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Y₁ =B₁ + B₁X₁ + e, (2) In which , and B, are OLS estimates of b, and b₁, respectively. n Σx, Yi (1) Prove the OLS estimate of B₁ is B₁= n [x² i=1 and the OLS estimate of B is B-Y-B‚¸Ñ n in which x₁ = X₁-X, X=-¶X₁ ni=1 n y₁=Y-Y, Y=LĖX ΣΥ ni=1

Y₁ =B₁ + B₁X₁ + e, (2) In which , and B, are OLS estimates of b, and b₁, respectively. n Σx, Yi (1) Prove the OLS estimate of B₁ is B₁= n [x² i=1 and the OLS estimate of B is B-Y-B‚¸Ñ n in which x₁ = X₁-X, X=-¶X₁ ni=1 n y₁=Y-Y, Y=LĖX ΣΥ ni=1

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 62CR
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Suppose the PRF of two-variable regression is represented in the equation (1) Y₁ = b + b₁X₁ +u₁, u~ii.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. Σ ‚X¡Yi i=1 (1) Prove the OLS estimate of ß, is B n Σx² i=1 and the OLS estimate of B is B-Y-Â₁X n in which x₁ = X₁-X, X = ²X₁ ΣΧ i=1 n y=Y-Y, Y=! Y ni=1
Transcribed Image Text:Suppose the PRF of two-variable regression is represented in the equation (1) Y₁ = b + b₁X₁ +u₁, u~ii.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. Σ ‚X¡Yi i=1 (1) Prove the OLS estimate of ß, is B n Σx² i=1 and the OLS estimate of B is B-Y-Â₁X n in which x₁ = X₁-X, X = ²X₁ ΣΧ i=1 n y=Y-Y, Y=! Y ni=1
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