TEST BANK FOR STATISTICS 36226-ALL ANSWERS CORREXT-GRADED A

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1. We’ve defined the simple linear regression model as: Yi = β0 + β1Xi + i where E[i] = 0, Var[i] = σ2 where i; j are uncorrelated. (a) Find E[Yi] and Var[Yi]. Noting that E[Yi] changes w... ith i, find E[Y¯ ] and Var[Y¯ ]. E[Yi] = E[β0 + β1Xi + i] = E[β0 + β1Xi] + E[i] = β0 + β1Xi + 0 = β0 + β1Xi Var[Yi] = Var[β0 + β1Xi + i] = Var[β0 + β1Xi] + Var[i] = 0 + σ2 = σ 2 E[Y¯ ] = E "n1 Xi=1 n Yi# = 1 n nX i =1 E[Yi] = 1 n nX i =1 β0 + β1Xi = 1 n nβ0 + β1 nX i =1 Xi! = β0 + β1X¯ Var[Y¯ ] = Var"n1 Xi=1 n Yi# Rebecca Nugent, Department of Statistics, Carnegie Mellon University, 2012 1 e/8965534/HW8Sol/ This study resourc [Show More]

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