Let ßo and ₁ be least square estimators for the simple linear regression model y = ßo+B₁x+ɛ. Prove that E(Bo) = 3o. Finish the proof based on the following hints. Hint 1: Note that Bo = y - B₁. E (B) = 6 (ỹ - B₁x) = 6 (Y) - E(B₁7) Hint 2: first calculate E(). Note that y = (y₁ + y2 +...+yn)/n. In the class we already calculated what is E(y₁), E(y₂),..., E(yn), based on these existing results, figure out what is E(ÿ). N € (y) = € ( = Y₁+ y₂ + y^²) ==√ √ E (Y₁+ y₂ + ... Yn) n Hint 3: next we calculate E(Â₁7). Note that if we treat x₁,x2,...,n as fixed (not random variable), then E(₁x) = ñ · E(ŝ₁).
Let ßo and ₁ be least square estimators for the simple linear regression model y = ßo+B₁x+ɛ. Prove that E(Bo) = 3o. Finish the proof based on the following hints. Hint 1: Note that Bo = y - B₁. E (B) = 6 (ỹ - B₁x) = 6 (Y) - E(B₁7) Hint 2: first calculate E(). Note that y = (y₁ + y2 +...+yn)/n. In the class we already calculated what is E(y₁), E(y₂),..., E(yn), based on these existing results, figure out what is E(ÿ). N € (y) = € ( = Y₁+ y₂ + y^²) ==√ √ E (Y₁+ y₂ + ... Yn) n Hint 3: next we calculate E(Â₁7). Note that if we treat x₁,x2,...,n as fixed (not random variable), then E(₁x) = ñ · E(ŝ₁).
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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Transcribed Image Text:Let Bo and ₁ be least square estimators for the simple linear regression model y = Bo+B₁x+e.
Prove that E(ŝo) = ßo. Finish the proof based on the following hints.
Hint 1: Note that Bo = ÿ – Â₁ñ.
-
E (B³) = € ( Ñ - B‹ ñ) = 6 (Y) – E(B₁A)
-
Hint 2: first calculate E(). Note that y = (y₁ + y₂ + ...
y2 +yn)/n. In the class we already
calculated what is E(y₁), E(y2),..., E(yn), based on these existing results, figure out what is
E(ÿ).
Yıt
2
€ (g) = € ( Y₁+ y₂ + ² X ²) = √( @cy₁+ y₂ + ... ₁₂)
есун
n
Yn)
., n as fixed (not random
..."
Hint 3: next we calculate E(₁). Note that if we treat x1, x2,
variable), then E(3₁x) = x · E(B₁).
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