## Sum of residuals ~ ε [Design Issues]

Hi both,

Perhaps I am getting it wrong; the sentence above sounds a little off and I have a feeling you may not be discussing the same thing?

The sum of residuals for a fitted normal linear model will be zero. Not asymptotically. If you sum them in R or any other software you will get zero, be it either like zero-zero or effectively zero, depending on the implementation.

This is because the underlying assumption is that epsilon be distributed with mean zero. If we end up with a non-zero sum, I'd say we have screwed up somewhere.

Try

❝ I disagree. In the *model* ε = 0. However in the *fit*, the sum of residuals is only asymptotically 0. We shouldn’t speak of bias when we obtain something sufficiently close to the numeric resolution of the machine.

Perhaps I am getting it wrong; the sentence above sounds a little off and I have a feeling you may not be discussing the same thing?

The sum of residuals for a fitted normal linear model will be zero. Not asymptotically. If you sum them in R or any other software you will get zero, be it either like zero-zero or effectively zero, depending on the implementation.

This is because the underlying assumption is that epsilon be distributed with mean zero. If we end up with a non-zero sum, I'd say we have screwed up somewhere.

Try

`sum(resid(M))`

—

Pass or fail!

ElMaestro

Pass or fail!

ElMaestro

### Complete thread:

- Should those subjects have only one period data be included in BE analysis? ssussu 2019-12-06 10:58 [Design Issues]
- No way! But... Beholder 2019-12-06 12:36
- No way! But... ElMaestro 2019-12-06 13:14
- No way! But... Helmut 2019-12-06 14:47
- No way! But... PharmCat 2019-12-06 23:46
- No way! But... wienui 2019-12-07 04:01
- EMA guideline: no way...: mittyri 2019-12-07 20:58
- EMA guideline: no way...: wienui 2019-12-09 05:25

- EMA guideline: no way...: mittyri 2019-12-07 20:58
- Slightly off topic, but related :-) ElMaestro 2019-12-08 01:31
- Slightly off topic, but related :-) Shuanghe 2019-12-09 12:00
- Slightly off topic, but related :-) PharmCat 2019-12-09 15:13
- Slightly off topic, but related :-) ElMaestro 2019-12-21 15:02
- Slightly off topic, but related :-) PharmCat 2019-12-22 01:12
- 2.220446e-16 ≈ 0 Helmut 2019-12-22 10:37
- The optional tolerance argument ElMaestro 2019-12-23 14:37
- 2.220446e-16 ≈ 0 PharmCat 2019-12-24 14:18
- Sum of residuals ~ ε Helmut 2019-12-24 14:54
- Sum of residuals ~ εElMaestro 2019-12-24 15:10
- Wrong terminology Helmut 2019-12-28 13:55

- Sum of residuals ~ ε PharmCat 2019-12-24 18:40

- Sum of residuals ~ εElMaestro 2019-12-24 15:10

- Sum of residuals ~ ε Helmut 2019-12-24 14:54

- Slightly off topic, but related :-) ElMaestro 2019-12-21 15:02

- No way! But... wienui 2019-12-07 04:01

- No way! But... PharmCat 2019-12-06 23:46

- No way! But... Helmut 2019-12-06 14:47

- No way! But... ElMaestro 2019-12-06 13:14

- No way! But... Beholder 2019-12-06 12:36