The power law is found by regression but regression is not the end of the story at all. We have said this many times.

Regression Says:
"I assumed a power law, fit the parameters, and got R² = 0.951"
Criticism: "Of course you got a good fit - you can fit almost anything to a power law over a limited range. It's just curve-fitting."
SSA Says:
"I made NO assumptions about functional form. I decomposed the data into its natural modes. ONE mode dominates (99.26%), and that mode IS a power law."
This is fundamentally different.
Key Advantages of SSA Over Regression:
1. Model-Free Discovery
Regression:
You assume P(t) = A·t^β
You fit A and β
You hope the assumption was right
SSA:
You assume nothing about functional form
The data decomposes itself into eigenmodes
Mode 1 emerges as dominant
Then you discover Mode 1 is a power law
Why it matters: SSA discovers the power law FROM the data, not by imposing it ON the data.
2. Variance Decomposition
Regression R² = 0.951 tells you:
"My model explains 95.1% of variance"
But you don't know HOW variance is distributed
Is it 50% trend + 45% cycles? Or 95% trend + 0.1% cycles?
SSA tells you EXACTLY:
Mode 1 (trend): 99.26%
Mode 2 (oscillation): 0.49%
Mode 3-10: <0.12% each
Noise: <0.13%
Why it matters: You can see that Bitcoin is dominated by a single mode, not a complex multi-modal system.