Maurice Tutor

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Category > Management Posted 06 Jan 2018 My Price 6.00

simple regression model

8    Consider the standard simple regression model y 5 b0 1 b1x 1 u under the Gauss-Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators bˆ and bˆ are unbiased for

0                1

their respective population parameters. Let b˜       1 be the estimator of b1 obtained by assuming

the intercept is zero (see Section 2.6).

(i)       Find E(b˜1) in terms of the xi, b0, and b1. Verify that b˜ 1 is unbiased for b1 when the population intercept (b0) is zero. Are there other cases where b˜ 1 is unbiased?

(ii)    

∑
 

Find the variance of b˜ 1. (Hint: The variance does not depend on b0.)

(iii)   

ˆ
 

2
 

Show that Var(b˜ 1) # Var(b1). [Hint: For any sample of data,

∑i51 (x 2 x¯) , with strict inequality unless x¯ 5 0.]

 

n

i51

 

xi 

 

n                        2

i

(iv)   Comment on the tradeoff between bias and variance when choosing between bˆ and b˜ .

1               1

                                                  

Answers

Maurice Tutor
(5)
Status NEW Posted 06 Jan 2018 04:01 PM My Price 6.00

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