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Let there be a simple regression yt = (alpha) + (beta)x + (ε), where ε~?(0, σ^2) Let ε(hat) be an OLS estimator of ε. Prove Sum(ε(hat)) = 0

Let there be a simple regression yt = (alpha) + (beta)x + (ε), where ε~?(0, σ^2) Let ε(hat) be an OLS estimator of ε. Prove Sum(ε(hat)) = 0

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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Can you solve the following: and provide workings?:

1) Let there be a simple regression yt = (alpha) + (beta)x + (ε), where ε~?(0, σ^2)

Let ε(hat) be an OLS estimator of ε. Prove Sum(ε(hat)) = 0

2)Let the share price of a listed company, S, have the following distribution:
S~N(100,225)

a)Suppose that, when the price of this share falls below the 10th percentile of its
distribution, it is a signal for buying. What is the maximum price at which you would
buy this share? 

b) Suppose that, when the price of this share rises beyond the 90th percentile of its
distribution, it is a signal for selling. What is the minimum price at which you would
sell this share? 

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