Still in connection with Example 6.3, show that the posterior distribution on (a, b, c, σ…

Still in connection with Example 6.3, show that the posterior distribution on (a, b, c, σ − 2) is a standard distribution made of a trivariate normal on (a, b, c) conditional on σ and the data and a gamma distribution on σ −2 given the data.

Example 6.3

The cars dataset relates braking distance (y) to speed (x) in a sample of cars. Figure 6.6 shows the data along with a fitted quadratic curve that is given by the R function lm. The model posited for this dataset is a quadratic model

where we assume that εij ∼ N(0, σ2) and independent.

 

 

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