How to chose the correct variable for a linear regression?

2021.11.29 08:53 Lazaryx How to chose the correct variable for a linear regression?

Hello,
I know the title is poor and inaccurate but I did not find a way to phrase it better.
I am having an issue with a linear regression and I hope you can be of help.
We have a set of 83 experimental values that we can simulate using quantuum chemistry.
So we have 2 sets of data, 83 experimental values and 83 calculated values.
According to the litterature the error on the experimental values is roughly a quarter to one half of the error on the calculated values (compared to the "real" value), so rougly 1.5 unit compared to roughly 3 to 4 units.
Here comes the issue: my boss insists I do my linear regression, via the least squared method, on the calculated values (i.e. the experimental values are our "x") so we can minimize the bigger error. While I would rather do the opposite because we get an easier equation to use for our experimental friends (and users when we publish that). (Basically I prefer to do multiplication then addition rather than addition then division to get the experimental value from my calculated one. Plus it feels more natural to go from simulation to real life rather than the opposite). On a more scientific note the second regression (i.e. the one on the experimental value in the "y" axis) has a lower root mean square error on the residual compared to the first regression (2.75 vs 3.6 units, when our measurements range on 300 units). I am not sure this difference is statistically significant nor how to check if it is.
Since the root mean square deviation on our residuals is comparable to the expected error I do feel we're good, that we don't introduce an additional error.
My question is therefore on how to select the correct "x"? After a 2h search online I am not even sure on how to formulate the question, let alone have a pist of reflexion on the issue.
Any help would be welcome.

I can provide the data if needed, once I am done teaching.
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2021.11.29 08:53 JCMS85 Meta Monday: 11/29/21

heck Best Coast Pairings for Lists

A slower weekend and very UK focused because of the holiday in the US. I will list WarFare 2021 and WG Presents- Fun & Fluff below but they won’t be in the data set as both are sub 2k tournaments.

Into The Hellstorm Gladius. Forest Rd, England. 42 Players. 6 Rounds.

  1. Iron Hands 6-0
  2. Orks 5-1
  3. Thousand Sons 5-1
  4. Drukhari 5-1
  5. Thousand Sons 5-1

The Hogtowner 2021. Toronto, Canada. 38 Players. 5 Rounds.
  1. Iron Hands 5-0
  2. Grey Knights 4-1
  3. Custodes 4-1
  4. Imperial Knights 4-1
  5. Dark Angels 4-1
  6. Drukhari 4-1
  7. Space Wolves 4-1
FactoruM GT. Sutton Veny, England. 36 Players. 5 Rounds.
  1. Drukhari 5-0
  2. Deathwatch 4-1
  3. Chaos 4-1
  4. Dark Angels 4-1
  5. Death Guard 4-1
  6. Grey Knights 4-1
Return of the Leftovers GT. Oak Ridge, TN. 32 Players. 5 Rounds.
  1. Grey Knights 5-0
  2. Orks 4-1
  3. Grey Knights 4-1
  4. Thousand Sons 4-1
  5. Choas Knights 4-1
  6. Craftworlds 4-1

NOT 2k.
(1750pts) Warfare 2021. 21 High Street England. 50 Players. 5 Rounds.
  1. Drukhari 5-0
  2. Drukhari 4-0-1
  3. Necrons 4-1
  4. Grey Knights 4-1
  5. Sisters 4-1
  6. 6 Grey Knights 4-1
  7. 7. Craftworlds 4-1
  8. 8. Craftworlds 4-1
(1500pts) WG Presents- Fun & Fluff. England. 49 Players. 5 Rounds.
  1. Drukhari 5-0
  2. Death Guard 4-1
  3. Death Guard 4-1
  4. Drukhari 4-1
  5. Orks 4-1
  6. Death Guard 4-1
  7. Harlequins 4-1
  8. Drukhari 4-1
  9. Drukhari 4-1

Takeaways:
Iron hands are seeing real play and success in the UK. A 71% weekend win rate is toxic from their few players but their 3 week win rate is as bad at 60%
Another great weekend for GK. Lots of play while maintaining a great win rate.
Necrons seeing a lot of play and a much better weekend for them then last but their 3 week win rate is still terrible (40%). I think we are still a few weeks out from finding their best new lists.
Thousand sons did great this weekend with top finishes and a 63% win rate.

Army Players Wins Games Win% 3WWin%
Adeptus Custodes 4 10 18 56 49
Adeptus Mechanicus 4 7 21 33 45
Astra Militarum 10 20 51 39 42
Aelderi 0 0 0 0 47
Black Templars 1 3 5 60 53
Blood Angels 8 17 41 41 41
Chaos 2 8 11 73 51
Chaos Daemons 3 8 17 47 47
Chaos Knights 5 14 25 56 44
Chaos Space Marines 5 9 23 39 36
Craftworld 2 7 10 70 53
Dark Angels 7 17 32 53 44
Death Guard 9 17 43 40 47
Deathwatch 2 7 10 70 35
Drukhari 4 16 21 76 56
Genestealer Cult 0 0 0 0 53
Grey Knights 12 38 61 62 57
Harlequins 2 5 11 45 49
Imperial Knights 8 19 43 44 45
Imperium 1 2 5 40 54
Necrons 10 28 55 51 40
Orks 10 28 51 55 53
Sisters of Battle 5 11 26 42 51
Space Wolves 6 11 24 46 46
Tau 4 7 18 39 38
Thousand Sons 6 20 32 63 47
Tyranids 3 8 15 53 51
Ynnari 0 0 0 0 22
Space Marines 15 39 81 48 44
Imperial Fists 2 3 11 27 29
Iron Hands 5 20 28 71 60
Raven Guard 1 2 5 40 33
Salamandars 4 7 20 35 46
Ultramarines 2 4 11 36 34
White Scars 1 3 6 50 45
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