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tresor4k

macalc

calculate_linear_regression

Compute the slope and intercept of a linear regression from summary statistics like means and sums.

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.
Behavior1/5

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

With no annotations, the description bears full responsibility for behavioral disclosure. It does not explain side effects, error conditions, output format, or permissions. The claim 'Returns: {error}' is confusing and incomplete, leaving the agent with no insight into tool behavior.

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

Conciseness3/5

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

The description is brief with two sentences, but the second sentence is a reference to list_bundles. The inclusion of 'Returns: {error}' appears to be a placeholder that undermines clarity and wastes space. It is concise but not well-structured for completeness.

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 the tool's moderate complexity, the description is incomplete. It fails to describe the output (slope and intercept) despite an output schema being present, and the error reference is unclear. The description does not compensate for the lack of annotations.

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?

The input schema covers all 5 parameters with descriptions, so baseline is 3. The description adds no extra meaning beyond 'from summary statistics', which is already implicit from parameter names. The error mention does not clarify parameters.

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

Purpose4/5

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

The description clearly states the tool calculates linear regression slope and intercept from summary statistics, which accurately identifies the verb, resource, and input constraints. However, it lacks explicit differentiation from sibling calculators, and the mention of 'Returns: {error}' introduces ambiguity about the actual output.

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

Usage Guidelines2/5

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

The description only provides a vague pointer to 'list_bundles' for related tools, but does not specify when to use this tool versus alternatives, nor does it offer exclusions or prerequisites. This provides minimal guidance for the agent.

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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