Description
Return weightedResidual=weight*(value-center), requiring nonnegative weight.
A statistical term depends on its data summaries, weighting convention, centering, denominator, and boundary rules. A contribution, derivative, domain check, or converted summary answers a narrower question than a complete estimator. Those conventions must match before terms are combined or compared.
Return weightedResidual=weight*(value-center), requiring nonnegative weight.
When to use this tool
Use Weighted Mean Centering Term when you need this specific summary conversion, contribution, domain rule, or sensitivity term with matching statistical conventions.
How to use the tool and how it works
- Enter value, center, weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weightedResidual. Use the output convention below.
Return weightedResidual=weight*(value-center), requiring nonnegative weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| center | Center | Required. Finite number. |
| weight | Supplied weight; interpretation follows the stated model rather than an inferred probability. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weightedResidual | Weighted Residual | Required. Finite number. |
{
"input": {
"value": 8,
"center": 5,
"weight": 2
},
"output": {
"weightedResidual": 6
}
}Limitations and assumptions
- Value and center share a measurement unit while weight has its supplied interpretation. This is one contribution, not an estimated mean, standardized residual, or full weighted dispersion statistic.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete estimator or model when a contribution, sensitivity, or domain check is insufficient. Verify the weight semantics, centering, denominator, and sampling assumptions before combining summaries.
References
Similar or alternative tools
- Weighted Mean Missing Weight Budget
Combine observedWeight*observedMean with missingWeight times each supplied missing bound, dividing by the positive combined weight for lowerMean and upperMean.
- Weighted Mean One Observation Deletion Term
Remove a supplied contribution using remainingMean=(mean*totalWeight-value*weight)/(totalWeight-weight).