Dear Sónia Ferreira ,

let x, y the coordinate system of your primary data.

The coordinate system of your log-log scaled may be x' and y'.

x and x' as well as y and y' are related by:

x' = log(x) and y' = log(y) respectively (conversion equations)

Your linear fit in the log-log system is for example described by :

y' = a +b*x' with a and b being values known from your fit.

So taking the conversion equation from above you get:

log(y) = a + b*log(x)

solving for y you will get:

y= 10log(y) =10(a + b*log(x)) = 10a * 10(b*log(x)) = 10a * 10(log(x)*b) = 10a * [10(log(x)]b

Please note that 10log(x) = x here.

So as result you will have:

y = 10a * xb

Here I have taken the 10 as the basis of the log operation (log = log10). In the case you have taken for example the Euler number e as the basis of your log scale (log = loge = ln), then you will have:

y= ea * xb

You have just to play around a bit with the basic mathematical power laws and rules for logarithms.

Best regards...

Thank's for the help! It makes more sense now!

Best regards

Find a copy of this book and work your way through the regression material. You are looking for "transformations to linearity".. Good luck, D. Booth link:

https://www.google.com/search?rlz=1C1CHBF_enUS874US874&q=statistics+for+engineering+and+the+sciences+6th+edition+pdf+download&sa=X&ved=2ahUKEwin3tu94P_mAhUaac0KHQwuCjcQ1QIoAHoECAsQAQ&biw=1034&bih=792

You might also try this link:

https://www.google.com/search?rlz=1C1CHBF_enUS874US874&biw=1034&bih=792&ei=OfQbXvOmIoiFtQb-tqDgDA&q=basic+regression+analysis+with+r&oq=basic+regression+analysis+with+r&gs_l=psy-ab.3..33i22i29i30l2.669925.688888..690016...1.2..3.236.7466.90j0j1......0....1..gws-wiz.....6..0i71j0j0i362i308i154i357j0i273j0i131j0i67j0i22i30.MaEs2gnHHlw&ved=0ahUKEwizp83a4P_mAhWIQs0KHX4bCMwQ4dUDCAs&uact=5