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

With no annotations, the description carries the full burden. It usefully discloses the algorithm (OLS), the model form, and that R-squared is returned, which is real behavioral content for a numeric tool. However, it omits edge-case/error behavior (mismatched x/y lengths, constant x making slope undefined) and the minItems=2 constraint.

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?

One front-loaded sentence that names the method, the exact model, and the key output statistic; there is no filler and nothing to trim.

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 deterministic single-call statistics tool with no output schema, the description should at minimum clarify return components (slope, intercept, R²) and failure modes for degenerate input. It hints at these via the formula but leaves error handling, input-length requirements, and sibling routing unaddressed.

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 description coverage is 0% and the single nested payload is undocumented beyond titles 'X' and 'Y'. The formula does assign roles—x is the predictor, y the response—which adds some meaning, but the required array pairing and the minimum-length constraint are left unexplained.

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 specific method and resource: ordinary least squares simple linear regression, with the model form (y = slope*x + intercept) and the reported statistic (R-squared). This distinguishes it from stats_correlation/stats_summary by naming the estimation technique, though it does not explicitly contrast with the nearest sibling (stats_correlation).

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?

The description says what the tool computes but gives no when-to-use guidance, prerequisites, or alternative selection (e.g., use stats_correlation for association only, stats_regression for a fitted model). The agent must infer context entirely from the method name.

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