Discussion
In a multiple linear regression set up \(y = XB + E\) under the assumption \(E(E) = 0\), \(\mathrm{Var}(E) = \sigma^{2}\). In the response variables \(y_{1} \ldots y_{n}\) are :
Answer: B
The responses are non-identical and uncorrelated.
\(E(y_{i}) = x_{i}'B\) depends on the \(i\)th row of X, so the responses have different means and are not identically distributed. The assumption \(\mathrm{Var}(E) = \sigma^{2}I\) gives them a common variance and zero covariances, so they are uncorrelated.
Independence is not implied: only first and second moments are assumed, and uncorrelated variables need not be independent unless normality is added. So 'non-identical and independent' says more than the model gives, and the 'identical' options ignore the different means.
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