By Edwin. Wolfe
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Extra info for Episodes with Gurdjieff
Example text
4) F i g. 1. 4). 4) might be mistaken for zero. 4). 4) causes η(x) to increase without bound. Often, however, responses either increase to an asymptote with x, or even pass through a maximum and then decrease. 2. 6) η(x) = 50 + 5x − 35x2 . 7) A second-order, or quadratic, model is symmetrical about its extreme, be it a maximum or a minimum. 5), with a positive coefficient of x2 , the minimum is at x = 7/6, outside the range of plotted values. 6) the extreme is again a minimum, as is indicated by the positive coefficient of 40 for x2 .
The preceding list of points suggests a direct path from problem formulation to solution. However, at each stage, the experimenter may have to reconsider decisions made at earlier stages of the investigation. Problems arising at intermediate stages may add to the eventual understanding of the problem. If the model fitted at stage 8 appears inadequate, this may be because the model is too simple, or there may be errors and outliers in the data owing, for example, to failures in measurement and recording devices, or in data transmission and entry.
N ). 5) For this simple linear regression model N (yi − β0 − β1 xi )2 . 6) (yi − β0 − β1 xi )xi . 7) i=1 N i=1 At the minimum both derivatives are zero. 8) where the sample averages are x ¯ = xi /N and y¯ = yi /N . Therefore the fitted least squares line passes through (¯ x, y¯) and has slope βˆ1 . The distribution of βˆ depends upon the distribution of the errors i . 9) yields the normal-theory assumptions. 8) are linear combinations of normally distributed observations, are then themselves normally distributed.
Episodes with Gurdjieff by Edwin. Wolfe
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