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Q6. Consider the following simple linear model Y₂ = ẞ0+ẞ₁Xi+e; where εi s are iid N(0, σ²), i = 1, 2,..., n. (a) Show that the covariance between the least squares estimators bo of Bo and b₁ of ẞ₁ is given by: Cov(bo, b1) = -Xo² Σ(Xi-X)² (b) Derive the sampling distribution of (Y-E{Y}), where Ŷ = b0+b₁Xr· s{Y} (c) Use part (b) to derive the expression for σ² {bo}.

Q6. Consider the following simple linear model Y₂ = ẞ0+ẞ₁Xi+e; where εi s are iid N(0, σ²), i = 1, 2,..., n. (a) Show that the covariance between the least squares estimators bo of Bo and b₁ of ẞ₁ is given by: Cov(bo, b1) = -Xo² Σ(Xi-X)² (b) Derive the sampling distribution of (Y-E{Y}), where Ŷ = b0+b₁Xr· s{Y} (c) Use part (b) to derive the expression for σ² {bo}.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Only for b and c show the calculation please

Q6. Consider the following simple linear model Y₂ = ẞ0+ẞ₁Xi+e; where εi s are iid N(0, σ²), i = 1, 2,..., n. (a) Show that the covariance between the least squares estimators bo of Bo and b₁ of ẞ₁ is given by: Cov(bo, b1) = -Xo² Σ(Xi-X)² (b) Derive the sampling distribution of (Y-E{Y}), where Ŷ = b0+b₁Xr· s{Y} (c) Use part (b) to derive the expression for σ² {bo}.
Transcribed Image Text:Q6. Consider the following simple linear model Y₂ = ẞ0+ẞ₁Xi+e; where εi s are iid N(0, σ²), i = 1, 2,..., n. (a) Show that the covariance between the least squares estimators bo of Bo and b₁ of ẞ₁ is given by: Cov(bo, b1) = -Xo² Σ(Xi-X)² (b) Derive the sampling distribution of (Y-E{Y}), where Ŷ = b0+b₁Xr· s{Y} (c) Use part (b) to derive the expression for σ² {bo}.
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