So it is relatively easy to show that there exists only one smooth structure on the real line $\mathbb{R}$. So here are 2 natural questions:

Q1: Up to equivalence, is there only one real analytic structure on $\mathbb{R}$? If so, then do we have a simple proof of that?

Q2: Where can I find the simplest proofs that there exists only one smooth structure on $\mathbb{R}^2$ and $\mathbb{R}^3$?

So I've heard that on $\mathbb{R}^4$ there are infinitly (in fact uncountably) many non-equivalent smooth structures, so what about real analytic strucutres? Is there some kind of moduli space of smooth structures on $\mathbb{R}^4$. if so, in how many ways is it possible to deform a smooth structure into a real analytic one?