v

Suppose $1, ..., In are known constants and that Y1, ..., Y,, satisfy the 'regression through the origin' model Y, = Br, +6, where the e, are independent NV(0, o') random variables. Show that the maximum likelihood estimator of B is B = Er,Y/ Er?. What is the distribution of B? Suppose we have data giving the distance, in miles, by road (y) and in a straight line (r;) for several different journeys. Why might we prefer to consider the model above to the model Y = at Bite? 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