[subsurface/subsurface] Indicate goodness of fit of regression line (#3148)

[Willem Ferguson]

I need to repeat:

Given a non-significant regression relationship between two variables, 
indicating any regression line at all is meaningless. In fact it is 
actively misleading, making you think that there may be a relationship. 
The slope of such a line has no meaning and henceforth is not useful for 
any interpretation.

The broad regression area that Robert indicates in his two diagrams are 
also not useful at all. If one were to plot a pink area of reliability, 
then a 1 standard deviation line is also not useful because it does not 
allow any reliable interpretation of the slope. If one were to do 
anything like this, one needs to indicate the 95% reliability area 
around the regression line, not a 1-sd line. The 1-sd line does not 
correspond to the statistical calculation that was done to generate the 
line. And then only individuals with some background in statistics would 
be able to interpret the 95% reliability area.

Honestly, my recommendation is not to show any regression line if there 
is not a statistically significant trend.

However, Dirk is correct in that it would help very much is some 
information about the regression line is shown. Probably something like 
"Linear regression line". If users could tolerate the statistical 
jargon, one could add the statistical probability, e.g. "p < 0.01".

I hope this makes sense???

Kind regards,

willem



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