Linear fit in log space

Linear fit in log space schen19  2021-06-08

Dear Skyline team,

I have a question about the Linear in Log Space regression fit in Skyline. My initial understanding is that the equation of the calibration curve using this fit is Log(Y) = slope*Log(X) + Y-intercept (Y is RatioLightToHeavy, X is Analyte Concentration). However, when I tried to use this equation to calculate X from Y using this equation, the result does not agree with the Calculated Concentration, which is the quantification value given directly by Skyline.

I tried to do a similar regression fit (Log-transformed both X and Y, then do a linear regression fit) in another software and it gives the same slope but different intercept. When using the slope and intercept given by that software and the Log(Y) = slope*Log(X) + Y-intercept equation, I get the same quant value as the Calculated Concentration given by Skyline. Based on this observation, the problem seems to be related to the Y-intercept value given by Skyline.

I am trying to understand what equation is Skyline using for the Linear in Log Space regression fit. Could you provide some guidance on that?

Thank you,

Nick Shulman responded:  2021-06-08
When Skyline takes the logarithm of the X and Y, it is using the natural logarithm (i.e. not base 10).

The slope ends up being the same regardless of whether you do the calculations using natural log, or log base 10 (since the X and Y coordinates both end up getting multiplied by the same factor depending on the base of the logarithm). The intercept does end up being different depending on which type of logarithm you use.

If changing the logarithm type does not fix your problem, then you can send us your Skyline document and I can walk you through the calculations for your specific data.
In Skyline you can use the menu item:
File > Share
to create a .zip file containing your Skyline document and supporting files including extracted chromatograms.

If that .zip file is less than 50MB you can attach it to this support request. Otherwise, you can upload it here:

-- Nick
schen19 responded:  2021-06-08
Thanks a lot! That solves my problem.

schen19 responded:  2021-06-09
I just have a follow-up question about the LN transformation in Skyline. I used the other software to reproduce the LN transformation and linear regression fit. The slope and intercept are the same as what is given in Skyline. However, the r^2 is still different. The other software gives better r^2 than Skyline. Is there a reason why this happens?

Nick Shulman responded:  2021-06-09
It's a bug in Skyline 21.1 (and all previous versions) that the R-squared for linear in log space fits is completely incorrect.

This bug is going to be fixed in the next update of Skyline-Daily, which will probably be released in a few days.
-- Nick
schen19 responded:  2021-06-09
Good to know. Thanks a lot!