Mean response or new response?

Topic: Bayesian linear regression · more questions on this topic
‹ Direct sampling or Gibbs? Independent and scaled priors ›

At a new predictor vector \widetilde{\boldsymbol{x}}, derive the posterior distribution of the fitted mean \widetilde{\boldsymbol{x}}^{\mathsf T}{\boldsymbol{\beta}} and the posterior predictive distribution of a new response. Account for the extra 1 in the new-response squared scale.

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