Timeline for For a linear regression of Y on X, when is the regression of X on Y linear? When is it non-linear?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jun 30, 2021 at 13:28 | vote | accept | user62421 | ||
| Jun 26, 2021 at 2:58 | comment | added | user62421 | @whuber Thanks! | |
| Jun 25, 2021 at 18:36 | comment | added | whuber♦ | +1. The relevant concept is exchangeability, implied by the iid assumption. Because of that and linearity of conditional expectation, $$y = E[Y\mid Y=y] = E[X_1+X_2\mid X_1+X_2=y] = E[X_1\mid X_1+X_2=y] + E[X_2\mid X_1+X_2=y].$$ Since the two terms are equal (by exchangeability), each must equal $y/2,$ QED. | |
| Jun 25, 2021 at 17:59 | history | edited | user62421 | CC BY-SA 4.0 |
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| Jun 25, 2021 at 17:48 | history | answered | user62421 | CC BY-SA 4.0 |