X1 = Y + X2 + X3, discard all X1 outside +/- 2 SD of mean

X2 = Y + X1 + X3, discard all X2 outside +/- 2 SD of mean

X3 = Y + X1 + X2, discard all X3 outside +/- 2 SD of mean

then

Y = X1 + X2 + X3

How statistically viable would this be? Also, would the standard error of the estimate and R square still be meaningful?

I have not seen or heard of this before, and I am a bit skeptical. Still, given that this observations in nature, and not social science the confidence interval of the estimate for the independent should be valid. What can make it fall apart is that the very outliers I am trying to get rid of, is included in the method. However, hoping this will be deflated to marginal influence in the method.

Purpose: pragmatic data mining and prediction, NOT for publication or science

Data: observations from nature, so a high degree of stability is expected in the relationships

N: approx. 15 k