6. (10pts) Consider the simple linear regression model Y = Bo + BX + e, with...
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6. (10pts) Consider the simple linear regression model Y₁ = Bo + B₁X₁ + e, with normal error, so e are iid N(0,02) random variables. Given n data points {(X₁,Y)=1, let bo and by be the least square estimates for 30 and 3₁. The i-th residual, e₁, is e; = Y - Y₁ = Y₁-bo-b₁X₁. (a) Given a fixed i, say i = 1, derive the distribution for e,. Hint: Write e; as e; = Σ, c₁Y; for some choice of C₁, C2, Cn. (b) Are the residuals independent? Given i #j, are e, and e, independent random variables ? Hint: Note that , ei = 0 always. 6. (10pts) Consider the simple linear regression model Y₁ = Bo + B₁X₁ + e, with normal error, so e are iid N(0,02) random variables. Given n data points {(X₁,Y)=1, let bo and by be the least square estimates for 30 and 3₁. The i-th residual, e₁, is e; = Y - Y₁ = Y₁-bo-b₁X₁. (a) Given a fixed i, say i = 1, derive the distribution for e,. Hint: Write e; as e; = Σ, c₁Y; for some choice of C₁, C2, Cn. (b) Are the residuals independent? Given i #j, are e, and e, independent random variables ? Hint: Note that , ei = 0 always.
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6a by OLS estimator of 31 X X 1 X X2 where l li i1 bo OLS estimator of Bo YbX ... View the full answer
Related Book For
Essentials of Business Analytics
ISBN: 978-1285187273
1st edition
Authors: Jeffrey Camm, James Cochran, Michael Fry, Jeffrey Ohlmann, David Anderson, Dennis Sweeney, Thomas Williams
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