Smoothing
Verification
Reference comparisons
On this page
Specifications
Export
Scope
Least-squares coefficients, standard errors, and confidence bands; loess fits, standard errors, degrees of freedom, residual standard errors, and confidence bands. Identical inputs and evaluation points across implementations.
References
- Reference
- R 4.6.1: lm(), predict(), loess(surface = "direct", statistics = "exact")
- Versions
- R 4.6.1
Data
- mtcars
- 32 rows, R's datasets package
- mpg
- 234 rows, ggplot2 4.0.3
Method
scripts/evidence/r-references.R computes the reference values in R and writes tests/fixtures/r-references.json. scripts/evidence/parity.php computes the same quantities with phiz's PHP implementations behind smooth() and compares them value by value.
- Check
- Comparison with a reference implementation
- Recorded
- 2026-11-02, PHP 8.5.11, Debian GNU/Linux 13 (trixie) (aarch64), commit b9272c6
Tolerances
|x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12)
Applies to: Numerical results
Fits, quantiles, intervals, and polygon points
exact equality
Applies to: Counts, levels, piece sizes, and colors
x: package value; r: reference value. Absolute error: |x − r|. Relative error: |x − r| / max(|r|, 1e-12). Max errors are over the values a row compares.
Results
13 comparisons in 3 cases: 13 pass, 0 fail, 0 skipped.
By case
| Case | Comparisons | Largest abs. error | Largest rel. error | Status |
|---|---|---|---|---|
| mtcars, mpg ~ wt | 4 | 2.1e-13 | 9.8e-15 | pass |
| mpg, hwy ~ displ, loess span 0.75 degree 2 | 5 | 1.6e-11 | 6.9e-14 | pass |
| mpg, hwy ~ displ, loess span 1.5 degree 1 | 4 | 3.8e-12 | 1.8e-14 | pass |
Every comparison
| Case | Quantity | Criterion | Values | Package value | Reference value | Max abs. error | Max rel. error | Status |
|---|---|---|---|---|---|---|---|---|
| mtcars, mpg ~ wt | lm coefficients | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 2 | 2.1e-13 | 9.8e-15 | pass | ||
| lm standard errors | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 2 | 6.7e-15 | 3.8e-15 | pass | |||
| residual degrees of freedom | exact equality | 1 | 30 | 30 | pass | |||
| 90% band at the ends of wt: fit, lower, upper | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 6 | 7.1e-15 | 6.7e-16 | pass | |||
| mpg, hwy ~ displ, loess span 0.75 degree 2 | fit at 5 points | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 5 | 8.3e-13 | 2.5e-14 | pass | ||
| standard errors at 5 points | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 5 | 1.3e-13 | 6.5e-14 | pass | |||
| degrees of freedom of the t interval | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 1 | 228.8880627 | 228.8880627 | 1.6e-11 | 6.9e-14 | pass | |
| residual standard error | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 1 | 3.372111038 | 3.372111038 | 2.2e-14 | 6.6e-15 | pass | |
| 95% band at the ends of displ: lower, upper | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 4 | 1.0e-12 | 3.6e-14 | pass | |||
| mpg, hwy ~ displ, loess span 1.5 degree 1 | fit at 5 points | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 5 | 1.1e-13 | 9.0e-15 | pass | ||
| standard errors at 5 points | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 5 | 1.4e-14 | 1.8e-14 | pass | |||
| degrees of freedom of the t interval | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 1 | 231.8607268 | 231.8607268 | 3.8e-12 | 1.7e-14 | pass | |
| residual standard error | |x − r| ≤ 1e-9 + 1e-9 × max(|r|, 1e-12) | 1 | 3.692445905 | 3.692445905 | 4.4e-15 | 1.2e-15 | pass |
Limitations
Known differences
- ggplot2's geom_smooth() interpolates the loess surface; phiz computes it directly, as loess(surface = "direct") does. ggplot2's curve can therefore differ slightly.
Reproduction
Rscript scripts/evidence/r-references.R
php scripts/evidence-parity.php- Raw record
- site/verifications/r-smoothing.json
- Full results
- site/verifications/r-smoothing.json
- Input data
- tests/fixtures/r-references.json