Description
Compute one simple-regression diagonal leverage and its complement from supplied centered predictor data with an intercept.
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.
Compute one simple-regression diagonal leverage and its complement from supplied centered predictor data with an intercept.
When to use this tool
Use Sample Leverage Complement 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 sampleSize, centeredPredictor, predictorSumSquares. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leverage, complement. Use the output convention below.
Calculate leverage=1/sampleSize+centeredPredictor²/predictorSumSquares and complement=1-leverage. Require sample size at least two, positive sum of squares, and the supplied centered-value feasibility bound.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sampleSize | Sample Size | Required. Safe integer; minimum 2. |
| centeredPredictor | Centered Predictor | Required. Finite number. |
| predictorSumSquares | Predictor Sum Squares | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leverage | Leverage | Required. Finite number. |
| complement | Complement | Required. Finite number. |
{
"input": {
"sampleSize": 5,
"centeredPredictor": 2,
"predictorSumSquares": 20
},
"output": {
"leverage": 0.4,
"complement": 0.6000000000000001
}
}Limitations and assumptions
- These are terms for a simple regression geometry with an intercept. Summaries are supplied; no model fitting, predictor verification, uncertainty calculation, or outlier decision is performed.
- 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
- Effective Sample Size Weight Split
Split oldWeight into firstPart and its remainder, replace its squared contribution in sumSquaredWeights, and compare effective sizes sumWeights²/squaredSum before and after.
- 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.