Replicating power law distribution

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Estimating powerlaws via linear regression hardly ever works – see Power-law distributions in empirical data for details and proper ML based estimation algorithms. Unfortunately, there only seems to be an abandoned package in Julia …
In any case, here is a quick estimate on your data using formula (B.17) from the paper and an arbitrary x_{min}:

julia> xmin = 23
23

julia> x = degrees[degrees .> xmin];

julia> 1 + inv(mean(log.(x ./ (xmin - 1/2))))
2.810142626941318

which is already much closer to the analytic exponent.

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