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Assume that each nutrient '''j''' of each ingredient '''i''' has an error '''σ<sub>ij</sub>'''. The combined error for the nutrient j is then:
 
Assume that each nutrient '''j''' of each ingredient '''i''' has an error '''σ<sub>ij</sub>'''. The combined error for the nutrient j is then:
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  (1) σ<sub>j</sub><sup>2</sup> = <big><big><big>Σ</big></big></big><sub>i=0</sub><sup><sup><sup><sup>N-1</sup></sup></sup></sup>β <sub>i</sub>σ<sub>ij</sub>
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  (1) σ<sub>j</sub><sup>2</sup> = <big><big><big>Σ</big></big></big><sub>i=0</sub><sup><sup><sup><sup><big><big>N-1</big></big></sup></sup></sup></sup>β<sub>i</sub><sup>2</sup>σ<sub>ij</sub><sup>2</sup>
    
With:
 
With:
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* '''N''' the number of ingredients in the recipe;
 
* '''N''' the number of ingredients in the recipe;
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This approach assumes that the ingredients are independent. And thus we have an estimated error for each estimated nutrient.
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This approach assumes that the ingredients are independent. And thus we have an estimated error for each estimated nutrient. And that the variability is normally distributed. We assume here that the contribution of the ingredient has no error.
    
What would be the errors on the estimated β<sub>i</sub>. Or are we then arguing in circles?
 
What would be the errors on the estimated β<sub>i</sub>. Or are we then arguing in circles?
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== References ==
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* [https://en.wikipedia.org/wiki/Propagation_of_uncertainty Propagation of uncertainty]
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* [https://stackoverflow.com/questions/36112290/weighted-non-negative-least-square-linear-regression-in-python Weighted NNLS] is this useful to add the error to the data?
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