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ĥ₁ = 10, 62 = 10, se(b₁) = 10, se(b2) = 5, R² = 0.5 Suppose we could increase the sample twenty-five times, N = 2500. Let the new estimates for the larger sample be ô, ô, sè(b₁)*, se(b2)*, R2*. According to the theory, what are the values we should expect from these estimates? Mark the CORRECT alternative: (a) We expect ô† < ô₁, but ôž > ĥ2 (b) We expect the R² to increase, that is, R²* > R² (c) We expect ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 5, se(b2)* ≈ 2.5, R²* ≈ 0.5 (d) We expect 6 ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 2, sè(b2)* ≈ 1, R²* ≈ 0.5 (e) We expect t-statistics to remain the same, that is, 61/sè(b₁)* ≈ 1, ô½/sè(b2)* ≈ 2.

ĥ₁ = 10, 62 = 10, se(b₁) = 10, se(b2) = 5, R² = 0.5 Suppose we could increase the sample twenty-five times, N = 2500. Let the new estimates for the larger sample be ô, ô, sè(b₁)*, se(b2)*, R2*. According to the theory, what are the values we should expect from these estimates? Mark the CORRECT alternative: (a) We expect ô† < ô₁, but ôž > ĥ2 (b) We expect the R² to increase, that is, R²* > R² (c) We expect ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 5, se(b2)* ≈ 2.5, R²* ≈ 0.5 (d) We expect 6 ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 2, sè(b2)* ≈ 1, R²* ≈ 0.5 (e) We expect t-statistics to remain the same, that is, 61/sè(b₁)* ≈ 1, ô½/sè(b2)* ≈ 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The regression above has N = 100 data points and we obtain the following estimates:

ĥ₁ = 10, 62 = 10, se(b₁) = 10, se(b2) = 5, R² = 0.5 Suppose we could increase the sample twenty-five times, N = 2500. Let the new estimates for the larger sample be ô, ô, sè(b₁)*, se(b2)*, R2*. According to the theory, what are the values we should expect from these estimates? Mark the CORRECT alternative: (a) We expect ô† < ô₁, but ôž > ĥ2 (b) We expect the R² to increase, that is, R²* > R² (c) We expect ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 5, se(b2)* ≈ 2.5, R²* ≈ 0.5 (d) We expect 6 ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 2, sè(b2)* ≈ 1, R²* ≈ 0.5 (e) We expect t-statistics to remain the same, that is, 61/sè(b₁)* ≈ 1, ô½/sè(b2)* ≈ 2.
Transcribed Image Text:ĥ₁ = 10, 62 = 10, se(b₁) = 10, se(b2) = 5, R² = 0.5 Suppose we could increase the sample twenty-five times, N = 2500. Let the new estimates for the larger sample be ô, ô, sè(b₁)*, se(b2)*, R2*. According to the theory, what are the values we should expect from these estimates? Mark the CORRECT alternative: (a) We expect ô† < ô₁, but ôž > ĥ2 (b) We expect the R² to increase, that is, R²* > R² (c) We expect ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 5, se(b2)* ≈ 2.5, R²* ≈ 0.5 (d) We expect 6 ≈ 10, 6½ ≈ 10, se(b₁)* ≈ 2, sè(b2)* ≈ 1, R²* ≈ 0.5 (e) We expect t-statistics to remain the same, that is, 61/sè(b₁)* ≈ 1, ô½/sè(b2)* ≈ 2.
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