Bundle map from $Spec(R[x_{1}, \dots, x_{n}])$ to $Spec(R)$

Question

My question: let $i: R \rightarrow R[x_{1}, \dots, x_{n}]$ be natural embedding, then $i^{*}: Spec(R[x_{1}, \dots, x_{n}]) \rightarrow Spec(R)$ is a bundle map. How should this conclusion be proven?
I am learning the correspondence between modules and vector bundles, which is a method I saw in a paper to construct vector bundles from modules, but I cannot prove that this is a vector bundle.
My attempt: Let $A = R[x_{1}, \dots, x_{n}]$. Clearly, $i^{*}$ is a continuous surjection. But the fibre $(i^{*})^{-1}(P) = Spec\left(\frac{A_{P}}{PA_{P}}\right)$。Is this a vector space? If so, what is the base domain $k$? And how to find local trivial mappings? Or more directly, how to prove that this is a vector bundle.