Consider a simple linear regression model y; = Briei, where the error terms 's are assumed...
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Consider a simple linear regression model y; = Briei, where the error terms 's are assumed to be i.i.d. N(0,0²). (a) Find the least square estimate of 3. (b) Suppose that we know the true value of o2, and we want to estimate 3 using a Bayesian approach. Suppose that we assume a prior distribution N(0, ²) for 3, where ² is some known constant. Find the posterior distribution of ß given the data. (c) Show that if we choose ² large, then the posterior mean behaves like the least square estimate. Consider a simple linear regression model y; = Briei, where the error terms 's are assumed to be i.i.d. N(0,0²). (a) Find the least square estimate of 3. (b) Suppose that we know the true value of o2, and we want to estimate 3 using a Bayesian approach. Suppose that we assume a prior distribution N(0, ²) for 3, where ² is some known constant. Find the posterior distribution of ß given the data. (c) Show that if we choose ² large, then the posterior mean behaves like the least square estimate.
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a ANS WER The variance of the least square estimate of B is ... View the full answer
Related Book For
Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish
Posted Date:
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