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

Annotations already declare this is a read-only, idempotent, non-destructive, closed-world computation, so the safety profile is covered. The description usefully adds what the operation produces (slope, intercept, r, r², SE, p-value, equation) in the absence of an output schema, but says nothing about failure modes or input constraints.

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

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

A single dense sentence, front-loaded with the method and then the returned statistics. Every clause carries information and there is no filler.

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

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

For a two-parameter statistical computation with full annotation coverage, the method and its outputs are adequately described. The only meaningful gap is input constraints and error behavior, which is a minor omission rather than a blocking one.

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

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

Schema coverage is 0%, so the schema alone leaves both parameters as bare number arrays. The phrase 'of y on x' does assign the response/predictor roles, which is genuine added meaning, but the description omits the equal-length and numeric-array constraints the caller must satisfy.

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

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

States a precise method and resource — 'Simple linear regression of y on x' — plus the exact quantities returned. An agent can identify it as the OLS fit tool without opening the schema, though it never references any sibling to sharpen the distinction from hypothesis_test or descriptive_stats.

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

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

There is no when-to-use guidance, no mention of when an alternative sibling (e.g. confidence_interval, hypothesis_test) is preferable, and no preconditions such as equal-length x/y arrays or minimum sample size. Usage is only inferable from the tool name itself.

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