Is the intercept term in a linear regression model the intercept term?

Question

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 ?

Answer 1

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.