Question 2 Suppose x1,..., xn are known constants and that Y1,..., Yn satisfy the 'regression through the origin' model Y; = Bx;+€i, where the e; are independent N(0, o²) random variables. Show that the maximum likelihood estimator of 3 is B = Ex;Y;/ 2x}. What is the distribution of B? Suppose we have data giving the distance, in miles, by road (y;) and in a straight line (x;) for several different journeys. Why might we prefer to consider the model above to the model Y; = a+ Bx; + e;? Assuming the 'regression through the origin' model, if the straight-line distance between two locations is 12 miles, how would you use the model to predict the expected distance by road? How could we find a 95% confidence interval for this expected distance?
Question 2 Suppose x1,..., xn are known constants and that Y1,..., Yn satisfy the 'regression through the origin' model Y; = Bx;+€i, where the e; are independent N(0, o²) random variables. Show that the maximum likelihood estimator of 3 is B = Ex;Y;/ 2x}. What is the distribution of B? Suppose we have data giving the distance, in miles, by road (y;) and in a straight line (x;) for several different journeys. Why might we prefer to consider the model above to the model Y; = a+ Bx; + e;? Assuming the 'regression through the origin' model, if the straight-line distance between two locations is 12 miles, how would you use the model to predict the expected distance by road? How could we find a 95% confidence interval for this expected distance?
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:Question 2
Suppose x1,..., xn are known constants and that Y1,..., Yn satisfy the 'regression through
the origin' model Y; = Bx;+€i, where the e; are independent N(0, o²) random variables. Show
that the maximum likelihood estimator of ß is ß = Ex;Y;i/Ex}. What is the distribution
of B?
Suppose we have data giving the distance, in miles, by road (y;) and in a straight line (x;) for
several different journeys. Why might we prefer to consider the model above to the model
Y; = a + Bx; +e;?
Assuming the 'regression through the origin' model, if the straight-line distance between two
locations is 12 miles, how would you use the model to predict the expected distance by road?
How could we find a 95% confidence interval for this expected distance?
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