Expectation, Unbiased And Variance for β1

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"Consider the standard simple regression model y= β0 + β1x +u under the gauss-Markov assumptions SLR.1 through SLR.5. the usual OLs estimators and are unbiased for their respective population parameters. Let β1 be the estimator of β1 obained by assuming the intercept is zero. i) Find E ( ) in terms of the xi, β0 and β1 . verify that β1 is unbiased for β1 when the population intercept (β0 ) is zero. Are there other cases where β1 is unbiased? ii) Find the variance ofβ . iii) Show that var β ≤ var β . iv) Comment on the tradeoff between bias and variance when choosing between β and β. "
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February 6, 2013
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762.67 KB
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