estimates, without which the procedure fails. To this end, we used the high school geometry principle of "'similar' figures have a common ratio of corresponding parts" to derive our initial estimates. Also in use were algebraic transforms (shifts, reflections, etc.). Thus we could provide SAS® with excellent starting points and get a fit for our data. The process was so much fun in its novelty and usefulness that we had to share it.
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