Prove that μ ^ Y = y ¯ + β ^ 1 ( μ x − x ¯ ) using the least-square estimators of β 0 and β 1 .

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Chapter 11.6, Problem 41E

a.

To determine

Prove that μ^Y=y¯+β^1(μx−x¯) using the least-square estimators of β0 and β1.

b.

To determine

Find the value of μ^Y provided that μX=74.0.

Find the 2-standard deviation bound on the error of estimation.

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