Question

Linear Regression conception

the true regression model is Y=B0+B1X+esilon

However, the sample simple regression line is Y_head=B0_head+B1_headX, and it doesn't have the error esilon, but why .Please explain it step by step and with some proof to support

***follow the comment***

Answer #1

**The
true regression model is**

**The sample regression line is**

**We note that the sample regression line does not have an
error term.**

**This is because of the fact that by the definition of
sample mean, the sum of residuals, which are not independent, in a
random sample is necessarily zero. The statistical errors, in the
population, on the other hand are necessarily independent, and
their sum is not necessarily zero.**

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