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Your preferences For When to Download: For more detailed guidance about when to download from sites like the iTunes Store and. com or just about anything, please see our. In this scene.Q:
Under what circumstance would the identity line get exchanged with the null line in classical linear regression?
In classical linear regression, the model is $Y = \mu + X\beta$, where $\mu$ is the mean of Y and X is the matrix of covariates.
From my understanding of the model, it is assumed that the actual values of Y is always bigger than the mean of Y (i.e., is always positive). If this assumption is false, then the line $\mu + X\beta$ would be an undefined line, therefore the identity line is exchanged with the null line and the intercept becomes $b_0$.
How can this be possible when the assumptions of classical linear regression is always true, or is my understanding wrong?
A:
From my understanding of the model, it is assumed that the actual values of Y is always bigger than the mean of Y (i.e., is always positive).
But what is that $\beta$ supposed to represent, if not a regression coefficient? So if $Y$ is by definition positive, that means the whole thing is $(Y-\mu)\beta$. The vector $(Y-\mu)\beta$ isn’t always larger than $\mu$.
It might seem you have conflated the difference between the mean of $Y$ and the mean of $(Y-\mu)\beta$. But note that the mean of $(Y-\mu)\beta$ isn’t the same as the mean of $Y$, because the $(Y-\mu)\beta$ represents the effect of some covariates on $\beta$.
You are right in saying $\mu+X\beta$ is undefined if $Y$ is not positive. But that’s a different story. Then the intercept would be $b_0=\mu$.
A:
So the line is not undefined, it’s still valid.
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