7.4 - Determination of the approximation line

 There are two ways to determine an approximate line from the logarithmic (and linearized) data. a) through linear regression (without prior linearization) b) by the existing minimum-maximum values Case b) will be discussed below, since case a) can be handled using a commercially available calculation program. We are now looking for the approximation line y = ax + b for the logarithmic values. In the following figure, the approximation line is shown as a dashed line.

Illustration 7.2 approximation line

There are n values ??given, namely: y0, y1, y2, ... yk, ... yn

with yk = ln wk

There is a minimum ymin and a maximum ymax

 The slope a of the approximation line can be determined from the min-max values ??and the new approximate numbering. The following applies:

 7.4.1 - Equation:

 Δ y is the difference between the minimum and maximum values:
 7.4.2 - Equation:

 Δ x is the maximum value of the new numbering:
 7.4.3 - Equation:

 The additive constant of the function you are looking for results from the smallest value:
 7.4.4 - Equation:

 The following applies to the approximation line:
 7.4.5 - Equation:

 Inserting all terms gives:
 7.4.6 - Equation:

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