# I Semi ln plot- uncertainty estimation

1. May 16, 2016

### Imperatore

Hello there!

There is a problem with calculating the uncertainty from semi- ln plot. The linear fitting gives standard errors as you can see in attached picture. In the Y axis are ln J values, obviously. If the intersection with y-axis, x=0, then we get the point y=b=-33,21, and it's ln J', so the J' equals: exp(-33,21), ok it works fine. But the uncertainty of J' gives then value of exp(0,212), which is about 10^14 factor greater than the calculated value of J'.

What's wrong with my solution?

#### Attached Files:

• ###### semi ln plot.jpg
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2. May 16, 2016

### Staff: Mentor

That is not what it gives. The uncertainty of 0.212 means your value 33.21 could also be 0.212 larger or smaller (there is a more mathematical statement behind it, but let's keep it at that level). What is exp(33.21 ± 0.212)?

3. May 16, 2016

### Imperatore

I got it. Uncertainty is |exp(-33.21-0.212)-exp(-33.21+0.212)| equals 1,6 e-15 Is it really that simple?

4. May 16, 2016

### Staff: Mentor

It is not that simple, and a better treatment would likely lead to asymmetric uncertainties. But looking at the up and down deviation gives some reasonable approximation.

5. May 16, 2016

### Imperatore

Oh, I should devided that relation |exp(-33.21-0.212)-exp(-33.21+0.212)| by 2, obviously.