Question

in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (a) True (b) False L(Y=y14=a,X=x) (2) π(a) is a jeffreys prior when we consider the likelihood (where we assume xis known) (a) True (b)False Y-XB+ σε where ε E R" is a random vector with Consider a linear regression model E[ε1-0, E[eErJ-1. , and no further assymptions are made about ε X is an n by p deterministic, and X'X is invertible. ơ > 0 is an unknown constant Let β denote the least squares estimator of β in this context .Determine whether each of the following statements is true or false. (1) B is the maximum likelihood estimator for B (a)True (b)False (2) with the model written as Y Χβ + σε, β has dimension 1 xp (ie) is a row vector of length p) (a) True (b) False B has a Gaussian distribution (even for small n). (3) (a) True (b)False 1 point possible (graded, results hidden) Under the setup and assumptions as in part (b), XB is... (Check all that apply.) Equal to (XTX)-TY O An unbiased estimator of XA O A vector in R Submit You have used 0 of 3 attempts Save 1 point possible (graded, results hidden) The estimator σ2-1Y-XB12 for σ2 (check all that apply) Satisfies E o (n - p) o2 O Is unbiased satisfies (n-p) σ2/σ2 ~ χ, None of the above 2.0 points possible (graded, results hidden) Let Y = a(X-b)3 + E where e ~ N (0,02 ) is independent of X. What is the regression function f (x) of Y given X? (Check all that apply) f () a(z-b) y=f(z)

Answer 1

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