Suppose that our data comprise a set of pairs (Yi, xi),

Chapter 12, Problem 13

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Suppose that our data comprise a set of pairs (Yi, xi), for i = 1,...,n. Here, each Yi is a random variable and each xi is a known constant. Suppose that we use a simple linear regression model in which E(Yi) = 0 + 1xi. Let 1 stand for the least squares estimator of 1. Suppose, however, that the Yis are actually random variables with translated and scaled t distributions. In particular, suppose that (Yi 0 1xi)/ are i.i.d. having the t distribution with k 5 degrees of freedom for i = 1,...,n. We can use simulation to estimate the standard deviation of the sampling distribution of 1. a. Prove that the variance of the sampling distribution of 1 does not depend on the values of the parameters 0 and 1. b. Prove that the variance of the sampling distribution of 1 is equal to v2, where v does not depend on any of the parameters 0, 1, and . c. Describe a simulation scheme to estimate the value v from part (b).