Derive Equations 6.12 by multiplying Equation 6.11 through by each of X 1 and X 2 . (Hints: Both X 1 and X 2 are uncorrelated with the regression error ε. Likewise, X 2 is uncorrelated with the...

Derive Equations 6.12 by multiplying Equation 6.11 through by each of X₁
and X₂. (Hints: Both X₁
and X₂
are uncorrelated with the regression error ε. Likewise, X₂
is uncorrelated with the measurement error δ. Show that the covariance of X₁
and δ is simply the measurement error variance σ2 δ by multiplying X₁
= τ þ δ through by δ and taking expectations.)