Difference between revisions of "Recipe/Example/Cake"

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The lm forced intercept gives optimal results.\, nnls is overdone.
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=== Salt ===
 
Largest residual for salt. Can we add that in?
 
Largest residual for salt. Can we add that in?
  
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==== Residuals ====
 
==== Residuals ====
 
The residuals for each nutrient are plotted in the graph. The amount of fiber is not well fitted (but still below 1). Can this be due to the nutritional values of flour? This is the only ingredient that contributes to fiber.
 
The residuals for each nutrient are plotted in the graph. The amount of fiber is not well fitted (but still below 1). Can this be due to the nutritional values of flour? This is the only ingredient that contributes to fiber.

Revision as of 13:41, 1 February 2025

Product

A plain cake (pound cake) with four ingredients, like this one. Or the category Pound cakes.

Data

Four scenarios:

Four nuts product
Nutrient Product Ciqual Cake Median Cake
Fat 24 25.6 23
Sat. Fat 15 15.8 7.4
Carbohydrates 48 46 49
Sugars 29 26.8 28
Fiber 2 1.1 1.2
Proteins 6 5.94 5.8
Salt 1.4 0.52 0.8

For easy reuse:

Product (24,15,48,29,2,6,1.4)
Ciqual (25.6,15.8,46,26.8,1.1,5.94,0.52)
Median (23,7.4,49,28,1.2,5.8,0.8)

The nutritional values for the Ciqual ingredients.

Ciqual ingredients
Nutrient Flour Sugar Egg Butter
Ciqual 9445 31016 22000 16400
Fat 1.18 0 9.83 82.9
Sat. Fat 0.17 0 2.64 55.4
Carbohydrates 73.2 99.8 0.27 0.9
Sugars 1.77 99.8 0.27 0.83
Fiber 4.2 0 0 0
Proteins 9.95 0 12.7 0.7
Salt 0 0.0054 0.31 0.063
Flour: (1.18,0.17,73.2,1.77,4.2,9.95,0)
Sugar: (0,0,99.8,99.8,0,0,0.0054)
Eggs: (9.83,2.64,0.27,0.27,0,12.7,0.31)
Butter: (82.9,55.4,0.90.83,0,0.7,0.063)

Least squares fit

First pass

The table below present fit results. This compares the product against the ciqual ingredients.

Fitting results
model Flour Sugar Butter Eggs Intercept sumR2
lm 0.265 0.274 0.249 0.182 0.994 0.30
lm forced intercept 0.267 0.283 0.257 0.250 - 2.468
nnls 0.267 0.283 0.257 0.250 - 2.486

The lm forced intercept gives optimal results.\, nnls is overdone.

Salt

Largest residual for salt. Can we add that in?

Fitting results
model Flour Sugar Butter Eggs Salt sumR2
lm forced intercept 0.267 0.283 0.257 0.250 0.013 0.783

Residuals

The residuals for each nutrient are plotted in the graph. The amount of fiber is not well fitted (but still below 1). Can this be due to the nutritional values of flour? This is the only ingredient that contributes to fiber.

Fit residuals for cake

Wheat types

Replace the wheat type 80 with Wheat type 110 (9410). This increases the amount of fiber from 4.2 to 6.8.

Wheat flour type 110: (1.5,0.27,68.6,1.6,6.8,9.61,0.13)

Residual for fiber is reduces to 0.07. The variance to 0.015 (was 0.783).

Wheat flour type 150 (9415): (1.52,0.22,64.9,1.77,10.2,11.4,0.035)

Residual for fiber changes to -1.0. And variance to 1.08. Wheat type 100 seems to give the best fit.

Butter oil

Instead of using butter we could use butter oil. The product mentions Beurre pâtissier, which is closer to butter oil. Try this (keeping the original wheat T80):

Butter oil: (99.9,61.9,0,0,0,0.28,0.005)

This increases the residual for fat to 0.8 and the variance to 1.712. Clearly a worse fit.

Dextrose

The ingredient list also mentions dextrose. This is not available in the Ciqual list. But probably the nutrients are the same as sugar and we probably will not be able to distinguish one from the other.

Probably this is due to the ratio Saturated Fat over Fat. For butter this is: 0.67 and for butter oil 0.62.

Conclusions

What is now the best recipe? Should we look at the overall variance or also take the maximum residual into account? A figure:

Comparing cake ingredients
  • Adding salt reduces the salt residual;
  • Find the correct wheat by trying several varieties;
  • Beurre pâtissier is closer to butter than butter oil;