Consider the simple linear model Y; = Bo + B1x; + €i, where e; is independent, identically distributed with mean 0 and variance o². Note: Must use the Linear combination of Y method! See Example 12 of 3 - Simple Linear Regression (Inference). a) Show that the least square estimator Bo =Ÿ – B1ữ is an unbiased of Bo- %3D b) Show that (i) Varlôo] = i Σ o2 (ii) and attains the minimum variance among all estimates that are linear combination of the response variable Y.

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Consider the simple linear model Y; = Bo + B1x; + €i, where e; is independent, identically
distributed with mean 0 and variance o?. Note: Must use the Linear combination of Y
method! See Example 12 of 3 - Simple Linear Regression (Inference).
a) Show that the least square estimator 30 = Ÿ – Biữ is an unbiased of Bo-
Σ
b) Show that (i) Var[Bo] = n (*; – ¤)²
(ii) and attains the minimum variance
-
hong all estimates that are linear combination of the response variable Y.
Transcribed Image Text:Consider the simple linear model Y; = Bo + B1x; + €i, where e; is independent, identically distributed with mean 0 and variance o?. Note: Must use the Linear combination of Y method! See Example 12 of 3 - Simple Linear Regression (Inference). a) Show that the least square estimator 30 = Ÿ – Biữ is an unbiased of Bo- Σ b) Show that (i) Var[Bo] = n (*; – ¤)² (ii) and attains the minimum variance - hong all estimates that are linear combination of the response variable Y.
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