Linear regression (OLS)

Fit a least-squares line y = slope·x + intercept to two equal-length series. Send POST /api/linear-regression with the required fields x and y and pay $0.001 per call over x402 or MPP, or call it free by solving a proof-of-work challenge. It returns a JSON object with n, slope, intercept, rSquared, equation and 1 more.

Returns slope, intercept, r² (variance explained), and optionally predicted y values for new x inputs - useful for trend extrapolation (e.g. project next quarter's revenue from the last 8 quarters).

Category: Live public data · Tags: stats regression ols trend slope intercept r-squared

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Parameters

Example request

curl -i -X POST https://agent402.tools/api/linear-regression \
  -H "Content-Type: application/json" \
  -d '{"x":[1,2,3,4,5],"y":[2.1,4,6.1,7.9,10.2],"predict":[6,7]}'

Without payment this returns HTTP 402 Payment Required with the exact price for linear-regression; any x402 v2 or MPP client pays it and retries.

Example response

{
  "n": 5,
  "slope": 2.01,
  "intercept": 0.03,
  "rSquared": 0.9997,
  "equation": "y = 2.01x + 0.03",
  "predictions": [
    {
      "x": 6,
      "y": 12.09
    },
    {
      "x": 7,
      "y": 14.1
    }
  ]
}

From an MCP client

catalog.call {
  "slug": "linear-regression",
  "params": {
    "x": [
      1,
      2,
      3,
      4,
      5
    ],
    "y": [
      2.1,
      4,
      6.1,
      7.9,
      10.2
    ],
    "predict": [
      6,
      7
    ]
  }
}

On the hosted connector at https://agent402.tools/mcp, catalog.call runs linear-regression free (rate-limited, no wallet). Local install: npx -y agent402-mcp.

Errors and behavior

• x and y are required. An input the tool rejects returns an HTTP 4xx whose body carries error, tool, expected, required and example, so the caller can correct it.
• A paid call that ends in any status of 400 or above is not charged over x402, MPP or a prepaid credits key: settlement is cancelled when the tool fails. The exception is a Tempo push credential, a transfer the buyer sent before the call: it settles before the tool runs, so if the tool then fails the payment is recorded as a refund owed to the paying wallet.
• Free tier: no outbound network call leaves the server for this tool, so proof-of-work (16 leading zero bits of sha256) pays for it.
• A GET or HEAD to /api/linear-regression returns the same 402 quote, so the price can be read without a body.
• An Idempotency-Key header makes a retried paid call replay the first 200 instead of charging again (an answer larger than 1 MB is not replayed).

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();
client.setSpendControls?.(false); // keep your own spending ceiling in code
registerExactEvmScheme(client, { signer: privateKeyToAccount(KEY) });
const payFetch = wrapFetchWithPayment(fetch, client);

const res = await payFetch("https://agent402.tools/api/linear-regression", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "x": [
      1,
      2,
      3,
      4,
      5
    ],
    "y": [
      2.1,
      4,
      6.1,
      7.9,
      10.2
    ],
    "predict": [
      6,
      7
    ]
  }),
});

No wallet? Pay with compute

Fetch a challenge, solve the sha256 puzzle (16 leading zero bits, a fraction of a second of CPU), 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=linear-regression")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/linear-regression", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"x":[1,2,3,4,5],"y":[2.1,4,6.1,7.9,10.2],"predict":[6,7]}) });

Part of these workflows

Linear regression (OLS) is one step in this skill pack, each sold as a single call:

• 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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