Does it matter which way I label my axis?

Are you familiar with Snell's Law? It links the angle of incident and refraction to the refractive indexes of two media: sini/sinr = n2/n1

I'm assuming that the data is for light going from air into another medium, and since the refractive index of air is taken to be 1, it ends up being sini/sinr = n2. Because the gradient is dy/dx, this means a graph of sini on the y axis again sinr on the x axis gives the refractive index of the second medium.
However your graph is sinr/sini, which gives 1/n2.