Consider the problem of regression through the origin (with normal error terms,

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Consider the problem of regression through the origin (with normal error terms, all with the same variance) where the X values in the training data set take on the values for some number n. Let beta denote the one-dimensional regression coefficient, and let sigma 2 denote the variability of the outcome around it's conditional expectation. Suppose now that we assume the beta has a normal prior with variance lambda -1 and expectation zero. Assume that Xnew will follow a uniform distribution on the unit interval. What is the posterior expectation of beta given the data?

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Consider the problem of regression through the origin (with normal error terms,

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