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**Unformatted text preview: **2 . Recall, for random variable Z the estimates of the mean and variance of Z based on n realization of Z are. Similarly, the estimate of 2 is S 2 is called the MSE Mean Square Error it is an unbiased estimator of 2 (proof later on). =-= n i i e n s 1 2 2 2 1 STA302/1001 week 2 4 Normal Error Regression Model In order to make inference we need one more assumption about i s. We assume that i s have a Normal distribution, that is i ~ N (0, 2 ). The Normality assumption implies that the errors i s are independent (since they are uncorrelated). Under the Normality assumption of the errors, the least squares estimates of and 1 are equivalent to their maximum likelihood estimators. This results in additional nice properties of MLEs: they are consistent, sufficient and MVUE....

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