Chlorophyll Phosphorus Regression Prediction

Fit a log-power chlorophyll/phosphorus relation to caller observations with within-range median prediction; no mutable published regression or uncorrected arithmetic-mean claim.

Description

A power relation between phosphorus and chlorophyll becomes linear after taking logarithms.

A power relation between phosphorus and chlorophyll becomes linear after taking logarithms. Fitting that transformed relation estimates coefficients from the supplied observations.^[1]

The tool returns fittedCoefficient, fittedExponent, predictedMedianChlorophyllMicrogramsPerLiter, logFitRSquared. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Chlorophyll Phosphorus Regression Prediction

Use this for the following task: Fit a log-power chlorophyll/phosphorus relation to caller observations with within-range median prediction; no mutable published regression or uncorrected arithmetic-mean claim. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Chlorophyll Phosphorus Regression Prediction and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter phosphorusMicrogramsPerLiter, chlorophyllMicrogramsPerLiter, queryPhosphorusMicrogramsPerLiter according to the field table, then run the tool.
Read fittedCoefficient, fittedExponent, predictedMedianChlorophyllMicrogramsPerLiter, logFitRSquared. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
phosphorusMicrogramsPerLiter	Phosphorus micrograms per liter	list of number	Required
chlorophyllMicrogramsPerLiter	Chlorophyll micrograms per liter	list of number	Required
queryPhosphorusMicrogramsPerLiter	Query phosphorus micrograms per liter	number	Required

Supply aligned positive phosphorus and chlorophyll observations with varying phosphorus, plus a positive query inside the observed phosphorus range. Fit least squares in natural-log space and return the back-transformed prediction and log-space R².

ln(chlorophyll)=intercept+exponent×ln(phosphorus); coefficient=exp(intercept)

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
fittedCoefficient	Fitted coefficient	number
fittedExponent	Fitted exponent	number
predictedMedianChlorophyllMicrogramsPerLiter	Predicted median chlorophyll micrograms per liter	number
logFitRSquared	Log fit r squared	number

json

{
  "input": {
    "phosphorusMicrogramsPerLiter": [
      1,
      2,
      4
    ],
    "chlorophyllMicrogramsPerLiter": [
      2,
      8,
      32
    ],
    "queryPhosphorusMicrogramsPerLiter": 3
  },
  "output": {
    "fittedCoefficient": 1.9999999999999998,
    "fittedExponent": 2,
    "predictedMedianChlorophyllMicrogramsPerLiter": 17.999999999999996,
    "logFitRSquared": 1
  }
}

Limitations and assumptions

The output is labeled a median prediction under the log-error interpretation. No correction to an arithmetic mean, extrapolation, uncertainty interval or causal diagnosis is provided.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Chlorophyll Target Load Back Calculation Tool when you need its operation: Compose inversion of a supplied chlorophyll/P power calibration with a steady Vollenweider-form loading model; excludes internal loads and does not guarantee a management outcome. Choose Chlorophyll A Extraction Concentration for the complementary operation: Convert blank-corrected multiwavelength extract absorbances with caller method coefficients and path/dilution/sample-volume correction; negative estimates are retained and solvent-specific calibration is external.

Background reference: Least squares estimation.

References

Least squares estimation — NIST/SEMATECH

Similar or alternative tools

Chlorophyll Target Load Back Calculation Tool
Compose inversion of a supplied chlorophyll/P power calibration with a steady Vollenweider-form loading model; excludes internal loads and does not guarantee a management outcome.
Chlorophyll A Extraction Concentration
Convert blank-corrected multiwavelength extract absorbances with caller method coefficients and path/dilution/sample-volume correction; negative estimates are retained and solvent-specific calibration is external.