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I am currently working on a linear regression task from a textbook and I have some questions. In the following you will find the task as well as some thoughts of mine to possible results.

Short description: A quadratic regression analysis shall be made for temperature data from France. The explained variable is given by: Quadratic regression

The conjugate prior is:

Conjugate prior

a) In the first task I shall determine the prior hyperparameters to suitable values:

hyperparameters

I can think about the prior mean as a guess of the average temperature in France (lets assume 20°C). But I can not make a sense out of the other parameters. How do I define the prior precision as well as the degrees of freedom and what are they telling me? I know that $\sigma^2$ can be derived from the Inv-$\chi^2$ distribution but how do I estimate $s_0^2$?

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