In reply to Herman's response :
>
> There is no reason to assume that the data are normal. For
> linear regression to be exactly the MLE procedure, it is the
> residuals from the true regression which need to have certain
> properties. In well designed experiments, the independent
> variables are never normal. Rarely will the dependent variables
> be close to normal, either.
>
> The key properties for the residuals are lack of correlation
> with the independent variables, independence, and homoscedasticity.
> Normality is well down the list. Remember that this is for
> the residuals, not the data. Linearity of the model is a
> consequence of these.
I do not agree entirely:
Suppose your model is as: Y = a + b*X + E (X=IDV, E=Error term)
You tell that E must be normal but not Y. It is not correct, because
(a + b*X ) is the expected value of Y given X, hence E and Y have
the same distribution given X.
The assumptions for the linear regression are related to DV (Y) (or to E)
conditionally to X.
But it is difficult to to check these assumptions from data unless you have
several duplications for each value of X. For this reason we limited to check
the assumptions on the residuals and not on the data.
--
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| Hassane ABIDI (PhD) |
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