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Suppose we have a linear model i.e

$y_i = \alpha + \beta x_i + \epsilon_i$

Now if I try lm(y ~ x) in R, what happens to my $\epsilon_i$ term? Or would there be no error since it is estimated by the residuals?

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The error term $\epsilon_i$ is something that you don't observe.

You assume a linear model $y_i = \alpha + \beta x_i + \epsilon_i$ for some $y$ and $x$, then you can estimate $\alpha$ and $\beta$ using lm(y ~ x), you can then compute the predictions $\hat{y}_i=\hat{\alpha}+\hat{\beta}x_i$ and the residuals $e_i = y_i-\hat{y}_i$.

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  • $\begingroup$ Thanks for the answer! Just a question relating to the $\hat{y}_i$. Now is this a fitted value or a predicted value or is there any difference? $\endgroup$ – Jdoe May 28 '20 at 20:50
  • $\begingroup$ Let's call it fitted value. They are the same but maybe prediction is a word used more in time series. $\endgroup$ – Ale May 29 '20 at 7:16

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