Correlation (Pearson)

Pearson correlation coefficient between two equal-length numeric series. Returns r (the correlation, -1 to 1), r² (variance explained), n (sample size). Use this to ask things like: is a stock's daily return correlated with a macro indicator? Are two FRED series moving together?

Input

Field	Type	Description
x *	array	First numeric series
y *	array	Second numeric series (same length as x)

Example output

{
  "n": 5,
  "r": 1,
  "rSquared": 1,
  "interpretation": "perfect positive linear relationship"
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/correlation \
  -H "Content-Type: application/json" \
  -d '{"x":[1,2,3,4,5],"y":[2,4,6,8,10]}'

The response is HTTP 402 Payment Required with exact payment requirements. Any x402 v2 client pays automatically and retries:

Paid call (JavaScript agent)

import { wrapFetchWithPayment } from "@x402/fetch";
import { x402Client } from "@x402/core/client";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

const client = new x402Client();
registerExactEvmScheme(client, { signer: privateKeyToAccount(KEY) });
const payFetch = wrapFetchWithPayment(fetch, client);

const res = await payFetch("https://agent402.tools/api/correlation", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "x": [
      1,
      2,
      3,
      4,
      5
    ],
    "y": [
      2,
      4,
      6,
      8,
      10
    ]
  }),
});

No wallet? Pay with compute

This is a pure-CPU tool, so an agent without a wallet can pay with proof-of-work instead of USDC: fetch a challenge, solve the sha256 puzzle (16 leading zero bits — a fraction of a second of CPU, no money, no AI tokens), and resend with the X-Pow-Solution header.

import { createHash } from "node:crypto";
const lz = (b) => { let t = 0; for (const x of b) { if (!x) { t += 8; continue; } t += Math.clz32(x) - 24; break; } return t; };
const c = await (await fetch("https://agent402.tools/api/pow/challenge?slug=correlation")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/correlation", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"x":[1,2,3,4,5],"y":[2,4,6,8,10]}) });

Part of these workflows

This tool is one step in a curated multi-tool workflow — agents can fetch the whole sequence as an MCP prompt or call https://agent402.tools/api/skill-packs/{slug}/prompt.

• Trend analysis — Take any numeric time series — a stock's daily close, a FRED macro indicator, a treasury yield history — and run it through the full quantitative workup: descriptives, moving averages, trend line, outliers, optional correlation against a benchmark, and a deterministic forecast forward with a 95% prediction interval. Everything an analyst writes a notebook for, in one chain of cheap calls.

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