Description
Calculate studentized=residual/(standardDeviation*sqrt(1-leverage)).
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.
Calculate studentized=residual/(standardDeviation*sqrt(1-leverage)).
When to use this tool
Use Studentized Residual Known Leverage Factor 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 residual, standardDeviation, leverage. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read studentized. Use the output convention below.
Calculate studentized=residual/(standardDeviation*sqrt(1-leverage)). Require positive standard deviation and leverage from zero inclusive to one exclusive.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residual | Signed discrepancy under the formula stated above. | Required. Finite number. |
| standardDeviation | Positive supplied regression residual scale in residual units. | Required. Finite number; strictly above 0. |
| leverage | Supplied value from zero inclusive through one exclusive. | Required. Finite number; minimum 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| studentized | Studentized | Required. Finite number. |
{
"input": {
"residual": 3,
"standardDeviation": 2,
"leverage": 0.75
},
"output": {
"studentized": 3
}
}Limitations and assumptions
- Residual, residual-scale estimate, and leverage are supplied and need a compatible regression model. No model is fitted and internally versus externally studentized conventions are not selected automatically.
- 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
- Mean Update Finite Precision Residual
Calculate incremental=oldMean+(value-oldMean)/(count+1) and residual=suppliedUpdatedMean-incremental.
- Normal Score One Observation Leverage
Calculate leverage=1/count+(value-mean)²/centeredSumSquares with positive centered sum of squares and integer count at least one.