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 

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

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 

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. 

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 

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