# Covariance, how to deduce from linear regression

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?