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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 σ 2 is • S 2 is called the MSE – Mean Square Error it is an unbiased estimator of σ 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 ε i ’s. • We assume that ε i ’s have a Normal distribution, that is ε i ~ N (0, σ 2 ). • The Normality assumption implies that the errors ε i ’s are independent (since they are uncorrelated). • Under the Normality assumption of the errors, the least squares estimates of β and β 1 are equivalent to their maximum likelihood estimators. • This results in additional nice properties of MLE’s: they are consistent, sufficient and MVUE....
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 Summer '09
 Linear Regression, Normal Distribution, Regression Analysis, Variance, Estimation theory

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