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tive population parameters. Let B, be the estimator of B, obtained by assuming (see Section 2-6). the intercept is 20 the population Find E(3₁) in terms of the x₁, Bo, and B₁. Verify that B₁ intercept (Bo) is zero. Are there other cases where B, is unbiased? depend on Bo.) B. Hint: The is unbiased for 3, when

tive population parameters. Let B, be the estimator of B, obtained by assuming (see Section 2-6). the intercept is 20 the population Find E(3₁) in terms of the x₁, Bo, and B₁. Verify that B₁ intercept (Bo) is zero. Are there other cases where B, is unbiased? depend on Bo.) B. Hint: The is unbiased for 3, when

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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family income. 8 Consider the standard simple regression model y = Bo + B₁x + u under the Gauss-Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators B, and 3, are unbiased for their respec- tive population parameters. Let ß, be the estimator of B, obtained by assuming the intercept is zero (see Section 2-6). (i) (ii) Find E(3₁) in terms of the x, Bo, and 3₁. Verify that B₁ is unbiased for ß, when the population intercept (Bo) is zero. Are there other cases where B₁ is unbiased? Find the variance of B₁. (Hint: The variance does not depend on Bo.)
Transcribed Image Text:family income. 8 Consider the standard simple regression model y = Bo + B₁x + u under the Gauss-Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators B, and 3, are unbiased for their respec- tive population parameters. Let ß, be the estimator of B, obtained by assuming the intercept is zero (see Section 2-6). (i) (ii) Find E(3₁) in terms of the x, Bo, and 3₁. Verify that B₁ is unbiased for ß, when the population intercept (Bo) is zero. Are there other cases where B₁ is unbiased? Find the variance of B₁. (Hint: The variance does not depend on Bo.)
gression Analysis with Cross-Sectional Data (iii) Show that Var(B₁) ≤ Var(B₁). [Hint: For any sample of data, Σ(x₁ - x)², with strict inequality unless = 0.] (iv) Comment on the tradeoff between bias and variance when choosing between 3₁ and 3₁.
Transcribed Image Text:gression Analysis with Cross-Sectional Data (iii) Show that Var(B₁) ≤ Var(B₁). [Hint: For any sample of data, Σ(x₁ - x)², with strict inequality unless = 0.] (iv) Comment on the tradeoff between bias and variance when choosing between 3₁ and 3₁.
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