  Let $\mathsf{B}_1$ be the polynomial ring $\mathbb{C}[a^{\pm1},b]$ with the
structure of a complex Hopf algebra induced from its interpretation as the
algebra of regular functions on the affine linear algebraic group of complex
invertible upper triangular 2-by-2 matrices of the form $\left(
\begin{smallmatrix}
  a&b\\0&1 \end{smallmatrix}\right)$. We prove that the universal invariant of
a long knot $K$ associated to $\mathsf{B}_1$ is the reciprocal of the
canonically normalised Alexander polynomial $\Delta_K(a)$. Given the fact that
$\mathsf{B}_1$ admits a $q$-deformation $\mathsf{B}_q$ which underlies the
(coloured) Jones polynomials, our result provides another conceptual
interpretation for the Melvin--Morton--Rozansky conjecture proven by Bar-Nathan
and Garoufalidis, and Garoufalidis and L\^e.
