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tresor4k

macalc

calculate_linear_regression

Calculate linear regression slope and intercept from summary statistics: provide means, sum of cross products, sum of squares, and sample size to get regression equation parameters.

Instructions

Calculate linear regression slope and intercept from summary statistics. Returns: {error}. See list_bundles for related 'math' calculators.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
x_meanYesMean of x values
y_meanYesMean of y values
sum_xyYesSum of (xi-x_mean)*(yi-y_mean)
sum_x2YesSum of (xi-x_mean)²
nYesNumber of data points

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultNoComputed result. Object whose fields depend on the tool (e.g. {tax, marginal_rate, brackets} for tax tools, {volume_l, gallons} for volume tools).
formulaNoHuman-readable formula or method used (e.g. "I=P·r·t", "Magnus formula").
sourceNoAuthoritative source for the rule or formula (e.g. "Article 197 CGI", "NF DTU 21").
reference_urlNoLink to a calcul2 page documenting the calculation in detail.
Behavior2/5

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

No annotations provided. The description only says 'Returns: {error}', which is vague and does not disclose that the tool requires precomputed summary statistics or any side effects. The description adds minimal behavioral context beyond the name.

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?

The description is extremely concise with two sentences, front-loading the purpose. Every sentence earns its place with no wasted words.

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

Completeness2/5

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

Given an output schema exists but description only mentions error return, it lacks completeness. For a statistical tool, it should explain expected output structure and any limitations. The description is insufficient for informed selection.

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 coverage is 100% with each parameter described in the schema. The description does not add new meaning beyond 'summary statistics', so baseline score of 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?

The description clearly states the tool's verb 'Calculate' and specific resources 'linear regression slope and intercept' from 'summary statistics'. It distinguishes itself from sibling calculators by specifying the exact computation and input type.

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?

It mentions 'See list_bundles for related math calculators', implying class but no explicit when-to-use or when-not-to-use. It does not clarify when to use this vs alternative regression methods, leaving context implied.

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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