using Plots
using PyFormattedStrings

xdata = [ 0.34482759,  0.68965517,  1.03448276,  1.37931034,
          1.72413793,  2.06896552,  2.4137931 ,  2.75862069,  3.10344828,
          3.44827586,  3.79310345,  4.13793103,  4.48275862,  4.82758621,
          5.17241379,  5.51724138,  5.86206897,  6.20689655,  6.55172414,
          6.89655172,  7.24137931,  7.5862069 ,  7.93103448,  8.27586207,
          8.62068966,  8.96551724,  9.31034483,  9.65517241, 10.        ]

ydata = [ 4.55459724,  5.2125257 ,  5.85608367,  6.28256403,
          5.3510909 ,  7.33644195,  8.74308925,  8.80680797,  7.91569673,
          8.80173903,  8.09422165,  8.75590574, 10.68847556, 10.08827538,
          9.67774597,  9.75957529, 10.68388337, 10.39037968, 10.83938351,
          11.8776604 , 11.97929326, 13.7156162 , 12.63125149, 13.24891817,
          12.23343525, 12.55352271, 13.23694   , 14.91190807, 14.93770334]

#-----------------------

A = [length(xdata)     sum(log.(xdata));
     sum(log.(xdata))  sum(log.(xdata).^2)]

b = [ sum(log.(ydata)),
      sum(log.(xdata).*log.(ydata)) ]

p = A\b
α = exp(p[1])
β = p[2]

println(f"α = {α:.3f}, β = {β:.3f}")


xx = LinRange(0,10,1000)
yy = α*xx.^β

a = 5
b = 0.45
xb = LinRange(0,10,30)
yb = (5*xb.^0.45) # .+ 3*(rand(length(x)) .- 0.5)

scatter(xdata,ydata, label="data", lw=2)
plot!(xx,yy,         label="model")
plot!(xb,yb, linestyle=:dash, color="gray", label="real", lw=2)
plot!(legend_foreground_color=nothing)
plot!(xlabel="x", ylabel="y")