Timeline for incorporating error in best fit line equation
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2022 at 18:05 | comment | added | Axxxxx | Hi, I updated the question with more info. | |
| Apr 15, 2022 at 13:51 | history | edited | frank | CC BY-SA 4.0 |
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| Apr 15, 2022 at 13:48 | comment | added | whuber♦ | I believe a bootstrap appropriately carried out might be able to identify and compensate for this bias. The details matter! | |
| Apr 15, 2022 at 13:36 | history | edited | frank | CC BY-SA 4.0 |
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| Apr 15, 2022 at 13:36 | comment | added | frank | @whuber Thank you for pointing that out. I have updated the answer. | |
| Apr 15, 2022 at 13:15 | comment | added | whuber♦ | See our posts that refer to "errors in variables" regression. This is a subtle but important issue. Intuitively, when the $x_i$ are measured with appreciable error (which means the variance is a sizable proportion of the overall variance of the $x_i$), the resulting horizontal "smearing" of the data tends to have a kind of regularizing effect to reduce the magnitude of the slope estimate. | |
| Apr 15, 2022 at 13:08 | comment | added | frank | @whuber Could you explain this a little more? I thought that I do address the situation where both $x$ and $y$ have error. | |
| Apr 15, 2022 at 13:02 | comment | added | whuber♦ | This answer does not address the unique and difficult part of the problem setting, which is that the explanatory (x) variable is also measured with appreciable error. Your approach yields biased estimates in that situation. Propagating the error will not remove that bias. | |
| Apr 15, 2022 at 11:41 | history | answered | frank | CC BY-SA 4.0 |