i≤ 5, Yi = ₁ + ₂ xi +€i, where , are unknown, {e}_1 are independent and E[ei] = 0 and Var[€;] data {x,yi1 are listed in the following table. i Xi Yi 1 2 3 0 1 2 1.08 2.19 2.95 4 3 3.89 Table 1: Data table. 5 4 5.09 = Determine the following using the data in the table. 1. The least square estimator 31, 32 for the true unknown parameters B₁, B. 2. Construct an unbiased estimator for ². o2 for all 1 ≤ i ≤ 5. The

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Author:Amos Gilat
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Yi = ß₁ + ß₂ · xi +€i,
V1≤ i ≤ 5,
where ß,ß are unknown, {€;}5_₁ are independent and E[€;] = 0 and Var[e;] = 0² for all 1 ≤ i ≤ 5. The
data {xi, Yi}_₁ are listed in the following table.
i=1
i
Xi
Yi
1
2
4
0
1
3
1.08 2.19 2.95 3.89
3
2
Table 1: Data table.
5
4
5.09
Determine the following using the data in the table.
1. The least square estimator 3₁, 32 for the true unknown parameters ß,ß.
2. Construct an unbiased estimator for o².
Transcribed Image Text:Yi = ß₁ + ß₂ · xi +€i, V1≤ i ≤ 5, where ß,ß are unknown, {€;}5_₁ are independent and E[€;] = 0 and Var[e;] = 0² for all 1 ≤ i ≤ 5. The data {xi, Yi}_₁ are listed in the following table. i=1 i Xi Yi 1 2 4 0 1 3 1.08 2.19 2.95 3.89 3 2 Table 1: Data table. 5 4 5.09 Determine the following using the data in the table. 1. The least square estimator 3₁, 32 for the true unknown parameters ß,ß. 2. Construct an unbiased estimator for o².
5
Suppose data {xi, Yi}{_1 are generated by the model
Transcribed Image Text:5 Suppose data {xi, Yi}{_1 are generated by the model
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