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Least-Squares Fit of General Functions

A straight-line least-squares fit is not limited to linear functions of x. It may be used with functions such as the exponential (y = ae ) or the power relationship (y = ax ) after an appropriate transformation of variables. For example, the exponential function can be written as [Pg.361]

When the variable is transformed, it is necessary to obtain the standard deviation of the new variable. In general, if one sets [Pg.362]

If the parameters are transformed, the standard deviation of the new constant is again determined by Eq. 11.29. In the example given above, a = In a and [Pg.362]

Example 11.4 The following table gives neutron-absorption cross-section values and their errors as a function of neutron kinetic energy. Determine the analytic function that fits this data set. [Pg.362]

Answer If one plots the data on log-log paper, the result is very close to a straight line (see Fig. 11.3). Therefore, the function to use is [Pg.363]


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