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In: Statistics and Probability

simple linear regression proof of variance of intercept estiamtor β0

simple linear regression proof of variance of intercept estiamtor β0

Solutions

Expert Solution

(estimate) is an unbiased estimator of .

Proof: = E(^)= E(Ci yi)

= Ci E(yi)

= Ci( o + 1Xi)

= oCi + 1CiXi equation 1

Now Ci= = = 1

= 0

Substituting values of and in equation 1

E(o^)= o

Hence o^ is an unbiased estimator ofo.

Var(o^)= Var()

= = =

= )

=

Note that

Var(o^) =  

Hence the result.

orchestra answered 2 years ago
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