2
$\begingroup$

Currently working through some notes on linear regression and they say the following:

In the linear model: $$Y=\alpha+\beta x$$ the intercept term is the mean value of the response."

However, I've been working through some examples in R, and for the two models I've fitted, R gives me an estimate for the intercept parameters that is not equal to the mean value of the response variables. Why is this so ?

$\endgroup$
  • $\begingroup$ If the quote hasn't omitted some relevant context, it's wrong. $\endgroup$ – Glen_b Dec 23 '19 at 1:31
2
$\begingroup$

Actually, intercept estimate is calculated as follows: $$\hat \alpha = \bar y - \hat\beta \bar x$$ In order for $\hat\alpha$ be equal to mean response, you'll need $\bar x=0$. This happens either by chance or if you standardize your features first and do the regression.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.