Suppose the PRF of two-variable regression is represented in the equation (1) Y₁ = b + b₁X₁ + u₁, u~i.i.d N(0,0²) (1) We use Ordinary Least Square (OLS) method to estimate the coefficients in (1), The OLS estimated SRF is represented in the equation (2) Y₁ =B₁ + B₁X₁ + e, (2) In which B and B, are OLS estimates of b and b₁, respectively. (2) Prove Σe, = 0 (3) Prove Σex, = 0

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Suppose the PRF of two-variable regression is represented in the equation (1)
Y₁ =b₁ + b₁X₁ + u₁, u~i.i.d N(0,0²)
(1)
We use Ordinary Least Square (OLS) method to estimate the coefficients in (1),
The OLS estimated SRF is represented in the equation (2)
Y₁ =B₁ + B₁X₁ + e,
(2)
In which , and B, are OLS estimates of b, and b, respectively.
(2) Prove Σe, = 0
(3) Prove Sex = 0
Transcribed Image Text:Suppose the PRF of two-variable regression is represented in the equation (1) Y₁ =b₁ + b₁X₁ + u₁, u~i.i.d N(0,0²) (1) We use Ordinary Least Square (OLS) method to estimate the coefficients in (1), The OLS estimated SRF is represented in the equation (2) Y₁ =B₁ + B₁X₁ + e, (2) In which , and B, are OLS estimates of b, and b, respectively. (2) Prove Σe, = 0 (3) Prove Sex = 0
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