Burs-IA Utils

Regresión lineal simple

stats-regression

Read-onlyIdempotent

Calcula el ajuste por mínimos cuadrados y = pendiente·x + intercepto, con R² y predicciones. Cuándo: un resultado numérico tiene que ser exacto o reproducible y no estimado. No para: medir cómo se mueven juntas dos series de igual longitud (stats-correlation). Efectos secundarios: ninguno (solo lectura, sin red, sin estado guardado). Determinista: la misma entrada da la misma salida. Límites: entrada JSON de hasta 64 KB, 1 s por llamada, resultado de hasta 1 MB.

EN: Least-squares fit y = slope·x + intercept with R², standard error, and optional predictions for new x values. When: a numeric result has to be exact or reproducible instead of estimated. Not for: measuring how two equal-length series move together (stats-correlation). Side effects: none (read-only, no network access, no stored state). Deterministic: the same input gives the same output. Limits: JSON input up to 64 KB, 1 s per call, result up to 1 MB.

Input Schema

Name	Required	Description
`x`	Yes	X values (array of number; required; at least 2 items).
`y`	Yes	Y values (array of number; required; at least 2 items).
`predict`	No	X values to predict (array of number; optional; default []; up to 1000 items).

Output Schema

Name	Required	Description	Default
`slope`	No
`intercept`	No
`r_squared`	No
`predictions`	No
`standard_error`	No

Schema Changelog

Changes observed during successful MCP inspections.

Changed2 schema fields changedNov 2, 2026
- addedInput schema / properties / x / examples
```
Added value: +[
+  [
+    1,
+    2,
+    3
+  ]
+]
```
- addedInput schema / properties / y / examples
```
Added value: +[
+  [
+    2,
+    4,
+    6
+  ]
+]
```
First observedNov 1, 2026

TDQS

A4.3/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare read-only, idempotent, closed-world and non-destructive, so the description's 'no side effects' restates them. It does add genuinely new behavior: determinism guarantees (same input → same output) and hard limits (64 KB JSON input, 1 s per call, 1 MB result) that an agent needs before sending a large array. Output format detail is carried by the output schema.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the operation and formula, then conditionally ordered (when / not for / effects / limits). It is verbose because the content is duplicated in Spanish and English, which is intentional for bilingual routing, but the same agent reads both halves.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given three simple flat parameters, full schema coverage, an output schema, and rich annotations, the description covers purpose, alternatives, determinism, and resource limits. Nothing essential for correct invocation is missing; only minor detail such as handling of unequal-length x/y (assumed equal-length) is left implicit.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100% and each property already documents type, requiredness, minimum/maximum items, and default. The description only adds that predict targets 'new x values', which is a marginal addition over the schema. Baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific operation (least-squares fit) with the exact model form y = slope·x + intercept and the outputs (R², standard error, predictions). It also explicitly names the sibling it must not be confused with (stats-correlation), so an agent can differentiate it without opening the schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Provides an explicit 'When' rule (numeric result must be exact/reproducible rather than estimated) and an explicit 'Not for' rule pointing to stats-correlation for co-movement of two equal-length series. Both the positive and negative selection conditions are stated.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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