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633 bytes added ,  18:15, 9 March 2021
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* linear - results in average values;
 
* linear - results in average values;
 
* logarithmic - results in smaller values;
 
* logarithmic - results in smaller values;
* power functions - results in larger values, but goes through (0,0);
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* power functions - results in larger values, but goes through the origin (0,0);
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The results of France show that the logarithmic function does not fit the data. The best fit is provided by a power functions. However this works only if there is enough data above a population fraction of 25%. The data below 25% heavily influences the outcome of a power functions. As an approximation a linear fit, without using the data at low values gives a better estimate. For France in fact the results are the same.
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The results of France show that the logarithmic function does not fit the data. The best fit is provided by a power function {f(x)=ax<sup>b</sup>}. However the fit works only if there is enough data above a population fraction of 25%. The data below 25% heavily influences the outcome of a power functions. As an approximation a linear fit can be used, without using the data at low ratios (<25%). For France in fact the results are the close (371 and 363).
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This suggests that the slope of a linear function is the same as the power function for the fitting purpose. To see this better a change (derivative) can be plotted.
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[[File:France departments - slope of size estimations.png|thumb|center|The slope of the weighted distances for France departments compared to the fits.]]
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As can be seen from the graph the slope does not stay constant as more and more departments are added. At this close inspection the power function fit is better. The linear fit to the slope (not the original data) confirms this conclusion and provides a better fit.
    
== Result ==
 
== Result ==
3,393

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