What happens to the error term when create a linear model in R?

Question

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?

Answer 1

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 $e_i = y_i-\hat{y}_i$.