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PolarisHub

Math-MCP

by PolarisHub

linear_regression

Performs linear regression to fit a least-squares line to paired data, returning slope, intercept, and R-squared.

Instructions

Fits the least-squares line y = slope*x + intercept and returns slope, intercept, and R-squared

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xValuesYes
yValuesYes
Behavior3/5

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

No annotations exist, so description carries full burden. It discloses the fitting method and outputs but omits assumptions (e.g., linearity, equal variance), error handling, or input constraints beyond basics.

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

Conciseness5/5

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

Single sentence front-loads the equation and outcome. No wasted words.

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?

For a simple tool with two required arrays and no output schema, description covers core functionality. Missing return structure (e.g., object with keys) but adequate for basic use.

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

Parameters2/5

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

Schema coverage is 0% (no parameter descriptions). Description only names xValues and yValues without adding constraints (e.g., must be same length, min length 2) or format details.

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?

Clearly states the tool fits a least-squares line and returns slope, intercept, and R-squared. This specific verb-resource pair (fit line) distinguishes it from siblings like 'correlation' or 'mean'.

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

Usage Guidelines3/5

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

No explicit guidance on when to use or avoid this tool. Among siblings, it's clear for simple linear regression, but no comparison to 'correlation' or 'solve_linear_system' is provided.

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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