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 ?

  • 1
    $\begingroup$ If the quote hasn't omitted some relevant context, it's wrong. $\endgroup$
    – Glen_b
    Commented Dec 23, 2019 at 1:31

1 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.


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