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Suppose all of the regression assumptions in Key Concept 4.3 are satisfied except that the first assumption is replaced with E(u₁|X) = 2. Which parts of Key Concept 4.40 continue to hold? Which change? Why? (Is, normally distributed in large samples with mean and variance given in Key Concept 4.40? What about Bo?)

Suppose all of the regression assumptions in Key Concept 4.3 are satisfied except that the first assumption is replaced with E(u₁|X) = 2. Which parts of Key Concept 4.40 continue to hold? Which change? Why? (Is, normally distributed in large samples with mean and variance given in Key Concept 4.40? What about Bo?)

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
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Suppose all of the regression assumptions in Key Concept 4.30 are satisfied except that the first assumption is replaced with E (u₁|X;) = 2. Which parts of Key Concept 4.40 continue to hold? Which change? Why? (Is, normally distributed in large samples with mean and variance given in Key Concept 4.40? What about Bo?)
Transcribed Image Text:Suppose all of the regression assumptions in Key Concept 4.30 are satisfied except that the first assumption is replaced with E (u₁|X;) = 2. Which parts of Key Concept 4.40 continue to hold? Which change? Why? (Is, normally distributed in large samples with mean and variance given in Key Concept 4.40? What about Bo?)
The Least Squares Assumptions Y=Bo+B₁X₁+₁,i = 1,..., n, where 1. The error term u, has conditional mean zero given X; E(u, X) = 0; 2. (X, Y),i=1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: X; and Y, have nonzero finite fourth moments. Large-Sample Distributions of Bo and ₁ If the least squares assumptions in Key Concept 4.3 hold, then in large samples Bo and , have a jointly normal sampling distribution. The large-sample normal dis- tribution of B₁ is N(B₁, o), where the variance of this distribution, o, is var[(X₁-x)] [var(X)]² The large-sample normal distribution of Bo is N(B), where 1 var(Hu) [E(H)2 where H₁=1- Hx (4.21) (4.22) KEY CONCEPT 4.3 KEY CONCEPT 4.4
Transcribed Image Text:The Least Squares Assumptions Y=Bo+B₁X₁+₁,i = 1,..., n, where 1. The error term u, has conditional mean zero given X; E(u, X) = 0; 2. (X, Y),i=1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: X; and Y, have nonzero finite fourth moments. Large-Sample Distributions of Bo and ₁ If the least squares assumptions in Key Concept 4.3 hold, then in large samples Bo and , have a jointly normal sampling distribution. The large-sample normal dis- tribution of B₁ is N(B₁, o), where the variance of this distribution, o, is var[(X₁-x)] [var(X)]² The large-sample normal distribution of Bo is N(B), where 1 var(Hu) [E(H)2 where H₁=1- Hx (4.21) (4.22) KEY CONCEPT 4.3 KEY CONCEPT 4.4
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