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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 22E

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