Expectation, Unbiased And Variance for β1

Business & Finance, Accounting, Auditing
Cover of the book Expectation, Unbiased And Variance for β1 by Homework Help Classof1, Classof1
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Author: Homework Help Classof1 ISBN: 1230000114652
Publisher: Classof1 Publication: March 12, 2013
Imprint: Language: English
Author: Homework Help Classof1
ISBN: 1230000114652
Publisher: Classof1
Publication: March 12, 2013
Imprint:
Language: English

"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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"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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