This is mainly concerning machine learning and linear regression, but I think my question still is mathrelated and for that reason I post my question here.

I have a linear regression looking like this:

$$t_i = w_0x_1 +w_1 + \epsilon = -1.5x_i - 0.5 + \epsilon$$

where $\epsilon \sim \mathcal{N}(0,\sigma)$, $\sigma = 0.3$. My issue is from this point to deduce the distribution of the prior, that is $p(w)\sim\mathcal{N}(w_\mu,\Sigma_w).$ I'm going to claim that the mean $w_\mu=0$ since I want to induce so called "sceptical prior". My issue is that I dont know what to select my $\Sigma_w$ as, the easiest would be to choose a diagonal matrix with $\sigma=0.3$ but what arguments do I have for doing this claim?


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