1 Consider the linear regression model Y i a b 1 X i U i Suppose that there are no data on X i but we have data on Z i a o a 1 X 1 , whrer a o and a 1 are arbitrary known constants Using data of variable Z i we can estimate Y i c o c 1 Z i U i Show how from the estimates of c o and c 1you can obtain the estimates of the original model

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Question: 1.Consider the linear regression model Y i =a +b 1 X i +U i Suppose that there are no data on X i but we

1.Consider the linear regression model

Y_i=a +b₁X_i +U_i

Suppose that there are no data on X_i but we have data on Z_i=a_o+a₁X₁, whrer a_o and a₁ are arbitrary known constants. Using data of variable Z_i we can estimate

Y_i=c_o+c₁Z_i +U_i

Show how from the estimates ofcoandc1you can obtain the estimates of the original model.

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