When reading on the wikipedia page of Calibration they said :

" A reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable "

Indeed, this confuses me ! For me I see calibration is a special case of regression, and not a reverse regression. So, can some one explain the stated in wikipedia, or in general what is the difference between regression and calibration?

  • $\begingroup$ Providing that the correlation between $X$ and $Y$ is not $\pm1$, regressing $X$ on $Y$ will suggest a different relationship between them compared with regressing $Y$ on $X$. So trying to predict a value $\hat{x}$ from an observation $y ( \not = E[Y])$ will usually give different results depending on whether you use direct regression or reverse regression $\endgroup$ – Henry Aug 24 '17 at 6:40
  • $\begingroup$ @Henry Thank you for your commetn, but to clarify my question, I am asking about calibration and not reverse regression ! $\endgroup$ – Nizar Aug 24 '17 at 7:24
  • $\begingroup$ For additional discussions of this please see stats.stackexchange.com/questions/31528 and stats.stackexchange.com/questions/38023. $\endgroup$ – whuber Aug 24 '17 at 14:27