Description
residualShare = residualSumSquares/totalSumSquares; explainedShare = 1-residualShare.
Regression diagnostics and robust covariance calculations combine design information, residual terms and estimator-specific normalization. One leverage quadratic form, outer product or correction factor is only part of the full procedure.
residualShare = residualSumSquares/totalSumSquares; explainedShare = 1-residualShare.
When to use this tool
Use Instrument First Stage Residual Share when checking one supplied design or covariance contribution.
How to use the tool and how it works
- Enter residualSumSquares, totalSumSquares. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residualShare, explainedShare. Use the output convention below.
Require positive totalSumSquares and nonnegative residualSumSquares. residualShare = residualSumSquares/totalSumSquares; explainedShare = 1-residualShare.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residualSumSquares | Residual Sum Squares | Required. Finite number; minimum 0. |
| totalSumSquares | Total Sum Squares | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residualShare | Residual Share | Required. Finite number. |
| explainedShare | Explained Share | Required. Finite number. |
{
"input": {
"residualSumSquares": 20,
"totalSumSquares": 100
},
"output": {
"residualShare": 0.2,
"explainedShare": 0.8
}
}Limitations and assumptions
- Explained share can be negative. This is an algebraic R-squared-style decomposition on supplied sums, not a regression fit or proof of explanatory power and causation.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete estimator with matching weighting, clustering, degrees-of-freedom and normalization conventions for inference.
References
Similar or alternative tools
- Heteroskedastic Sandwich One Outer Product
Return one weighted residual-score outer product for a sandwich covariance middle-matrix contribution.
- Hac One Lag Covariance Weight
bartlettWeight = 1-lag/(bandwidth+1) for lag <= bandwidth, otherwise zero; contribution = bartlettWeight*covariance.