Regression coefficients check

regression-coefficients-check · version 1.0.0 · Numbers & math · free, no key needed

Check claimed least-squares regression coefficients against exact samples; reports rank and the first mismatch.

Use when you need to: verify least squares regression coefficients · check claimed linear regression fit exactly · is this regression line correct.

Decide before calling

Read the versioned contract and the supported scope below. Reuse regression-coefficients-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use regression-coefficients-check@1.0.0 for verify least squares regression coefficients. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• verify least squares regression coefficients
• check claimed linear regression fit exactly
• is this regression line correct
• validate ols coefficients from data
• check slope and intercept of a fitted line
• verify multiple regression coefficients exactly
• בדיקת מקדמי רגרסיה לינארית

Not supported

• weighted, ridge or robust regression
• p-values, standard errors or confidence intervals
• nonlinear models (use polynomial features as columns)
• approximate or tolerance-based comparison

Behavior

• Reference: NIST/SEMATECH e-Handbook of Statistical Methods sec. 4.1.4.1 and 4.4.3.1 (ordinary least squares, normal equations); exact rational arithmetic.
• Model (NIST e-Handbook 4.1.4.1): y_i = sum_j beta_j X_ij + e_i; X has a leading column of ones when intercept is true (required, no default), then the x features in order; coefficient 0 is the intercept when present.
• Values are exact strings: integer, decimal ("3.5") or fraction ("7/2"), never JSON numbers or exponents; comparisons are exact and outputs canonical reduced fractions. difference = claimed - actual.
• Ragged rows, len(y) != rows or empty x are invalid_input; a claimed vector of the wrong length is valid:false dimension_mismatch, checked first.
• Rank is exact; dependent_column is the first column of X that is a combination of earlier columns. rank < k (including fewer samples than columns) is singular_design: the least-squares coefficients are not unique.
• Check order: dimensions, then rank (singular_design; no coefficient is compared because the solution is ambiguous), then coefficients in index order (coefficient_mismatch). coefficients is the exact least-squares solution when rank = k, else null.
• Limits: 256 samples, 8 features, 30 digits per sample value, 1000 digits per claimed value, 9 claimed coefficients, 256 claimed residuals, and common denominators of at most 100 digits for the x values and for the y values and 1000 digits for the claimed coefficients; over a limit is limit_exceeded.

Input

• x (array of array of string, required): min items 1; max items 256; each min items 1; each max items 8; each each pattern ^-?(0|[1-9][0-9]*)(\.[0-9]+|/[1-9][0-9]*)?$
• y (array of string, required): min items 1; max items 256; each pattern ^-?(0|[1-9][0-9]*)(\.[0-9]+|/[1-9][0-9]*)?$
• intercept (boolean, required)
• coefficients (array of string, required): max items 9; each pattern ^-?(0|[1-9][0-9]*)(\.[0-9]+|/[1-9][0-9]*)?$

Output

• valid (boolean, required)
• reason (one of null, "dimension_mismatch", "singular_design", "coefficient_mismatch", required)
• rank (integer, required): min 0
• coefficients (array or null, required)
• first_discrepancy (object or null, required)
• reference_version (constant "NIST/SEMATECH e-Handbook of Statistical Methods sec. 4.1.4.1 and 4.4.3.1 (ordinary least squares, normal equations); exact rational arithmetic", required)

Limits

• max samples: 256
• max features: 8
• max sample digits: 30
• max claim digits: 1000
• max data denominator digits: 100
• max claim denominator digits: 1000

Example

Request input:

{
  "x": [
    [
      "1"
    ],
    [
      "2"
    ],
    [
      "3"
    ],
    [
      "4"
    ]
  ],
  "y": [
    "6",
    "5",
    "7",
    "10"
  ],
  "intercept": true,
  "coefficients": [
    "3.5",
    "1.4"
  ]
}

Response:

{
  "result": {
    "valid": true,
    "reason": null,
    "rank": 2,
    "coefficients": [
      "7/2",
      "7/5"
    ],
    "first_discrepancy": null,
    "reference_version": "NIST/SEMATECH e-Handbook of Statistical Methods sec. 4.1.4.1 and 4.4.3.1 (ordinary least squares, normal equations); exact rational arithmetic"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "regression-coefficients-check",
  "version": "1.0.0",
  "input": {
    "x": [
      [
        "1"
      ],
      [
        "2"
      ],
      [
        "3"
      ],
      [
        "4"
      ]
    ],
    "y": [
      "6",
      "5",
      "7",
      "10"
    ],
    "intercept": true,
    "coefficients": [
      "3.5",
      "1.4"
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/regression-coefficients-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"x":[["1"],["2"],["3"],["4"]],"y":["6","5","7","10"],"intercept":true,"coefficients":["3.5","1.4"]}'

The machine-readable contract is at /v1/tools/regression-coefficients-check/versions/1.0.0.

CLI

node cli.mjs run regression-coefficients-check 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Regression residuals check: Check claimed residuals and SSE for given regression coefficients and exact samples; reports the first wrong residual.
• Lp primal feasibility check: Check that a claimed LP point satisfies x >= 0 and Ax <= b exactly; report the first violated bound or row.
• Linear residual check: Check a claimed residual r = b - A x (per component and/or its max norm) exactly for an approximate solution x.
• Polynomial division check: Check a claimed polynomial division A = BQ + R over exact rationals: remainder degree, quotient degree, coefficients.
• Rational expression check: Check a claimed exact rational value of an integer/fraction expression; reports the true value and the difference.
• Regression normal equations check: Check that claimed coefficients and residuals satisfy X^T e = 0 exactly; rejects singular, ambiguous designs.