# compare Bayesian linear regression vs standard linear regression

1st question,

I recently learnt bayesian linear regression, but I'm confused that in what situation we should use bayesian linear regression, and when to use standard linear regression? What is the advantage of bayesian linear regression over standard one?

2nd question,

Also, another thing I'm confused with is that for a simple linear regression whose formula is $$𝑦_𝑖=α+β𝑥_𝑖+𝜀$$, why the bayesian version is as:

$$𝑢_𝑖=α+β𝑥_𝑖$$

$$𝑦_𝑖∼\mathcal{N}(𝜇_𝑖,𝜎)$$

I read from other place that $$μ_𝑖$$ corresponds to $$𝑦_𝑖=α+β𝑥_𝑖$$, what does σ correspond to? And how is the version transformation realize?

3nd question,

Last question, does $$𝑦_𝑖∼\mathcal{N}(𝜇_𝑖,𝜎)$$

mean that each value y $$\in𝑌$$ is a normal distribution, instead of the observed data is a normal distribution?

• $μ_𝑖$ is the mean of each $𝑦_𝑖$ and $\sigma$ it's just the variance of $𝑦_𝑖$. So $\sigma$ 'corresponds' to $y_i$ aswell. – Isa Feb 21 at 5:48
• It would be a good idea if you could post the definitions of bayesian linear regression and standard linear regression or the source of these terms. – Isa Feb 21 at 5:53