Hi,

I forgot to say that this works of course also if you want to add legends.

M = 10; data = RandomReal[1, M];
Manipulate[
 Show[ListPlot[data, PlotStyle -> Red], 
  Plot[Evaluate[
    Normal[NonlinearModelFit[data, 
      Evaluate[Sum[Subscript[a, i] x^i, {i, 0, d}]], 
      Evaluate[Table[Subscript[a, i], {i, 0, d}]], x]]], {x, 0, 
    M + 1}, PlotRange -> All , 
   PlotLegends -> 
    Placed["Polynomial \nf(x)=" <> 
      ToString[
       TraditionalForm[
        Evaluate[
         Normal[NonlinearModelFit[data, 
           Evaluate[Sum[Subscript[a, i] x^i, {i, 0, d}]], 
           Evaluate[Table[Subscript[a, i], {i, 0, d}]], x]]]]], 
     Below]]], {d, 0, 10}]

Cheers,

M.