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Linear Regression conception the true regression model is Y=B0+B1X+esilon However, the sample simple regression line is...

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

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Math   Statistics-And-Probability   
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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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