Fit a Student (t) linear regression to astronomy data from Rousseeuw (1991) relating to the star cluster

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Fit a Student \(t\) linear regression to astronomy data from Rousseeuw (1991) relating to the star cluster CYG OBI, which contains 47 stars in the direction of Cygnus. The predictor ( \(\mathrm{x}[\mathrm{i}]\) in the data in Exercise 4.2. odc) is the logarithmic temperature at the star surface and \(y_{i}\) is the log of the star's light intensity. Compare the LPML of a model with \(v\) set at 5, and a model with \(v\) as an unknown. For example, \(v\) may be assigned an exponential prior (Geweke, 1993), or a uniform prior assumed on \(1 / u\), such as \(1 / v \sim U(1,0.01)\) so that \(v\) will be between 1 and 100 .

Data from Example 4.2
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rate among a minority of subjects.

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