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Linear calibration residual worksheet

Fit reference values to instrument readings and inspect observed residuals.

01Enter your values

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Fit y=a+bx by unweighted least squares using 3–200 paired observations. Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span. Predict only inside the observed reading range.

Example

How it works

Fit reference values to instrument readings and inspect observed residuals.

b=Σ((x−x̄)(y−ȳ))/Σ(x−x̄)²; a=ȳ−bx̄; eᵢ=yᵢ−(a+bxᵢ); E%=100 max|eᵢ|/(max y−min y)

Runs in your browser

Discovery source

Your data stays yours

Inputs are processed on this page and are never sent to a server.

About this tool

Fit reference values to instrument readings and inspect observed residuals.

Fit y=a+bx by unweighted least squares using 3–200 paired observations. Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span. Predict only inside the observed reading range.

Use tool ↑

How to use it

  1. Enter your values

    Calibration observations · Reading to interpolate

  2. Calculate / generate

    Fit reference values to instrument readings and inspect observed residuals.

  3. Result

    Fitted reference value: 2 Slope: 2 Intercept: 1

Calculation method

  1. Fit y=a+bx by unweighted least squares using 3–200 paired observations.
  2. Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span.
  3. Predict only inside the observed reading range.
b=Σ((x−x̄)(y−ȳ))/Σ(x−x̄)²; a=ȳ−bx̄; eᵢ=yᵢ−(a+bxᵢ); E%=100 max|eᵢ|/(max y−min y)
Example scenario

Linear calibration residual worksheet

Calibration observations
Instrument reading: 0, Reference value: 1 Instrument reading: 1, Reference value: 3 Instrument reading: 2, Reference value: 5
Reading to interpolate
0.5
Result
Fitted reference value: 2
Slope: 2
Intercept: 1

Frequently asked questions

Limits and key assumptions

Use consistent units within each column. Reference values and readings must both vary. This is a descriptive linear fit, not a calibration certificate, uncertainty budget or independent accuracy validation. Outliers and nonlinear response can invalidate its use.

Where does my data go?

Calculations run on your device. Form inputs are not sent to a server.

Terms and definitions

Enter your values

Calibration observations

Fit y=a+bx by unweighted least squares using 3–200 paired observations.

Enter one item per row; each column describes that item.

Instrument reading

Predict only inside the observed reading range.

Enter a numerical value for this quantity.

Minimum: -1000000000 · Maximum: 1000000000

Reference value

Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span.

Enter a numerical value for this quantity.

Minimum: -1000000000 · Maximum: 1000000000

Reading to interpolate

Predict only inside the observed reading range.

Enter a numerical value for this quantity.

Minimum: -1000000000 · Maximum: 1000000000

Result

Result

Fit y=a+bx by unweighted least squares using 3–200 paired observations. Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span. Predict only inside the observed reading range.

Calculated from your entries using the method below.

Fitted reference value

Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span.

Calculated from your entries using the method below.

Slope

Fit y=a+bx by unweighted least squares using 3–200 paired observations. Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span. Predict only inside the observed reading range.

Calculated from your entries using the method below.

Intercept

Fit y=a+bx by unweighted least squares using 3–200 paired observations. Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span. Predict only inside the observed reading range.

Calculated from your entries using the method below.

Residual / maximum absolute residual

Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span.

Calculated from your entries using the method below.

Maximum residual / observed reference span

Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span.

Calculated from your entries using the method below.

Instrument reading

Predict only inside the observed reading range.

Calculated from your entries using the method below.

Reference value

Report each reference minus fitted value, the largest absolute residual and its percentage of the observed reference span.

Calculated from your entries using the method below.

Common mistakes and quick fixes

Limits and key assumptions

Mistake: Treating a result as valid outside the described scope.

Fix: Use consistent units within each column. Reference values and readings must both vary. This is a descriptive linear fit, not a calibration certificate, uncertainty budget or independent accuracy validation. Outliers and nonlinear response can invalidate its use.

Limits and key assumptions

  • Use consistent units within each column. Reference values and readings must both vary. This is a descriptive linear fit, not a calibration certificate, uncertainty budget or independent accuracy validation. Outliers and nonlinear response can invalidate its use.
  • Predict only inside the observed reading range.
  • Displayed results may be rounded; rounding does not add measurement precision.