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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Sign up to join this communityThe 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 $e_i = y_i-\hat{y}_i$.