Answered: Let there be a simple regression yt =…

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

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Question

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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