How (un)reasonable is graphic linear regression in a monolog graphic?

[DaTario]

TL;DR Summary

Consider two different data sets whose contexts are not related. One is ploted in a linear graphic and the other in a monolog graphic. Both data sets end up looking the same in each graphic. How (un)reasonable is to proceed to a graphic method of linear regression in a monolog graphic?

Hi All,

Consider two different data sets whose contexts are not related. One is ploted in a linear graphic and the other in a monolog graphic. Both data sets end up looking the same in each graphic. How (un)reasonable is to proceed to a graphic method of linear regression in a monolog graphic?

With respect to the figure below, where the lines were drawn by hand as a visual estimate of the best line to represent the data, is the straight line drawn in the monolog graphic usefull to produce any reliable information? The measurement of distances in a monolog graphic is in general rather different from what we do in linear graphics.

Best wishes,

DaTario

 

[renormalize]

TL;DR Summary: Consider two different data sets whose contexts are not related. One is ploted in a linear graphic and the other in a monolog graphic. Both data sets end up looking the same in each graphic. How (un)reasonable is to proceed to a graphic method of linear regression in a monolog graphic?

A linear-fit to a semi-log (monolog) graph corresponds to an exponential-fit on a linear graph. A semi-log straight-line-fit is then quite reasonable if your data happens to exhibit exponential growth or decay when plotted on a linear scale.

 

[DaTario]

A linear-fit to a semi-log (monolog) graph corresponds to an exponential-fit on a linear graph. A semi-log straight-line-fit is then quite reasonable if your data happens to exhibit exponential growth or decay when plotted on a linear scale.

Thank you, renormalize, but an important point in my question is: is the best straight line fitting in linear graph the best straight line fitting in semi-log ? (consider the two data sets I presented in the figure, which look identical)

As we are dealing here with a visual estimate of the best straight line, I am insterested in possible technical differences between drawing the two (best) lines as they appear in the figure I presented in the OP.

 

[renormalize]

Thank you, renormalize, but an important point in my question is: is the best straight line fitting in linear graph the best straight line fitting in semi-log ? (consider the two data sets I presented in the figure, which look identical)

As we are dealing here with a visual estimate of the best straight line, I am insterested in possible technical differences between drawing the two (best) lines as they appear in the figure I presented in the OP.

To answer, you have to tell us what your technical criteria are (using equations) for measuring goodness-of-fit.

 

[DaTario]

If I took the second data set and stick to the pairs $(x, ln(y))$, I could obtain by calculations the parameters of the best straight line to draw in the semi-log graph. Is this calculated straight line similar to the ones one usually draws by hand in a linear graph with points with the same relative position?