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Suppose we have data set (Xi, Yi) with npoints. We want to perform a linear regression, but first we sort the X; values and 442 the Y;values independently of each other, forming data set (Xj, Y,). Is there any meaningful interpretation of the regression on the new data set? Does this have a name? I imagine this is a silly question so I apologize, I'm not formally trained in statistics. In my mind this completely destroys our data and the regression is meaningless. But my manager says he gets "better regressions most of the time" when he does this (here "better"means more predictive). I have a feeling he is deceiving himself. EDIT: Thank you for all of your nice and patient examples. I showed him the examples by @RUser4512 and @gung and he remains staunch. He's becoming irritated and I'm becoming exhausted. I feel crestfallen. I will probably begin looking for other jobs soon.
